Efficient broadband 400 nm noncollinear secondharmonic generation of chirped femtosecond laser pulses in BBO and LBO O. Gobert,1 G. Mennerat,1 R. Maksimenka,1,2 N. Fedorov,1 M. Perdrix,1 D. Guillaumet,1 C. Ramond,3,4 J. Habib,3,4,5,6 C. Prigent,3,4 D. Vernhet,3,4 T. Oksenhendler,2 and M. Comte1,* 1
CEA-Saclay, IRAMIS, Laboratoire Interactions, Dynamique et Lasers, 91191 Gif-sur-Yvette, France
2
FASTLITE, Centre scientifique d’Orsay, bât. 503, Plateau du Moulon, BP 45, 91401 Orsay, France 3
CNRS, UMR 7588, Institut des NanoSciences de Paris (INSP), F-75005 Paris, France
4
Sorbonne Universités, UPMC Univ. Paris 06, UMR 7588, INSP, F-75005 Paris, France
5 6
Postdoctoral fellow of the ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum, 64291 Darmstadt, Germany
Present address: Faculty of Engineering, Holy Spirit University of Kaslik (USEK), P.O. Box 446, Jounieh, Lebanon *Corresponding author: [email protected] Received 22 January 2014; revised 19 March 2014; accepted 21 March 2014; posted 24 March 2014 (Doc. ID 204771); published 17 April 2014
We report on 400 nm broadband type I frequency doubling in a noncollinear geometry with pulse-fronttilted and chirped femtosecond pulses (λ0 800 nm; Fourier transform limited pulse duration, 45 fs). With moderate power densities (2 to 10 GW∕cm2 ) thus avoiding higher-order nonlinear phenomena, the energy conversion efficiency was up to 65%. Second-harmonic pulses of Fourier transform limited pulse duration shorter than the fundamental wave were generated, exhibiting good beam quality and no pulse-front tilt. High energy (20 mJ/pulse) was produced in a 40 mm diameter and 6 mm thick LBO crystal. To the best of our knowledge, this is the first demonstration of this optical configuration with sub-100-fs pulses. Good agreement between experimental results and simulations is obtained. © 2014 Optical Society of America OCIS codes: (190.7110) Ultrafast nonlinear optics; (190.2620) Harmonic generation and mixing; (320.1590) Chirping. http://dx.doi.org/10.1364/AO.53.002646
1. Introduction
Second-harmonic generation (SHG) in nonlinear optical crystals has been the subject of countless studies over the past 50 years. For relatively long laser pulses (i.e., whose duration exceeds typically 100 ps), conversion efficiencies even greater than 80% have been obtained [1–3]. Regarding the field of ultrashort pulses (femtosecond regime), frequency 1559-128X/14/122646-10$15.00/0 © 2014 Optical Society of America 2646
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doubling also has many attractive features, such as extending the wavelength range, improving the pulse temporal contrast, or obtaining even shorter pulses. However, femtosecond SHG faces several specific and major difficulties mainly due to the phase-matching condition to be fulfilled on a very broad spectrum and to the high electric field associated with ultrashort laser pulses, which can induce unwanted disturbing phenomena. For femtosecond pulse durations, phase mismatch (which at first order corresponds to group-velocity mismatch) leads to temporal broadening (spectral bandwidth
narrowing) and reduces the energy conversion. At high intensities, third-order nonlinear phenomena (self-phase modulation, cross-phase modulation, self-focusing, etc.) can decrease the conversion efficiency and alter the second-harmonic beam quality. In order to overcome these effects, the simplest solution is to use a thin crystal and to moderate the power density at the expense of the conversion efficiency. The problem of obtaining high conversion efficiency at high energy levels without spectral narrowing has been extensively studied in recent years, and several solutions have been proposed [4–17]. Achromatic phase matching for SHG of femtosecond pulses was described in [4,18], and a similar arrangement was later published in [5]. The method is based on the introduction of spectral angular dispersion so that the different spectral components propagate at their phase-matching angle, which is equivalent to cancel the group-velocity mismatch. Wide-bandwidth frequency doubling with high conversion efficiency was discussed in [19], and a variant of the method using pulse-front distortion compensation [20] has led to terawatt 10 fs blue pulses by broadband frequency doubling. Sub-10-fs ultraviolet (UV) pulses were more recently generated by achromatic frequency doubling [21]. A noncollinear geometry was also independently proposed [6] in order to achieve phase and group-velocity matching for SHG of femtosecond pulses. This scheme has several specific advantages, such as the direct separation of the three interacting waves. However, to the best of our knowledge, this method was never applied to the generation of sub-100-fs doubled pulses at high conversion efficiency levels (around 50%). Smith [8] and later Liu et al. [16] have detailed an analysis of the three-wave-mixing ultrabroadband phase-matching conditions using the concept of pulse-front tilt (PFT). We apply in this paper their model to design an original setup for high-efficiency achromatic femtosecond 400 nm type I noncollinear SHG with tilted pulse fronts in two nonlinear crystals, beta-barium borate (BBO) and lithium triborate (LBO). One of the originalities of the method presented here lies in the systematic use of chirped pulses. As will be detailed later in the paper, this makes it possible to obtain simultaneously high conversion efficiency and broad frequency spectrum (i.e., short SHG pulse duration after compression). Moreover, reasonably thick crystals can be used (a few millimeters, whereas most SHG experiments use typically a few hundred micrometers thick crystals), and thus only moderate input intensities (GW∕cm2 range) are needed. Conversely, chirped pulses imply generally the use of a recompression setup after the doubling process. This, however, is balanced by the other advantages of the method. 2. Noncollinear SHG in the Femtosecond Regime
We only give main results for noncollinear SHG applied to BBO and LBO. We will show that compared to collinear SHG, this configuration has many
Fig. 1. Noncollinear SHG with PFT.
advantages in the case of very short pulses. From now on, only type I SHG will be considered. A. Noncollinear SHG Phase-Matching and PFT Angle
Following [8,16], it can be seen that for an appropriate crossing angle and PFT of the input beams (Fig. 1), one can balance the group velocity of the second harmonic and that of the fundamental harmonic along the same direction. For type I phase matching, this leads [16] to
v1 v2 v ; vshg v cos δ
1
where v1 v2 and vshg are, respectively, the group velocity of the first- and second-harmonic waves, and δ is half the angle between the two fundamental beams. When the pulse fronts of the three waves are simultaneously exactly matched as well as the group velocities, the wave-vector mismatch is cancelled to first order and a broadband SHG is achieved. From now on, we also suppose that the beam diameter d0 has been chosen large enough compared to the crystal’s thickness L for the effect of spatial walkoff to be negligible (L ≪ d0 ∕ρ, ρ being the SHG spatial walk-off angle in the case of a negative uniaxial crystal and type I SHG). 1. Application to BBO and LBO BBO is a negative uniaxial crystal [22] and belongs to noncentrosymmetric trigonal point group 3 m. Using the results of [8,16] and the Sellmeier equations [23] of BBO, the phase-matching angle and the noncollinear angle δ (between the second- and first-harmonic waves) compensating the wave-vector mismatch to first order are calculated. LBO is a biaxial crystal with mm2 orthorhombic point group symmetry [24]. Its principal axes X, Y, and Z (principal refractive indices nz > ny > nx ) are parallel to the crystallographic axes a, b, c (c < a < b). Wave-vector directions are given in a polar coordinate system related to the principal axes by the polar and azimuthal angles θ (measured from Z) and φ (measured from X). Effective nonlinear coefficients have maximum values when light propagates in the principal planes. Considering only type I SHG with waves propagating in the XY principal plane (θ 90°), LBO behaves like a negative uniaxial crystal and 20 April 2014 / Vol. 53, No. 12 / APPLIED OPTICS
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Table 1.
Wave-Vector Mismatch Compensated Noncollinear 800 nm Type I SHG in BBO and LBO
BBO
LBO
Fundamental wavelength: 800 nm Phase-matching angle (°): θ 41.4 θ; φ 90; 65.9 External noncollinear angle δ (°): 6.65 13.17 External angular Dispersion (μrad/nm): 372. 293 Effective nonlinear coefficient (pm/V): 1.87 0.38
calculations are similar to those in BBO using the Sellmeier equations of [25]. Table 1 sums up the main characteristics of noncollinear SHG in BBO and LBO. B.
Comparison with Collinear SHG
Noncollinear SHG requires a more complicated experimental setup than collinear SHG. It is thus useful to point out the potential advantages of this scheme. Indeed, these rely mainly on the possibility of obtaining simultaneously high conversion efficiencies and broad frequency spectra (i.e., potentially shorter pulse durations after recompression). To illustrate this, we first estimate the spectral acceptance for chirped pulses in the noncollinear configuration using the weak conversion approximation and compare it to the case of collinear SHG. In a second step, using numerical results obtained with the SNLO software [8,26], we give examples of spectral bandwidth limitations in collinear SHG. 1. Spectral Acceptance for Noncollinear SHG Let us consider noncollinear SHG and suppose that the wave-vector condition is fulfilled at central fundamental angular frequency ωf ωf 2πc∕λf ; λf 800 nm and second-harmonic angular frequency ωshg ωshg 2πc∕λshg ; λshg λf ∕2. With the notations of [8], the wave-vector mismatch jΔkj can be calculated for a given fundamental angular frequency ωm and the corresponding second-harmonic frequency (ωn 2ωm ): jΔkj Δkz
∂2 kf z 1 ∂2 kshg 2 ω −ωn − ωf −ωm 2 ; (2) 2 ∂ω2 ωshg shg ∂ω2 ωf
where Δkz is the wave-vector mismatch along the z axis, and kshg and kf are the second- and firstharmonic wave-vectors. Δωshg ωshg , where ωn is the deviation from the central angular frequency of a second-harmonic component wave at angular frequency ωn, and Δωf ωf − ωm is the deviation from the central angular frequency of a firstharmonic component wave at angular frequency ωm . Plotting jΔkj as a function of λm 2πc∕ωm, one can derive the noncollinear spectral acceptance in the weak conversion approximation (Fig. 2 in the case of BBO). 2648
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Fig. 2. Wave-vector mismatch jΔkj in BBO as a function of firstharmonic wavelength and corresponding noncollinear spectral bandwidth for a 3 mm thick crystal.
In this regime, the output intensity I SHG L at the exit of a crystal of thickness L is proportional to sinc2 ΔkL∕2. Defining the fundamental wavelength spectral acceptance bandwidth Δλ by the condition sinc2 ΔkL∕2 ≤ 1∕2, one obtains (for a given crystal width, here L 3 mm, for example) a maximum value of Δλ around 34 nm for BBO (limited by the group-velocity dispersion). This corresponds at 800 nm to a 26.5 fs pulse duration. Similarly, using Eq. (2), an approximate value of the maximum crystal thickness that preserves a given SHG wavelength bandwidth [that is to say a given Fourier transform limited (FTL) duration] can be derived. As an example, for the spectral bandwidth of an 800 nm, 45 fs FTL pulse with around 20 nm full waist at half maximum (FWHM), one obtains for BBO a maximum crystal thickness around 8.6 mm in the noncollinear configuration. This is to be compared with the corresponding value in type I collinear SHG [27], which is 0.25 mm. Similarly, the maximum crystal thickness preserving a 20 nm bandwidth is around 13 mm in the noncollinear configuration in LBO and only of 0.4 mm in the collinear configuration. 2. Numerical Simulations Illustrating Spectral Bandwidth Limitations in Collinear SHG Time-dependent equations corresponding to sum frequency generation (in collinear geometry) in the paraxial approximation with the inclusion of diffraction and walk-off are given in [28]. Dispersion is taken into account up to the second order via the group delay dispersion (GDD). These equations are solved by SNLO, which is a free software developed by Dr. Arlee Smith, using a split-step Fourier method [29]. In the “2D short-pulse mixing” module mainly used here, Gaussian (or super-Gaussian) spatial and temporal input profiles can be used. Linear frequency chirp and delays can also be imposed on the input pulses. The code allows us to follow the stepwise time evolution of each beam on a 2D spatial grid of intensity and phase. Using this module for collinear SHG with FTL pulses, one plots (Fig. 3) the 400 nm wavelength bandwidth and the corresponding conversion efficiency as a function of the crystal thickness L.
2 1∕2 ΔνSHG τ 4 − 3 FTL : ΔνFH τL
Fig. 3. Collinear geometry: SNLO calculated (“2D short-pulse mixing” module) 400 nm collinear SHG spectral width and corresponding conversion efficiency as a function of crystal thickness (a) in BBO (input 800 nm laser fluence 1.8 mJ∕cm2 ) and (b) in LBO (input laser fluence 3.6 mJ∕cm2 ). 800 nm FTL pulse duration, 45 fs (20 nm bandwidth); beam diameter, 7 mm; super-Gaussian coefficient, 2; radius of curvature, 104 cm. In each case, the input laser fluence is chosen in order to reach around 80% conversion efficiency after 1.5 mm propagation in the crystal.
This is done for a typical set of input 800 nm laser parameters (FTL pulse duration, 45 fs; beam diameter, 7 mm; super-Gaussian coefficient, order of 2; input laser fluence, 1.8 mJ∕cm2 for BBO and 3.6 mJ∕cm2 for LBO). The induced fundamental B integral is evaluated around 0.25 rad in both crystals [30,31]. The conclusion that can be derived from these curves is that if one wants to avoid notably reducing the spectral width, one must use very thin crystals and very high power densities for efficient collinear femtosecond SHG. This is precisely the technique of [17], where power densities around a few TW∕cm2 are incident in typically 400 μm thick potassium dihydrogen phosphate (KDP) crystals. The authors propose to angularly compensate the nonlinear phase mismatch but have to manage self-focusing effects that become important at this power level. In contrast, the alternative noncollinear technique that is described in this paper uses moderate input power densities to generate the second-harmonic wave, with a potentially high conversion efficiency. C.
(3)
τL is the temporal FWHM fundamental frequency chirped pulsewidth, and τFTL is the temporal FWHM fundamental FTL width. When τL ≫ τFTL , the SHG spectral width is twice the fundamental spectral width (i.e., the SHG FTL pulse duration is potentially two times shorter than the FTL fundamental pulse duration). In contrast, for unchirped pulses (τL τFTL ), the SHG FTL pulse duration cannot be lower than the first-harmonic FTL duration (ΔνSHG ΔνFH ). Frequency chirping is thus attractive to obtain short pulses at high conversion efficiency, and this technique will be used here for noncollinear SHG in BBO and LBO. Another consequence of using chirped fundamental pulses is, however, that the SHG pulses are to be compressed in order to get near FTL pulses. This can lead to energy loss. D.
Crystal Thickness in Noncollinear SHG
The crystal thickness has to be optimized to obtain simultaneously the maximum efficiency and the broader frequency spectrum at a given input fluence and a given chirp. To optimize this choice, we use a plane wave version of the SHG equations, solved with the “PW-mix-SP” module of SNLO. Noncollinear geometry is taken into account in a qualitative approach by using the calculated group velocities along the z axis (see Fig. 1 and corresponding text) and the individual group-velocity dispersion of the second-harmonic wave. As an example, Fig. 4 plots, for a typical fluence of 3.6 mJ∕cm2 in BBO and LBO, the noncollinear SHG efficiency as a function of the crystal thickness for a few pulse durations in the range of 150–1300 fs. Figure 4(a) shows in this case that a 1.25 mm thick BBO crystal should be preferred for 300 fs input pulses, whereas a 2.6 mm thick
Frequency Chirp of the Input Fundamental Wave
Frequency chirp has two main advantages: to reduce the input power density in order to avoid nonlinear effects that can lower the SHG conversion efficiency and to obtain a larger SHG frequency spectrum and thus shorter pulses. As shown in [9], for a temporally Gaussian pulse, in the limit of high-efficiency conversion, the ratio of the second-harmonic to fundamental spectral width is given by
Fig. 4. Noncollinear geometry: SNLO calculated (module “PW-SP mixing”) (a) BBO and (b) LBO noncollinear SHG efficiencies as a function of crystal thickness for various pulse durations. Input fluence is 3.6 mJ∕cm2 . Beam diameters of 5 and 5.8 mm, respectively, are assumed for BBO and LBO. 20 April 2014 / Vol. 53, No. 12 / APPLIED OPTICS
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crystal is to be chosen for 1300 fs pulses. For LBO [Fig. 4(b)], 4 mm thick crystals give higher conversion efficiency for 150 fs duration pulses, but ∼6 mm thick crystals are to be preferred for 300 fs pulses. Shorter pulses should lead generally to higher conversion efficiency but also to narrower second-harmonic frequency spectra (Section 2.C), and one has to take this into account to optimize a given situation. 3. Experimental Setup A.
800 nm Ultrashort Ti:Sa Laser Source
The laser source is composed of a Coherent MIRA fs Kerr lens mode-locked Ti:Sa laser oscillator pumped by a Coherent Verdi laser, a Pockels cell pulse selector, an Öffner-type stretcher, a Ti:Sa regenerative amplifier, and a multipass Ti:Sa amplifier, both pumped by frequency-doubled Nd:YAG lasers. After the first amplification stages, beamsplitters distribute the laser beam to multiple lines, which can be amplified once again before compression. The 800 nm FTL pulse duration is about 45 fs. Adjustment of the chirp parameter at the input of the noncollinear SHG system is done with one of the two-pass grating compressors of the Ti:S laser system. Input 800 nm spectral phase and pulse duration are measured with a homemade SPIDER [32]. B.
Prisms Noncollinear SHG Setup
Figure 5 presents a simple noncollinear SHG setup, using two prisms to achieve PFT. Because of the angular dispersion (downstream of the prisms), it is necessary to image the exit plane of the dispersive element on the entrance plane of the nonlinear crystal. Taking into account the magnification ratio of two afocal telescopes (focal lens f 1 f 2 200 mm and f 3 , f 4 depending on the crystal), two prisms P1 and P2 (25 mm base, SF11, apex angle 60° used at minimum deviation) are needed to obtain the desired tilt. Using an aperture D positioned just behind the first prism, one obtains in the crystal an almost flat 800 nm beam spatial profile (quasi-super-Gaussian of order >2), with an axisymmetric top-hat envelope and a similar 400 nm spatial profile (Fig. 6). Because
Fig. 6. 800 nm beam spatial profile in the entrance plane and 400 nm profile at the output of the nonlinear crystal.
of possible unwanted nonlinear effects that can be generated at high power density in the prisms and that may deteriorate the conversion efficiency (selffocusing, self-phase modulation, etc.), this setup is generally well adapted to moderate input energy. It has also to be noticed that using a prism for PFT has another drawback. Indeed, as it passes through the prism, a ray acquires an induced GDD that varies with the impact point. This effect has a negligible consequence as long as the chirp induced by the prism is lower than the chirp of the first-harmonic pulse. It can nevertheless be a true limitation for very short pulses if not corrected. 4. Experimental Results A. Low-Energy Prisms Noncollinear SHG Setup
The noncollinear SHG setup of Fig. 5 was tested with BBO and LBO. The diameter of the aperture D near P1 was chosen around 7 mm. As the target PFTs are not the same, the magnification ratios are not identical for BBO and LBO. This leads to 800 nm beam sizes near the crystal that are slightly different (FWHM around 5 and 6 mm, respectively). BBO crystals (Castech) of 3 and 1 mm thickness and LBO crystals of 5 mm (Castech) and 6 mm (Cristal Laser) thickness were used. Table 2 gives the main useful experimental data. Table 2.
Main Characteristics of BBO and LBO Low-Energy Optical Configuration
BBO
Fig. 5. Noncollinear SHG setup using two prisms in order to achieve PFT. The Mi (i 0 to 8) are high-reflectivity mirrors, and BS is a 50% beamsplitter. Other components are defined in the text. 2650
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Afocal telescope: f 3 ; f 4 mm PFT angle (°) Beam diameter on crystal (mm): 800 nm spatial profile: Typical pulse energy range: Max. Corr. fluence mJ∕cm2 : Pulse duration range investigated:
LBO
(300,200) (300,250) 17.1 13.7 5 5.8 Supergaussian, order 2 0 to 1.5 mJ 7.2 5 45 fs (FTL) to 1800 fs
The total input energy per pulse was varied in the range of 0–1.5 mJ (which corresponds to a maximum fluence around 7 mJ∕cm2 in BBO and 5 mJ∕cm2 in LBO). Energy measurements were achieved with a pyroelectric joule-meter (Gentec sensor QE25SPS-MT-DO). The influence of the 800 nm chirp on 400 nm conversion efficiency and on the spectral bandwidth was studied. 1. Noncollinear Conversion Efficiency and Spectral Bandwidth as a Function of 800 nm Chirp Noncollinear conversion efficiency as a function of input fundamental energy for several chirps, i.e., different pulse durations τL from 45 fs (FTL) to around 1.5 ps, was measured as well as the corresponding 400 nm spectral bandwidth. The conversion efficiency is defined as the SHG energy divided by the total input energy. At maximum compression, the measured conversion efficiency is always below 40% and the SHG spectral width is low, of the order of 2.5 nm. The main reason is related to the imperfect overlap of the two 800 nm pulse fronts that becomes very critical for the shortest pulse durations and also to the tranverse variation of the pulse duration (due to the prisms). For frequency chirped 800 nm pulses, typical maximum conversion efficiency is around 60%. For BBO, Fig. 7 compares the measured and calculated SHG conversion efficiency as a function of the input 800 nm fluence for some pulse durations τL in (a) 3 mm and (b) 1 mm thick crystals, respectively. Calculations were done with the 2D short-pulse mixing module where spatial walk-off was neglected. The input beam diameter is 5 mm with a superGaussian spatial distribution of order 2 and 7 m radius of curvature of the wave front (this value minimizes the difference between experiments and simulations and is compatible with our setup). In order to describe more accurately the experiment, the two input 800 nm energies are slightly unbalanced (the input energy in one arm is about 9% higher than in the other arm). For similar reasons, the 400 nm group-velocity index is determined using the experimental value of the PFT and is not strictly equal to the 800 nm group-velocity index due to the difference between the target and experimental PFTs. At maximum conversion efficiency, for highly chirped pulses, one obtains relatively large spectral bandwidths: in a 3 mm thick BBO crystal, for 1300 fs 800 nm pulse duration, the 400 nm spectral bandwidth is about 1.6 times the 800 nm spectral bandwidth [Fig. 7(a1)] and approximately 1.9 times the 800 nm spectral bandwidth in 1 mm thick BBO for 770 fs fundamental pulse duration [Fig. 7(b1)]. These values are consistent with the discussion of Section 2.C. In LBO (5 and 6 mm thick), results are globally equivalent, taking into account the difference between the effective nonlinear coefficients of the two crystals (Table 1) with, however, slightly higher
Fig. 7. Noncollinear SHG in BBO. Measured (red dots) and SNLO calculated (blue solid line) SHG conversion efficiency as a function of the 800 nm peak fluence in (a) 3 mm and (b) 1 mm thick BBO crystal, for several 800 nm pulse durations. Corresponding measured and calculated wavelength spectra are given on the right for (a1) 1300 fs (BBO 3 mm) and (b1) 770 fs (BBO 1 mm) 800 nm duration.
conversion efficiency, but lower spectral enlargement. Figure 8 plots, at fixed total incident fluence (∼3.7 mJ∕cm2 ) and for a 6 mm thick LBO crystal, the experimental and calculated noncollinear conversion efficiency as a function of pulse duration (i.e., second-order phase ϕ2 ). Calculations are made in the same way as described before, and the beam diameter is assumed 5.8 mm. In this case, at maximum conversion efficiency, the spectral bandwidth is around 6.7 nm (Fig. 8). This corresponds to an increase of about 1.5 compared to the initial 800 nm frequency spectrum. Experiment and calculations show the same tendency and are in rather good agreement for chirped 800 nm pulses, considering that calculations are made with idealized temporal and phase profiles and that noncollinear SHG is described with a simplified model. Looking at Fig. 8, there seems to be good agreement even at maximum compression. In fact, for very short pulse durations, the doubling efficiency decreases not only because of backconversion (which SNLO can take into account) but also because of imperfect spatial overlap of the two input 20 April 2014 / Vol. 53, No. 12 / APPLIED OPTICS
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Fig. 8. Noncollinear SHG in LBO. Measured and SNLO calculated SHG conversion efficiency at fixed input 800 nm fluence (3.7 mJ∕cm2 ), as a function of the pulse duration in a 6 mm thick LBO crystal. The wavelength spectrum is given at the top for a 800 m pulse duration τL 550 fs (∼55%), with good agreement between the measured (pink solid line) and the calculated spectra (blue solid line).
beams and because of spatial chirp effects due to the prisms (effects that are not taken into account in SNLO). The main parameters of the calculation are given in Table 3. For sufficiently chirped pulses and moderate input power densities (before backconversion plays a major role), simulations show that the conversion efficiency is mainly determined by the input power density. At constant input pulse energy, shortening the pulse duration, for example, leads to displacing the maximum conversion efficiency to lower fluence, which can be viewed as due to the enhancement of the power density. This can be clearly observed by plotting the calculated conversion efficiency (using the “PW-mix-SP” module) as a function of power density for different pulse durations or chirps. As an
Table 3.
Parameters of Calculations for BBO and LBO
BBO
LBO
Module 2D SP mixing of SNLO 800 nm FTL pulse 45 duration (fs): Input 800 nm spatial Super-Gaussian order 2 profile: FWHM beam 5 6 diameter (mm): Indices of refraction: Calculated using the data of [24,25] Calculated using the data of [24,25] GVia and GDD: Walkoff-angle: Neglected Radius of curvature (mm): 7000 1.87 0.38 deff (pm/V): a GVi (group-velocity index) values take into account the difference between the target and experimental PFT. This leads to a 400 nm GVi that is slightly different from the 800 nm value.
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Fig. 9. Noncollinear SHG in BBO. SNLO calculated conversion efficiency (“PW-mix-SP” mixing module) as a function of input 800 nm power density in 3 mm thick BBO for several chirp parameters corresponding to 800 nm pulse durations varying between 150 and 1300 fs.
example, Fig. 9 corresponds to a 3 mm thick BBO crystal. In this case, one obtains quasi-identical conversion efficiency profiles for 800 nm durations exceeding 200–300 fs (τL 300, 600, and 1300 fs) at moderate power densities (typically less than 15–20 GW∕cm2 ). We restrict to chirped pulses corresponding to durations longer than 300 fs (in order to maximize the SHG bandwidth and avoid problems of overlapping between the two pulse fronts) and to power densities less than 15 GW∕cm2 (to avoid thirdorder nonlinear phenomena). In this case, adjusting the input power density provides a way to optimize the conversion efficiency. For instance, Fig. 9 shows that in a 3 mm thick BBO crystal, at a given input laser fluence (or energy per pulse), the frequency chirp should ideally be managed in order to obtain a power density around 2 or 3 GW∕cm2 (which leads to a calculated conversion efficiency around 60%– 70%). This result agrees well with the experimental data of Fig. 7, and similar conclusions can be derived for different crystal thicknesses and in LBO. 2. Pulse Compression (400 nm) In the case of 1 mm thick BBO, compression of the SHG pulse was achieved with the help of a 105 mm long silica Dove prism (second-order dispersion ∼8000 fs2 at 400 nm) inserted on the 400 nm beam. The 800 nm second-order phase ϕ2 was adjusted using a grating compressor around −16; 000 fs2 (pulse duration τL ∼ 960 fs) at the input of the crystal in order to minimize the output 400 nm pulse duration. For an input intensity of 5.6 GW∕cm2, the 400 nm FWHM pulse duration was measured around 40 fs (FTL pulse duration 34 fs) with a UV Wizzler (Fastlite) [33]. For LBO (5 or 6 mm), analogous measurements lead to slightly larger 400 nm pulse durations than in BBO (typically around 45 fs FWHM) as expected from the compared width of the SHG spectra (Figs. 7 and 10).
Fig. 10. Experimental high-energy SHG setup (LBO). The Mi (i 1 to 7) are high-reflectivity mirrors, and S is a 50% beamsplitter.
B.
High-Energy SHG
When one aims to maximize the (400 nm) output energy, it is necessary to reduce the energy losses. In this case, it may be interesting to use a noncollinear SHG setup where the first-harmonic pulse compression and PFT are generated by the same setup and adjusted independently without the need of another grating that could induce supplementary energy loss. Figure 10 presents a practical realization of such a scheme. This setup is inserted at the end of the Ti:S amplification stage (Fig. 6). The main part of the setup is constituted by a four identical 1200 gr∕mm grating (G1 , G2 , G3 , G4 ) pulse compressor arrangement, which is equivalent to a doublepass grating pair compressor with a retro-reflecting mirror. When using this system for standard pulse compression, gratings G1 and G2 are parallel. The first grating G1 disperses the ultrashort pulse into its spectral components, and the second one G2 recollimates the beam so that the angular dispersion produced by G1 is fully compensated. The addition of another pair of gratings (G3 and G4 ) in a configuration that is symmetrical to the first pair compensates for the induced spatial chirp on the beam. The pulse duration is varied by adjusting the distance between G1 and G2 . A two-lens cylindrical afocal telescope (focal lens f 01 −750 mm and f 02 1000 mm) at the entrance of the system compensates for the gratings induced anamorphosis, whereas a two-lens afocal telescope (focal lens f 1 800 mm and f 2 800 mm) makes an image of the last grating plane G4 on the crystal in order to cancel the combined effects of angular dispersion and propagation. This setup was finally tested with an LBO crystal. The high-energy UV beam was intended to be used in the study of x-ray emission from interaction with rare gas clusters as a function of pulse duration, and the objective was to deliver around 10 mJ laser pulses at 400 nm with pulse durations that could be varied between 50 fs and 2 ps. LBO was preferred to BBO as it is possible to obtain very large aperture crystals [34] in order to reduce the laser fluence when using high-energy beams. The four-grating system transmission efficiency was around 60%. The measured energy per
pulse at the entrance of the LBO crystal was 55 mJ with a beam diameter of 40 mm (FWHM, superGaussian profile, fluence around 4 mJ∕cm2 ). Maximization of the SHG conversion efficiency was done by adjusting the distance between the two gratings G1 and G2 . An energy of 22 mJ per pulse was measured at 400 nm with a rather homogeneous spatial profile for an 800 nm chirp corresponding to 1 ps pulse duration. This leads to 43% conversion efficiency, a value that, even if slightly lower, is compatible with the results obtained before. In practice, optimizing the output 400 nm energy by varying the chirp parameter cannot be done continuously (without motorized translation stages for G2 and G3 ). In order to leave the beam position unchanged at the output of the system, one has to modify by the same amount the distances G1 G2 and G3 G4 . The setup was thus not completely optimized, and this could explain why conversion efficiency was less than 50%, but as the performances were sufficient for the intended application and because of time constraints, we did not try to further improve the results. It is worth noting that this level of performance is among the best reported until now. The 400 nm pulse was finally compressed with a two-grating compressor (60% global transmission efficiency). An energy of 12 mJ per pulse was obtained, and the duration was 45 fs (measured with a Wizzler). Figure 11 plots (a) the second-harmonic intensity profile, the wavelength spectrum, and the temporal or spectral phase and (b) the 800 nm spectrum. It has to be noticed finally that our four-grating system used to compress and tilt the front pulse replaces a classical two-grating two-pass compressor and is thus not to be taken into account for evaluating the noncollinear SHG conversion efficiency. C.
Efficiency of the Noncollinear SHG System
As we defined it before, it is clear that the conversion efficiency of the noncollinear SHG process does not include the energy lost in the first part of the setup (see Fig. 5), which is intended to obtain the required PFT as well as the spatial, temporal, and spectral energy distribution on the crystal. In the case of
Fig. 11. Spectral and temporal measurements at (a) 400 nm and (b) 800 nm wavelength spectra. 20 April 2014 / Vol. 53, No. 12 / APPLIED OPTICS
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the prism setup, as only reflecting mirrors or prisms are needed, these losses can, however, be made negligible by choosing appropriate high-quality optical elements. When using a grating instead of a prism to induce the PFT, the same conclusion can be made. This definition of the conversion efficiency, however, does not include the energy lost for the 400 nm compression. These losses can be considered as negligible when using a bulk of silica but may not be when using a 400 nm grating compressor, which can be necessary in some applications. In our “high-energy experiment,” we used (Section 4.B) a 60% transmission single-path compressor based on two standard commercial gratings. With specifically designed gratings, it is certainly possible to reach a higher transmission, around 80%, but this would lead to a more expensive system. In that case, the net overall conversion efficiency of the system can be around 80% of the noncollinear SHG conversion efficiency as obtained in our experiments—that is to say, about 50% in the best case. 5. Conclusion
In summary, highly efficient femtosecond noncollinear achromatic SHG was demonstrated in BBO and LBO at 800 nm. A practical and simple method for optimizing noncollinear achromatic SHG has been detailed. When applied to these two crystals, very good conversion efficiency performances were obtained. Several experimental setups using prisms or gratings were investigated in order to exactly match simultaneously the pulse fronts of the three waves as well as their group velocity and cancel the wave-vector mismatch to first order. They all proved to be very efficient and extremely robust. When using moderate energy levels (∼1 mJ∕pulse), more than 65% SHG efficiency was measured in BBO and LBO. Once temporally compressed (without any loss of pulse energy), the FWHM 400 nm pulse duration was measured around 42 fs in the case of BBO (FTL pulse duration 34 fs) and around 46 fs (FTL pulse duration 45 fs) in LBO. To our knowledge, this is one of the best results obtained. At higher energies, with a specific and original setup that allows the simultaneous management of the pulse front and of the pulse compression, more than 22 mJ at 400 nm was obtained with conversion efficiency around 43% in LBO. In this case, using a classical grating compressor, temporal compression was achieved resulting in 45 fs FWHM pulse duration at 400 nm (i.e., of the same order as the 800 nm wave). The high-energy UV beam is believed to be of immediate interest for many spectroscopic experiments. It was indeed successfully used in the study of x-ray emission from interaction with rare gas clusters as a function of pulse duration. During the one-month experiment, it proved to be a very rugged and reliable tool. We thank D. Lupinski (Cristal Laser) for providing the high-aperture, high-quality LBO crystal as well as for many helpful discussions. The research 2654
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described here has been supported by “Triangle de la physique,” contract SOLAMU 2007-020T, and by specific funds (“crédits d’intervention 2010”) from the CNRS. Two of us benefited from either a Ph.D. grant from the CNRS (C. Ramond) or a postdoctoral fellowship from the EMMI, contract no. HA216-UPR. References 1. A. J. W. Brown, M. S. Bowers, K. W. Kangtas, and C. H. Fisher, “High-energy, high-efficiency second-harmonic generation of 1064-nm radiation in KTP,” Opt. Lett. 17, 109–111 (1992). 2. W. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, and R. S. Craxton, “Demonstration of high efficiency third harmonic conversion of high power Nd-glass laser radiation,” Opt. Commun. 34, 469–473 (1980). 3. G. Mennerat, J. Rault, O. Bonville, P. Canal, O. Hartmann, E. Mazataud, L. Marmande, L. Patissou, J. Charrier, and C. Lepage, “Very high efficiency high-energy frequency doubling in the Alisé facility,” in Advanced Solid-State Photonics, OSA Technical Digest (Optical Society of America, 2010), paper ATuA24G. 4. O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989). 5. G. Szabo and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990). 6. T. R. Zhang, H. R. Choo, and M. C. Downer, “Phase and group-velocity matching for second harmonic generation of femtosecond pulses,” Appl. Opt. 29, 3927–3933 (1990). 7. B. Richman, S. Bisson, R. Trebino, E. Sidick, and A. Jacobson, “Efficient broadband second harmonic generation by dispersive achromatic nonlinear conversion using only prisms,” Opt. Lett. 23, 497–499 (1998). 8. A. V. Smith, “Group-velocity-matched three-wave mixing in birefringent crystals,” Opt. Lett. 26, 719–721 (2001). 9. N. V. Didenko, A. V. Konyashchenko, L. L. Losev, V. S. Pazyuk, and S. Y. Tenyakov, “Femtosecond pulse compression based on second harmonic generation from a frequency chirped pulse,” Opt. Commun. 282, 997–999 (2009). 10. T. Zhang and M. Yonemura, “Pulse compression with a noncollinear type I frequency doubling crystal,” Jpn. J. Appl. Phys. 37, 542–543 (1998). 11. M. Aoyama, T. Zhang, M. Tsukakoshi, and K. Yamakawa, “Noncollinear second-harmonic generation with compensation of phase mismatch by controlling frequency chirp and tilted pulse fronts of femtosecond laser pulses,” Jpn. J. Appl. Phys. 39, 3394–3399 (2000). 12. C. Radzewicz, Y. B. Band, G. W. Pearson, and J. S. Krasinski, “Short pulse nonlinear frequency conversion without group-velocity-mismatch broadening,” Opt. Commun. 117, 295–302 (1995). 13. S. Ashihara, T. Shimura, and K. Kuroda, “Group-velocity matched second-harmonic generation in tilted quasi-phasematched gratings,” J. Opt. Soc. Am. B 20, 853–856 (2003). 14. A. Dubietis, G. Valiulis, R. Danielius, and A. Piskarskas, “Nonlinear pulse compression by optical frequency mixing in crystals with second-order nonlinearity,” Pure Appl. Opt. 7, 271–279 (1998). 15. A. Andreoni, M. Bondani, and M. A. C. Potenza, “Ultrabroadband and chirp-free frequency doubling in β-barium borate,” Opt. Commun. 154, 376–382 (1998). 16. H. Liu, W. Zhao, Y. Yang, H. Wang, Y. Wang, and G. Chen, “Matching of both group velocity and pulse-front for ultrabroadband three-wave-mixing with non-collinear angularly dispersed geometry,” Appl. Phys. B 82, 585–594 (2006). 17. S. Y. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron 18, 7–13 (2012). 18. V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, “Method for compensating the phase-matching
19. 20.
21. 22. 23. 24. 25. 26. 27.
dispersion in nonlinear optics,” Sov. J. Quantum Electron. 4, 1090–1098 (1975). R. A. Cheville, M. T. Reiten, and N. J. Halas, “Wide-bandwidth frequency doubling with high conversion efficiency,” Opt. Lett. 17, 1343–1345 (1992). D. T. Kanai, X. Zhou, T. Liu, A. Kosuge, T. Sekikawa, and S. Watanabe, “Generation of terawatt 10-fs blue pulses by compensation for pulse-front distortion in broadband frequency doubling,” Opt. Lett. 29, 2929–2931 (2004). P. Baum, S. Lochbrunner, and E. Riedle, “Tunable sub-10-fs ultraviolet pulses generated by achromatic frequency doubling,” Opt. Lett. 29, 1686–1688 (2004). D. N. Nikogosyan, “Beta barium borate. A review of its properties and applications,” Appl. Phys. A 52, 359–368 (1991). D. X. Zhang, Y. F. Kong, and J. Y. Zhang, “Optical parametric properties of 532-nm-pumped beta-barium-borate near the infrared absorption edge,” Opt. Commun. 184, 485–491 (2000). C. Chen, Y. Wu, A. Jiang, B. Wu, G. You, R. Li, and S. Lin, “New nonlinear-optical crystal: LiB3O5,” J. Opt. Soc. Am. B 6, 616–621 (1989). K. Kato, “Temperature-tuned 90° phase-matching properties of LiB3O5,” IEEE J. Quantum Electron. 30, 2950–2952 (1994). SNLO, nonlinear optics code available from A. V. Smith, AS-Photonics, Albuquerque, N. Mex. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer, 1999).
28. A. V. Smith, D. J. Armstrong, and W. J. Alford, “Increased acceptance bandwidths in optical frequency conversion by use of multiple walk-off-compensating nonlinear crystals,” J. Opt. Soc. Am. B 15, 122–141 (1998). 29. T. R. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation,” J. Cell. Comp. Physiol. 55, 203–230 (1984). 30. G. Rodriguez and A. J. Taylor, “Measurement of cross-phase modulation in optical materials through the direct measurement of the optical phase change,” Opt. Lett. 23, 858–860 (1998). 31. H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mater. 15, 237–242 (2001). 32. C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998). 33. A. Moulet, S. Grabielle, C. Cornaggia, N. Forget, and T. Oksenhendler, “Single-shot, high-dynamic-range measurement of sub-15 fs pulses by self-referenced spectral interferometry,” Opt. Lett. 35, 3856–3858 (2010). 34. A. Kokh, N. Kononova, G. Mennerat, P. Villeval, S. Durst, D. Lupinski, V. Vlezko, and K. Kokh, “Growth of high quality large size LBO crystals for high energy second harmonic generation,” J. Cryst. Growth 312, 1774–1778 (2010).
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CEA-Saclay, IRAMIS, Laboratoire Interactions, Dynamique et Lasers, 91191 Gif-sur-Yvette, France
2
FASTLITE, Centre scientifique d’Orsay, bât. 503, Plateau du Moulon, BP 45, 91401 Orsay, France 3
CNRS, UMR 7588, Institut des NanoSciences de Paris (INSP), F-75005 Paris, France
4
Sorbonne Universités, UPMC Univ. Paris 06, UMR 7588, INSP, F-75005 Paris, France
5 6
Postdoctoral fellow of the ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum, 64291 Darmstadt, Germany
Present address: Faculty of Engineering, Holy Spirit University of Kaslik (USEK), P.O. Box 446, Jounieh, Lebanon *Corresponding author: [email protected] Received 22 January 2014; revised 19 March 2014; accepted 21 March 2014; posted 24 March 2014 (Doc. ID 204771); published 17 April 2014
We report on 400 nm broadband type I frequency doubling in a noncollinear geometry with pulse-fronttilted and chirped femtosecond pulses (λ0 800 nm; Fourier transform limited pulse duration, 45 fs). With moderate power densities (2 to 10 GW∕cm2 ) thus avoiding higher-order nonlinear phenomena, the energy conversion efficiency was up to 65%. Second-harmonic pulses of Fourier transform limited pulse duration shorter than the fundamental wave were generated, exhibiting good beam quality and no pulse-front tilt. High energy (20 mJ/pulse) was produced in a 40 mm diameter and 6 mm thick LBO crystal. To the best of our knowledge, this is the first demonstration of this optical configuration with sub-100-fs pulses. Good agreement between experimental results and simulations is obtained. © 2014 Optical Society of America OCIS codes: (190.7110) Ultrafast nonlinear optics; (190.2620) Harmonic generation and mixing; (320.1590) Chirping. http://dx.doi.org/10.1364/AO.53.002646
1. Introduction
Second-harmonic generation (SHG) in nonlinear optical crystals has been the subject of countless studies over the past 50 years. For relatively long laser pulses (i.e., whose duration exceeds typically 100 ps), conversion efficiencies even greater than 80% have been obtained [1–3]. Regarding the field of ultrashort pulses (femtosecond regime), frequency 1559-128X/14/122646-10$15.00/0 © 2014 Optical Society of America 2646
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doubling also has many attractive features, such as extending the wavelength range, improving the pulse temporal contrast, or obtaining even shorter pulses. However, femtosecond SHG faces several specific and major difficulties mainly due to the phase-matching condition to be fulfilled on a very broad spectrum and to the high electric field associated with ultrashort laser pulses, which can induce unwanted disturbing phenomena. For femtosecond pulse durations, phase mismatch (which at first order corresponds to group-velocity mismatch) leads to temporal broadening (spectral bandwidth
narrowing) and reduces the energy conversion. At high intensities, third-order nonlinear phenomena (self-phase modulation, cross-phase modulation, self-focusing, etc.) can decrease the conversion efficiency and alter the second-harmonic beam quality. In order to overcome these effects, the simplest solution is to use a thin crystal and to moderate the power density at the expense of the conversion efficiency. The problem of obtaining high conversion efficiency at high energy levels without spectral narrowing has been extensively studied in recent years, and several solutions have been proposed [4–17]. Achromatic phase matching for SHG of femtosecond pulses was described in [4,18], and a similar arrangement was later published in [5]. The method is based on the introduction of spectral angular dispersion so that the different spectral components propagate at their phase-matching angle, which is equivalent to cancel the group-velocity mismatch. Wide-bandwidth frequency doubling with high conversion efficiency was discussed in [19], and a variant of the method using pulse-front distortion compensation [20] has led to terawatt 10 fs blue pulses by broadband frequency doubling. Sub-10-fs ultraviolet (UV) pulses were more recently generated by achromatic frequency doubling [21]. A noncollinear geometry was also independently proposed [6] in order to achieve phase and group-velocity matching for SHG of femtosecond pulses. This scheme has several specific advantages, such as the direct separation of the three interacting waves. However, to the best of our knowledge, this method was never applied to the generation of sub-100-fs doubled pulses at high conversion efficiency levels (around 50%). Smith [8] and later Liu et al. [16] have detailed an analysis of the three-wave-mixing ultrabroadband phase-matching conditions using the concept of pulse-front tilt (PFT). We apply in this paper their model to design an original setup for high-efficiency achromatic femtosecond 400 nm type I noncollinear SHG with tilted pulse fronts in two nonlinear crystals, beta-barium borate (BBO) and lithium triborate (LBO). One of the originalities of the method presented here lies in the systematic use of chirped pulses. As will be detailed later in the paper, this makes it possible to obtain simultaneously high conversion efficiency and broad frequency spectrum (i.e., short SHG pulse duration after compression). Moreover, reasonably thick crystals can be used (a few millimeters, whereas most SHG experiments use typically a few hundred micrometers thick crystals), and thus only moderate input intensities (GW∕cm2 range) are needed. Conversely, chirped pulses imply generally the use of a recompression setup after the doubling process. This, however, is balanced by the other advantages of the method. 2. Noncollinear SHG in the Femtosecond Regime
We only give main results for noncollinear SHG applied to BBO and LBO. We will show that compared to collinear SHG, this configuration has many
Fig. 1. Noncollinear SHG with PFT.
advantages in the case of very short pulses. From now on, only type I SHG will be considered. A. Noncollinear SHG Phase-Matching and PFT Angle
Following [8,16], it can be seen that for an appropriate crossing angle and PFT of the input beams (Fig. 1), one can balance the group velocity of the second harmonic and that of the fundamental harmonic along the same direction. For type I phase matching, this leads [16] to
v1 v2 v ; vshg v cos δ
1
where v1 v2 and vshg are, respectively, the group velocity of the first- and second-harmonic waves, and δ is half the angle between the two fundamental beams. When the pulse fronts of the three waves are simultaneously exactly matched as well as the group velocities, the wave-vector mismatch is cancelled to first order and a broadband SHG is achieved. From now on, we also suppose that the beam diameter d0 has been chosen large enough compared to the crystal’s thickness L for the effect of spatial walkoff to be negligible (L ≪ d0 ∕ρ, ρ being the SHG spatial walk-off angle in the case of a negative uniaxial crystal and type I SHG). 1. Application to BBO and LBO BBO is a negative uniaxial crystal [22] and belongs to noncentrosymmetric trigonal point group 3 m. Using the results of [8,16] and the Sellmeier equations [23] of BBO, the phase-matching angle and the noncollinear angle δ (between the second- and first-harmonic waves) compensating the wave-vector mismatch to first order are calculated. LBO is a biaxial crystal with mm2 orthorhombic point group symmetry [24]. Its principal axes X, Y, and Z (principal refractive indices nz > ny > nx ) are parallel to the crystallographic axes a, b, c (c < a < b). Wave-vector directions are given in a polar coordinate system related to the principal axes by the polar and azimuthal angles θ (measured from Z) and φ (measured from X). Effective nonlinear coefficients have maximum values when light propagates in the principal planes. Considering only type I SHG with waves propagating in the XY principal plane (θ 90°), LBO behaves like a negative uniaxial crystal and 20 April 2014 / Vol. 53, No. 12 / APPLIED OPTICS
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Table 1.
Wave-Vector Mismatch Compensated Noncollinear 800 nm Type I SHG in BBO and LBO
BBO
LBO
Fundamental wavelength: 800 nm Phase-matching angle (°): θ 41.4 θ; φ 90; 65.9 External noncollinear angle δ (°): 6.65 13.17 External angular Dispersion (μrad/nm): 372. 293 Effective nonlinear coefficient (pm/V): 1.87 0.38
calculations are similar to those in BBO using the Sellmeier equations of [25]. Table 1 sums up the main characteristics of noncollinear SHG in BBO and LBO. B.
Comparison with Collinear SHG
Noncollinear SHG requires a more complicated experimental setup than collinear SHG. It is thus useful to point out the potential advantages of this scheme. Indeed, these rely mainly on the possibility of obtaining simultaneously high conversion efficiencies and broad frequency spectra (i.e., potentially shorter pulse durations after recompression). To illustrate this, we first estimate the spectral acceptance for chirped pulses in the noncollinear configuration using the weak conversion approximation and compare it to the case of collinear SHG. In a second step, using numerical results obtained with the SNLO software [8,26], we give examples of spectral bandwidth limitations in collinear SHG. 1. Spectral Acceptance for Noncollinear SHG Let us consider noncollinear SHG and suppose that the wave-vector condition is fulfilled at central fundamental angular frequency ωf ωf 2πc∕λf ; λf 800 nm and second-harmonic angular frequency ωshg ωshg 2πc∕λshg ; λshg λf ∕2. With the notations of [8], the wave-vector mismatch jΔkj can be calculated for a given fundamental angular frequency ωm and the corresponding second-harmonic frequency (ωn 2ωm ): jΔkj Δkz
∂2 kf z 1 ∂2 kshg 2 ω −ωn − ωf −ωm 2 ; (2) 2 ∂ω2 ωshg shg ∂ω2 ωf
where Δkz is the wave-vector mismatch along the z axis, and kshg and kf are the second- and firstharmonic wave-vectors. Δωshg ωshg , where ωn is the deviation from the central angular frequency of a second-harmonic component wave at angular frequency ωn, and Δωf ωf − ωm is the deviation from the central angular frequency of a firstharmonic component wave at angular frequency ωm . Plotting jΔkj as a function of λm 2πc∕ωm, one can derive the noncollinear spectral acceptance in the weak conversion approximation (Fig. 2 in the case of BBO). 2648
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Fig. 2. Wave-vector mismatch jΔkj in BBO as a function of firstharmonic wavelength and corresponding noncollinear spectral bandwidth for a 3 mm thick crystal.
In this regime, the output intensity I SHG L at the exit of a crystal of thickness L is proportional to sinc2 ΔkL∕2. Defining the fundamental wavelength spectral acceptance bandwidth Δλ by the condition sinc2 ΔkL∕2 ≤ 1∕2, one obtains (for a given crystal width, here L 3 mm, for example) a maximum value of Δλ around 34 nm for BBO (limited by the group-velocity dispersion). This corresponds at 800 nm to a 26.5 fs pulse duration. Similarly, using Eq. (2), an approximate value of the maximum crystal thickness that preserves a given SHG wavelength bandwidth [that is to say a given Fourier transform limited (FTL) duration] can be derived. As an example, for the spectral bandwidth of an 800 nm, 45 fs FTL pulse with around 20 nm full waist at half maximum (FWHM), one obtains for BBO a maximum crystal thickness around 8.6 mm in the noncollinear configuration. This is to be compared with the corresponding value in type I collinear SHG [27], which is 0.25 mm. Similarly, the maximum crystal thickness preserving a 20 nm bandwidth is around 13 mm in the noncollinear configuration in LBO and only of 0.4 mm in the collinear configuration. 2. Numerical Simulations Illustrating Spectral Bandwidth Limitations in Collinear SHG Time-dependent equations corresponding to sum frequency generation (in collinear geometry) in the paraxial approximation with the inclusion of diffraction and walk-off are given in [28]. Dispersion is taken into account up to the second order via the group delay dispersion (GDD). These equations are solved by SNLO, which is a free software developed by Dr. Arlee Smith, using a split-step Fourier method [29]. In the “2D short-pulse mixing” module mainly used here, Gaussian (or super-Gaussian) spatial and temporal input profiles can be used. Linear frequency chirp and delays can also be imposed on the input pulses. The code allows us to follow the stepwise time evolution of each beam on a 2D spatial grid of intensity and phase. Using this module for collinear SHG with FTL pulses, one plots (Fig. 3) the 400 nm wavelength bandwidth and the corresponding conversion efficiency as a function of the crystal thickness L.
2 1∕2 ΔνSHG τ 4 − 3 FTL : ΔνFH τL
Fig. 3. Collinear geometry: SNLO calculated (“2D short-pulse mixing” module) 400 nm collinear SHG spectral width and corresponding conversion efficiency as a function of crystal thickness (a) in BBO (input 800 nm laser fluence 1.8 mJ∕cm2 ) and (b) in LBO (input laser fluence 3.6 mJ∕cm2 ). 800 nm FTL pulse duration, 45 fs (20 nm bandwidth); beam diameter, 7 mm; super-Gaussian coefficient, 2; radius of curvature, 104 cm. In each case, the input laser fluence is chosen in order to reach around 80% conversion efficiency after 1.5 mm propagation in the crystal.
This is done for a typical set of input 800 nm laser parameters (FTL pulse duration, 45 fs; beam diameter, 7 mm; super-Gaussian coefficient, order of 2; input laser fluence, 1.8 mJ∕cm2 for BBO and 3.6 mJ∕cm2 for LBO). The induced fundamental B integral is evaluated around 0.25 rad in both crystals [30,31]. The conclusion that can be derived from these curves is that if one wants to avoid notably reducing the spectral width, one must use very thin crystals and very high power densities for efficient collinear femtosecond SHG. This is precisely the technique of [17], where power densities around a few TW∕cm2 are incident in typically 400 μm thick potassium dihydrogen phosphate (KDP) crystals. The authors propose to angularly compensate the nonlinear phase mismatch but have to manage self-focusing effects that become important at this power level. In contrast, the alternative noncollinear technique that is described in this paper uses moderate input power densities to generate the second-harmonic wave, with a potentially high conversion efficiency. C.
(3)
τL is the temporal FWHM fundamental frequency chirped pulsewidth, and τFTL is the temporal FWHM fundamental FTL width. When τL ≫ τFTL , the SHG spectral width is twice the fundamental spectral width (i.e., the SHG FTL pulse duration is potentially two times shorter than the FTL fundamental pulse duration). In contrast, for unchirped pulses (τL τFTL ), the SHG FTL pulse duration cannot be lower than the first-harmonic FTL duration (ΔνSHG ΔνFH ). Frequency chirping is thus attractive to obtain short pulses at high conversion efficiency, and this technique will be used here for noncollinear SHG in BBO and LBO. Another consequence of using chirped fundamental pulses is, however, that the SHG pulses are to be compressed in order to get near FTL pulses. This can lead to energy loss. D.
Crystal Thickness in Noncollinear SHG
The crystal thickness has to be optimized to obtain simultaneously the maximum efficiency and the broader frequency spectrum at a given input fluence and a given chirp. To optimize this choice, we use a plane wave version of the SHG equations, solved with the “PW-mix-SP” module of SNLO. Noncollinear geometry is taken into account in a qualitative approach by using the calculated group velocities along the z axis (see Fig. 1 and corresponding text) and the individual group-velocity dispersion of the second-harmonic wave. As an example, Fig. 4 plots, for a typical fluence of 3.6 mJ∕cm2 in BBO and LBO, the noncollinear SHG efficiency as a function of the crystal thickness for a few pulse durations in the range of 150–1300 fs. Figure 4(a) shows in this case that a 1.25 mm thick BBO crystal should be preferred for 300 fs input pulses, whereas a 2.6 mm thick
Frequency Chirp of the Input Fundamental Wave
Frequency chirp has two main advantages: to reduce the input power density in order to avoid nonlinear effects that can lower the SHG conversion efficiency and to obtain a larger SHG frequency spectrum and thus shorter pulses. As shown in [9], for a temporally Gaussian pulse, in the limit of high-efficiency conversion, the ratio of the second-harmonic to fundamental spectral width is given by
Fig. 4. Noncollinear geometry: SNLO calculated (module “PW-SP mixing”) (a) BBO and (b) LBO noncollinear SHG efficiencies as a function of crystal thickness for various pulse durations. Input fluence is 3.6 mJ∕cm2 . Beam diameters of 5 and 5.8 mm, respectively, are assumed for BBO and LBO. 20 April 2014 / Vol. 53, No. 12 / APPLIED OPTICS
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crystal is to be chosen for 1300 fs pulses. For LBO [Fig. 4(b)], 4 mm thick crystals give higher conversion efficiency for 150 fs duration pulses, but ∼6 mm thick crystals are to be preferred for 300 fs pulses. Shorter pulses should lead generally to higher conversion efficiency but also to narrower second-harmonic frequency spectra (Section 2.C), and one has to take this into account to optimize a given situation. 3. Experimental Setup A.
800 nm Ultrashort Ti:Sa Laser Source
The laser source is composed of a Coherent MIRA fs Kerr lens mode-locked Ti:Sa laser oscillator pumped by a Coherent Verdi laser, a Pockels cell pulse selector, an Öffner-type stretcher, a Ti:Sa regenerative amplifier, and a multipass Ti:Sa amplifier, both pumped by frequency-doubled Nd:YAG lasers. After the first amplification stages, beamsplitters distribute the laser beam to multiple lines, which can be amplified once again before compression. The 800 nm FTL pulse duration is about 45 fs. Adjustment of the chirp parameter at the input of the noncollinear SHG system is done with one of the two-pass grating compressors of the Ti:S laser system. Input 800 nm spectral phase and pulse duration are measured with a homemade SPIDER [32]. B.
Prisms Noncollinear SHG Setup
Figure 5 presents a simple noncollinear SHG setup, using two prisms to achieve PFT. Because of the angular dispersion (downstream of the prisms), it is necessary to image the exit plane of the dispersive element on the entrance plane of the nonlinear crystal. Taking into account the magnification ratio of two afocal telescopes (focal lens f 1 f 2 200 mm and f 3 , f 4 depending on the crystal), two prisms P1 and P2 (25 mm base, SF11, apex angle 60° used at minimum deviation) are needed to obtain the desired tilt. Using an aperture D positioned just behind the first prism, one obtains in the crystal an almost flat 800 nm beam spatial profile (quasi-super-Gaussian of order >2), with an axisymmetric top-hat envelope and a similar 400 nm spatial profile (Fig. 6). Because
Fig. 6. 800 nm beam spatial profile in the entrance plane and 400 nm profile at the output of the nonlinear crystal.
of possible unwanted nonlinear effects that can be generated at high power density in the prisms and that may deteriorate the conversion efficiency (selffocusing, self-phase modulation, etc.), this setup is generally well adapted to moderate input energy. It has also to be noticed that using a prism for PFT has another drawback. Indeed, as it passes through the prism, a ray acquires an induced GDD that varies with the impact point. This effect has a negligible consequence as long as the chirp induced by the prism is lower than the chirp of the first-harmonic pulse. It can nevertheless be a true limitation for very short pulses if not corrected. 4. Experimental Results A. Low-Energy Prisms Noncollinear SHG Setup
The noncollinear SHG setup of Fig. 5 was tested with BBO and LBO. The diameter of the aperture D near P1 was chosen around 7 mm. As the target PFTs are not the same, the magnification ratios are not identical for BBO and LBO. This leads to 800 nm beam sizes near the crystal that are slightly different (FWHM around 5 and 6 mm, respectively). BBO crystals (Castech) of 3 and 1 mm thickness and LBO crystals of 5 mm (Castech) and 6 mm (Cristal Laser) thickness were used. Table 2 gives the main useful experimental data. Table 2.
Main Characteristics of BBO and LBO Low-Energy Optical Configuration
BBO
Fig. 5. Noncollinear SHG setup using two prisms in order to achieve PFT. The Mi (i 0 to 8) are high-reflectivity mirrors, and BS is a 50% beamsplitter. Other components are defined in the text. 2650
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Afocal telescope: f 3 ; f 4 mm PFT angle (°) Beam diameter on crystal (mm): 800 nm spatial profile: Typical pulse energy range: Max. Corr. fluence mJ∕cm2 : Pulse duration range investigated:
LBO
(300,200) (300,250) 17.1 13.7 5 5.8 Supergaussian, order 2 0 to 1.5 mJ 7.2 5 45 fs (FTL) to 1800 fs
The total input energy per pulse was varied in the range of 0–1.5 mJ (which corresponds to a maximum fluence around 7 mJ∕cm2 in BBO and 5 mJ∕cm2 in LBO). Energy measurements were achieved with a pyroelectric joule-meter (Gentec sensor QE25SPS-MT-DO). The influence of the 800 nm chirp on 400 nm conversion efficiency and on the spectral bandwidth was studied. 1. Noncollinear Conversion Efficiency and Spectral Bandwidth as a Function of 800 nm Chirp Noncollinear conversion efficiency as a function of input fundamental energy for several chirps, i.e., different pulse durations τL from 45 fs (FTL) to around 1.5 ps, was measured as well as the corresponding 400 nm spectral bandwidth. The conversion efficiency is defined as the SHG energy divided by the total input energy. At maximum compression, the measured conversion efficiency is always below 40% and the SHG spectral width is low, of the order of 2.5 nm. The main reason is related to the imperfect overlap of the two 800 nm pulse fronts that becomes very critical for the shortest pulse durations and also to the tranverse variation of the pulse duration (due to the prisms). For frequency chirped 800 nm pulses, typical maximum conversion efficiency is around 60%. For BBO, Fig. 7 compares the measured and calculated SHG conversion efficiency as a function of the input 800 nm fluence for some pulse durations τL in (a) 3 mm and (b) 1 mm thick crystals, respectively. Calculations were done with the 2D short-pulse mixing module where spatial walk-off was neglected. The input beam diameter is 5 mm with a superGaussian spatial distribution of order 2 and 7 m radius of curvature of the wave front (this value minimizes the difference between experiments and simulations and is compatible with our setup). In order to describe more accurately the experiment, the two input 800 nm energies are slightly unbalanced (the input energy in one arm is about 9% higher than in the other arm). For similar reasons, the 400 nm group-velocity index is determined using the experimental value of the PFT and is not strictly equal to the 800 nm group-velocity index due to the difference between the target and experimental PFTs. At maximum conversion efficiency, for highly chirped pulses, one obtains relatively large spectral bandwidths: in a 3 mm thick BBO crystal, for 1300 fs 800 nm pulse duration, the 400 nm spectral bandwidth is about 1.6 times the 800 nm spectral bandwidth [Fig. 7(a1)] and approximately 1.9 times the 800 nm spectral bandwidth in 1 mm thick BBO for 770 fs fundamental pulse duration [Fig. 7(b1)]. These values are consistent with the discussion of Section 2.C. In LBO (5 and 6 mm thick), results are globally equivalent, taking into account the difference between the effective nonlinear coefficients of the two crystals (Table 1) with, however, slightly higher
Fig. 7. Noncollinear SHG in BBO. Measured (red dots) and SNLO calculated (blue solid line) SHG conversion efficiency as a function of the 800 nm peak fluence in (a) 3 mm and (b) 1 mm thick BBO crystal, for several 800 nm pulse durations. Corresponding measured and calculated wavelength spectra are given on the right for (a1) 1300 fs (BBO 3 mm) and (b1) 770 fs (BBO 1 mm) 800 nm duration.
conversion efficiency, but lower spectral enlargement. Figure 8 plots, at fixed total incident fluence (∼3.7 mJ∕cm2 ) and for a 6 mm thick LBO crystal, the experimental and calculated noncollinear conversion efficiency as a function of pulse duration (i.e., second-order phase ϕ2 ). Calculations are made in the same way as described before, and the beam diameter is assumed 5.8 mm. In this case, at maximum conversion efficiency, the spectral bandwidth is around 6.7 nm (Fig. 8). This corresponds to an increase of about 1.5 compared to the initial 800 nm frequency spectrum. Experiment and calculations show the same tendency and are in rather good agreement for chirped 800 nm pulses, considering that calculations are made with idealized temporal and phase profiles and that noncollinear SHG is described with a simplified model. Looking at Fig. 8, there seems to be good agreement even at maximum compression. In fact, for very short pulse durations, the doubling efficiency decreases not only because of backconversion (which SNLO can take into account) but also because of imperfect spatial overlap of the two input 20 April 2014 / Vol. 53, No. 12 / APPLIED OPTICS
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Fig. 8. Noncollinear SHG in LBO. Measured and SNLO calculated SHG conversion efficiency at fixed input 800 nm fluence (3.7 mJ∕cm2 ), as a function of the pulse duration in a 6 mm thick LBO crystal. The wavelength spectrum is given at the top for a 800 m pulse duration τL 550 fs (∼55%), with good agreement between the measured (pink solid line) and the calculated spectra (blue solid line).
beams and because of spatial chirp effects due to the prisms (effects that are not taken into account in SNLO). The main parameters of the calculation are given in Table 3. For sufficiently chirped pulses and moderate input power densities (before backconversion plays a major role), simulations show that the conversion efficiency is mainly determined by the input power density. At constant input pulse energy, shortening the pulse duration, for example, leads to displacing the maximum conversion efficiency to lower fluence, which can be viewed as due to the enhancement of the power density. This can be clearly observed by plotting the calculated conversion efficiency (using the “PW-mix-SP” module) as a function of power density for different pulse durations or chirps. As an
Table 3.
Parameters of Calculations for BBO and LBO
BBO
LBO
Module 2D SP mixing of SNLO 800 nm FTL pulse 45 duration (fs): Input 800 nm spatial Super-Gaussian order 2 profile: FWHM beam 5 6 diameter (mm): Indices of refraction: Calculated using the data of [24,25] Calculated using the data of [24,25] GVia and GDD: Walkoff-angle: Neglected Radius of curvature (mm): 7000 1.87 0.38 deff (pm/V): a GVi (group-velocity index) values take into account the difference between the target and experimental PFT. This leads to a 400 nm GVi that is slightly different from the 800 nm value.
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Fig. 9. Noncollinear SHG in BBO. SNLO calculated conversion efficiency (“PW-mix-SP” mixing module) as a function of input 800 nm power density in 3 mm thick BBO for several chirp parameters corresponding to 800 nm pulse durations varying between 150 and 1300 fs.
example, Fig. 9 corresponds to a 3 mm thick BBO crystal. In this case, one obtains quasi-identical conversion efficiency profiles for 800 nm durations exceeding 200–300 fs (τL 300, 600, and 1300 fs) at moderate power densities (typically less than 15–20 GW∕cm2 ). We restrict to chirped pulses corresponding to durations longer than 300 fs (in order to maximize the SHG bandwidth and avoid problems of overlapping between the two pulse fronts) and to power densities less than 15 GW∕cm2 (to avoid thirdorder nonlinear phenomena). In this case, adjusting the input power density provides a way to optimize the conversion efficiency. For instance, Fig. 9 shows that in a 3 mm thick BBO crystal, at a given input laser fluence (or energy per pulse), the frequency chirp should ideally be managed in order to obtain a power density around 2 or 3 GW∕cm2 (which leads to a calculated conversion efficiency around 60%– 70%). This result agrees well with the experimental data of Fig. 7, and similar conclusions can be derived for different crystal thicknesses and in LBO. 2. Pulse Compression (400 nm) In the case of 1 mm thick BBO, compression of the SHG pulse was achieved with the help of a 105 mm long silica Dove prism (second-order dispersion ∼8000 fs2 at 400 nm) inserted on the 400 nm beam. The 800 nm second-order phase ϕ2 was adjusted using a grating compressor around −16; 000 fs2 (pulse duration τL ∼ 960 fs) at the input of the crystal in order to minimize the output 400 nm pulse duration. For an input intensity of 5.6 GW∕cm2, the 400 nm FWHM pulse duration was measured around 40 fs (FTL pulse duration 34 fs) with a UV Wizzler (Fastlite) [33]. For LBO (5 or 6 mm), analogous measurements lead to slightly larger 400 nm pulse durations than in BBO (typically around 45 fs FWHM) as expected from the compared width of the SHG spectra (Figs. 7 and 10).
Fig. 10. Experimental high-energy SHG setup (LBO). The Mi (i 1 to 7) are high-reflectivity mirrors, and S is a 50% beamsplitter.
B.
High-Energy SHG
When one aims to maximize the (400 nm) output energy, it is necessary to reduce the energy losses. In this case, it may be interesting to use a noncollinear SHG setup where the first-harmonic pulse compression and PFT are generated by the same setup and adjusted independently without the need of another grating that could induce supplementary energy loss. Figure 10 presents a practical realization of such a scheme. This setup is inserted at the end of the Ti:S amplification stage (Fig. 6). The main part of the setup is constituted by a four identical 1200 gr∕mm grating (G1 , G2 , G3 , G4 ) pulse compressor arrangement, which is equivalent to a doublepass grating pair compressor with a retro-reflecting mirror. When using this system for standard pulse compression, gratings G1 and G2 are parallel. The first grating G1 disperses the ultrashort pulse into its spectral components, and the second one G2 recollimates the beam so that the angular dispersion produced by G1 is fully compensated. The addition of another pair of gratings (G3 and G4 ) in a configuration that is symmetrical to the first pair compensates for the induced spatial chirp on the beam. The pulse duration is varied by adjusting the distance between G1 and G2 . A two-lens cylindrical afocal telescope (focal lens f 01 −750 mm and f 02 1000 mm) at the entrance of the system compensates for the gratings induced anamorphosis, whereas a two-lens afocal telescope (focal lens f 1 800 mm and f 2 800 mm) makes an image of the last grating plane G4 on the crystal in order to cancel the combined effects of angular dispersion and propagation. This setup was finally tested with an LBO crystal. The high-energy UV beam was intended to be used in the study of x-ray emission from interaction with rare gas clusters as a function of pulse duration, and the objective was to deliver around 10 mJ laser pulses at 400 nm with pulse durations that could be varied between 50 fs and 2 ps. LBO was preferred to BBO as it is possible to obtain very large aperture crystals [34] in order to reduce the laser fluence when using high-energy beams. The four-grating system transmission efficiency was around 60%. The measured energy per
pulse at the entrance of the LBO crystal was 55 mJ with a beam diameter of 40 mm (FWHM, superGaussian profile, fluence around 4 mJ∕cm2 ). Maximization of the SHG conversion efficiency was done by adjusting the distance between the two gratings G1 and G2 . An energy of 22 mJ per pulse was measured at 400 nm with a rather homogeneous spatial profile for an 800 nm chirp corresponding to 1 ps pulse duration. This leads to 43% conversion efficiency, a value that, even if slightly lower, is compatible with the results obtained before. In practice, optimizing the output 400 nm energy by varying the chirp parameter cannot be done continuously (without motorized translation stages for G2 and G3 ). In order to leave the beam position unchanged at the output of the system, one has to modify by the same amount the distances G1 G2 and G3 G4 . The setup was thus not completely optimized, and this could explain why conversion efficiency was less than 50%, but as the performances were sufficient for the intended application and because of time constraints, we did not try to further improve the results. It is worth noting that this level of performance is among the best reported until now. The 400 nm pulse was finally compressed with a two-grating compressor (60% global transmission efficiency). An energy of 12 mJ per pulse was obtained, and the duration was 45 fs (measured with a Wizzler). Figure 11 plots (a) the second-harmonic intensity profile, the wavelength spectrum, and the temporal or spectral phase and (b) the 800 nm spectrum. It has to be noticed finally that our four-grating system used to compress and tilt the front pulse replaces a classical two-grating two-pass compressor and is thus not to be taken into account for evaluating the noncollinear SHG conversion efficiency. C.
Efficiency of the Noncollinear SHG System
As we defined it before, it is clear that the conversion efficiency of the noncollinear SHG process does not include the energy lost in the first part of the setup (see Fig. 5), which is intended to obtain the required PFT as well as the spatial, temporal, and spectral energy distribution on the crystal. In the case of
Fig. 11. Spectral and temporal measurements at (a) 400 nm and (b) 800 nm wavelength spectra. 20 April 2014 / Vol. 53, No. 12 / APPLIED OPTICS
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the prism setup, as only reflecting mirrors or prisms are needed, these losses can, however, be made negligible by choosing appropriate high-quality optical elements. When using a grating instead of a prism to induce the PFT, the same conclusion can be made. This definition of the conversion efficiency, however, does not include the energy lost for the 400 nm compression. These losses can be considered as negligible when using a bulk of silica but may not be when using a 400 nm grating compressor, which can be necessary in some applications. In our “high-energy experiment,” we used (Section 4.B) a 60% transmission single-path compressor based on two standard commercial gratings. With specifically designed gratings, it is certainly possible to reach a higher transmission, around 80%, but this would lead to a more expensive system. In that case, the net overall conversion efficiency of the system can be around 80% of the noncollinear SHG conversion efficiency as obtained in our experiments—that is to say, about 50% in the best case. 5. Conclusion
In summary, highly efficient femtosecond noncollinear achromatic SHG was demonstrated in BBO and LBO at 800 nm. A practical and simple method for optimizing noncollinear achromatic SHG has been detailed. When applied to these two crystals, very good conversion efficiency performances were obtained. Several experimental setups using prisms or gratings were investigated in order to exactly match simultaneously the pulse fronts of the three waves as well as their group velocity and cancel the wave-vector mismatch to first order. They all proved to be very efficient and extremely robust. When using moderate energy levels (∼1 mJ∕pulse), more than 65% SHG efficiency was measured in BBO and LBO. Once temporally compressed (without any loss of pulse energy), the FWHM 400 nm pulse duration was measured around 42 fs in the case of BBO (FTL pulse duration 34 fs) and around 46 fs (FTL pulse duration 45 fs) in LBO. To our knowledge, this is one of the best results obtained. At higher energies, with a specific and original setup that allows the simultaneous management of the pulse front and of the pulse compression, more than 22 mJ at 400 nm was obtained with conversion efficiency around 43% in LBO. In this case, using a classical grating compressor, temporal compression was achieved resulting in 45 fs FWHM pulse duration at 400 nm (i.e., of the same order as the 800 nm wave). The high-energy UV beam is believed to be of immediate interest for many spectroscopic experiments. It was indeed successfully used in the study of x-ray emission from interaction with rare gas clusters as a function of pulse duration. During the one-month experiment, it proved to be a very rugged and reliable tool. We thank D. Lupinski (Cristal Laser) for providing the high-aperture, high-quality LBO crystal as well as for many helpful discussions. The research 2654
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described here has been supported by “Triangle de la physique,” contract SOLAMU 2007-020T, and by specific funds (“crédits d’intervention 2010”) from the CNRS. Two of us benefited from either a Ph.D. grant from the CNRS (C. Ramond) or a postdoctoral fellowship from the EMMI, contract no. HA216-UPR. References 1. A. J. W. Brown, M. S. Bowers, K. W. Kangtas, and C. H. Fisher, “High-energy, high-efficiency second-harmonic generation of 1064-nm radiation in KTP,” Opt. Lett. 17, 109–111 (1992). 2. W. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, and R. S. Craxton, “Demonstration of high efficiency third harmonic conversion of high power Nd-glass laser radiation,” Opt. Commun. 34, 469–473 (1980). 3. G. Mennerat, J. Rault, O. Bonville, P. Canal, O. Hartmann, E. Mazataud, L. Marmande, L. Patissou, J. Charrier, and C. Lepage, “Very high efficiency high-energy frequency doubling in the Alisé facility,” in Advanced Solid-State Photonics, OSA Technical Digest (Optical Society of America, 2010), paper ATuA24G. 4. O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989). 5. G. Szabo and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990). 6. T. R. Zhang, H. R. Choo, and M. C. Downer, “Phase and group-velocity matching for second harmonic generation of femtosecond pulses,” Appl. Opt. 29, 3927–3933 (1990). 7. B. Richman, S. Bisson, R. Trebino, E. Sidick, and A. Jacobson, “Efficient broadband second harmonic generation by dispersive achromatic nonlinear conversion using only prisms,” Opt. Lett. 23, 497–499 (1998). 8. A. V. Smith, “Group-velocity-matched three-wave mixing in birefringent crystals,” Opt. Lett. 26, 719–721 (2001). 9. N. V. Didenko, A. V. Konyashchenko, L. L. Losev, V. S. Pazyuk, and S. Y. Tenyakov, “Femtosecond pulse compression based on second harmonic generation from a frequency chirped pulse,” Opt. Commun. 282, 997–999 (2009). 10. T. Zhang and M. Yonemura, “Pulse compression with a noncollinear type I frequency doubling crystal,” Jpn. J. Appl. Phys. 37, 542–543 (1998). 11. M. Aoyama, T. Zhang, M. Tsukakoshi, and K. Yamakawa, “Noncollinear second-harmonic generation with compensation of phase mismatch by controlling frequency chirp and tilted pulse fronts of femtosecond laser pulses,” Jpn. J. Appl. Phys. 39, 3394–3399 (2000). 12. C. Radzewicz, Y. B. Band, G. W. Pearson, and J. S. Krasinski, “Short pulse nonlinear frequency conversion without group-velocity-mismatch broadening,” Opt. Commun. 117, 295–302 (1995). 13. S. Ashihara, T. Shimura, and K. Kuroda, “Group-velocity matched second-harmonic generation in tilted quasi-phasematched gratings,” J. Opt. Soc. Am. B 20, 853–856 (2003). 14. A. Dubietis, G. Valiulis, R. Danielius, and A. Piskarskas, “Nonlinear pulse compression by optical frequency mixing in crystals with second-order nonlinearity,” Pure Appl. Opt. 7, 271–279 (1998). 15. A. Andreoni, M. Bondani, and M. A. C. Potenza, “Ultrabroadband and chirp-free frequency doubling in β-barium borate,” Opt. Commun. 154, 376–382 (1998). 16. H. Liu, W. Zhao, Y. Yang, H. Wang, Y. Wang, and G. Chen, “Matching of both group velocity and pulse-front for ultrabroadband three-wave-mixing with non-collinear angularly dispersed geometry,” Appl. Phys. B 82, 585–594 (2006). 17. S. Y. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron 18, 7–13 (2012). 18. V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, “Method for compensating the phase-matching
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