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Parametric laser pulse shortening Yu-Chung Chiu, Yen-Chieh Huang,* and Chia-Hsiang Chen HOPE Laboratory, Institute of Photonics Technologies, Department of Electrical Engineering, National Tsinghua University, Hsinchu 30013, Taiwan *Corresponding author: [email protected] Received May 9, 2014; revised June 24, 2014; accepted July 7, 2014; posted July 16, 2014 (Doc. ID 211667); published August 8, 2014 We report simultaneous laser pulse shortening and wavelength conversion based on spectral-temporal correlation in high-gain optical parametric generation (OPG). By spectrally filtering the off-peak signal energy, we shortened a 560 ps pump pulse at 1064 nm to an 80 ps signal pulse at 1.5 μm from a 45 mm long PPLN optical parametric generator with 60 μJ pump energy from a passively Q-switched Nd:YAG laser. Using the same technique, we further demonstrated a 3.6 time shortened laser pulse at 1072 nm from noncollinearly phase matched OPG in a 44 mm long lithium niobate crystal with 3 mJ amplified pump energy from the same Nd:YAG laser. © 2014 Optical Society of America OCIS codes: (190.4410) Nonlinear optics, parametric processes; (190.4975) Parametric processes; (140.3540) Lasers, Q-switched. http://dx.doi.org/10.1364/OL.39.004792
Pulse lasers offer high peak power and time resolution for numerous applications. Mode-locked and Q-switched lasers are the most popular pulsed lasers to date. A modelocked laser often generates a laser pulse in the fs-ps regime, whereas a Q-switched laser can generate a laser pulse in the ns regime. The former is apparently more delicate and costly than the latter. The energy in a Qswitched laser can be transferred to that of a modelocked laser pulse through some amplification process. For example, a GW fs laser is often realized by pumping Q-switched laser energy to a regenerative or multipass amplifier seeded by a mode-locked laser oscillator. During the development of a solid state laser source, there has been a sub-ns pulse gap between the Q-switched and the mode-locked lasers [1]. The demand for lasers having a pulse width in the sub-ns pulse gap has increased considerably in industrial and scientific applications. Recently Lehneis et al. [2] demonstrated a 3.7 time pulse shortening for a 118 ps passively Q-switched laser with 11% energy efficiency by spectrally filtering the selfphase modulated laser pulse in an optical fiber. This group further demonstrated sub-ps laser pulse generation by first performing chirped pulse compression of a passively Q-switched laser in a grating compressor and spectrally filtering the self-phase-modulated laser pulse from an optical fiber. However self-phase modulation introduces an asymmetric frequency shift around the temporal peak of an input laser pulse, resulting in satellite pulses in the spectrally filtered output. Here we suggest an optical parametric scheme, which takes advantage of the exponential gain and phase modulation in optical parametric generation (OPG) to produce an output laser that is significantly shorter than the pump pulse and contains no satellite pulses. As the following two experiments will show, this technique also offers additional flexibility for generating a pulse-shortened laser output near or far away from the pump laser wavelength. Laser pulse width variation in an optical parametric process with strong material dispersion and pulse walkoff has been studied in the past [3–6]. The work in this Letter focuses on laser pulse widths of the order of 100 ps, at which group-velocity mismatch and groupvelocity dispersion are not important in most nonlinear 0146-9592/14/164792-04$15.00/0
optical materials. In such a quasi-static or long-pulse regime, without pump depletion and idler seeding, the signal-gain expression in a pulsed OPG process can be obtained by inserting a time-varying pump field into the continuous-wave gain expression, given by [7] Gs λs ; t
I s t sinh2 gλs ; tL − 1 Γ2 λs ; tL2 ; I s0 gλs ; tL2
(1)
where Is0 is the seed signal intensity, λs is the signal wavelength, t is the time variable for a pulsed pump, L is the nonlinear crystal length, and gλs ; t is the parametric gain coefficient, given by gλs ; t
q Γ2 λs ; t − Δk∕22 ;
(2)
where Γλs ; t is the phase matched parametric gain coefficient and Δk is the wave number mismatch of the mixing waves. Assume the temporal profile of the pump field is Gaussian, expressed by jE p tj E p0 × exp−2 ln 2 × t2 ∕τ2p , where E p0 is the peak field amplitude and τp is the full width at half-maximum (FWHM) of the pump intensity. The specific expression of Γλs ; t as a function of time is therefore s 4π 2 d2eff 2 2 2 2 Γλs ; t E e−2 ln 2×t ∕τp Γ0 e−2 ln 2×t ∕τp ; (3) ni ns λs λi p0 where Γ0 is the peak gain coefficient, deff is the effective nonlinear coefficient, λi 1∕λp − 1∕λs −1 is the idler wavelength with λp being the pump wavelength, and ns and ni are the refractive indices of the signal and idler waves, respectively. In the high gain regime, Γ ≫ Δk, Eq. (1) reduces to Gs λs ; t ∼
I s t e2Γλs ;tL 1 2 2 exp2Γ0 L × e−2 ln 2×t ∕τp ; ∼ 4 I s0 4 (4)
which yields a signal pulse width of © 2014 Optical Society of America
August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS
τp τs p : Γ0 L
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(5)
The assumption to derive Eq. (5) from Eq. (4) is Γ0 L ≫ ln 2∕2 ∼ 0.35, which is certainly valid for most OPG having Γ0 L > 10. Equation (5) clearly shows a laser pulse shortening from the exponential gain of an OPG process. The signal gain bandwidth is determined from the wave-number mismatch term Δk kp − ks − ki 2πnp ∕λp − ns ∕λs − ny ∕λi , where np is the refractive index at the pump wavelength λp . Given a pump wavelength λp and the relationship λi 1∕λp − 1∕λs −1 , the wave-number mismatch is a function of the signal wavelength, denoted by Δkλs . For example, in the high-gain regime, the signal gain bandwidth is given by [7] ΔkB λs
p 4Γλs ; t ln 2∕L;
(6)
which, according to (3), is proportional to the square root of the pump field. Equation (6) indicates a spectraltemporal correlation in the output signal pulse produced by a pulsed optical parametric generator. First of all, the larger the pump intensity I P , the broader the signal bandwidth. The phase mismatched component needs a larger pump intensity to build up. The temporal peak of a pump pulse is therefore correlated to the off-peak spectral energy of the OPG output spectrum. Figure 1(a) shows the mesh plot of the signal intensity profile as a function of the normalized time t∕τp and phase mismatch Δkλs L with Γ0 L 13.4 for a peak parametric gain of 1011 . The 1011 parametric gain is sufficient to amplify a vacuum noise photon at 1.5 μm to 10 nJ energy. It is seen from Fig. 1(b) that the sliced signal pulse width varies with Δkλs L or signal wavelength λs . In particular, the pulse width decreases as the phase mismatch jΔkλs Lj increases. Even at the spectral center Δkλs L 0, the signal pulse width is already significantly shorter than the pump pulse width or τs ∕τp < 1 because of the exponential gain in an OPG process. Therefore, the idea in this Letter is to spectrally filter the off-peak spectrum of an OPG output signal to generate a laser pulse that is significantly shorter than the pump pulse. Two experiments are presented below, one with ∼50% wavelength shifted signal and the other with 6% wavelength shifted signal from the pump one. In our experiment, the pump laser is a passively Qswitched Nd:YAG laser at 1064 nm with a pulse width of 560 ps and a maximum pulse energy of 60 μJ. Figure 2 depicts the setup of our first experiment, wherein the pump laser is focused into a 45 mm long, 1 mm thick periodically poled lithium niobate (PPLN) crystal to perform type-0 phase matched OPG. To satisfy the phase matching condition in the crystal, we first aligned the pump laser polarization along the crystallographic z direction of the PPLN crystal by using a half-wave plate (HWP). The PPLN crystal has a domain period of 29.6 μm, permitting a quasi-phase match of the OPG process for a signal wavelength near 1.550 μm at 125°C. The dichroic mirror after the PPLN, which is highly reflecting (HR) at 1064 nm and anti-reflecting (AR) at the signal wavelength, dumps the pump laser to a beam dump (BD)
Fig. 1. (a) Theoretically calculated OPG gain versus time and signal wavelength and (b) pulse width variation versus signal wavelength. The time axis is normalized to the pump pulse width τp and the signal wavelength λs is embedded in the phase mismatch ΔkL for a given pump wavelength λp . The signal pulse width decreases as the signal wavelength deviates from the phase matched one.
and transmits the OPG signal to a 0.5 m grating monochromator. The monochromator serves as a spectral filter for the OPG output signal. We employed a fast photodiode (PD) with a 35 ps rise time to measure the
Fig. 2. Schematic of the first experiment to demonstrate parametric pulse shortening in a collinear phase matched OPG. A passively Q-switched Nd:YAG laser is focused into a PPLN optical parametric generator, from which the output signal pulse near 1.5 μm is spectrally filtered in a grating monochromator and measured by a fast photodiode (PD). The dichroic mirror after the PPLN crystal is highly reflective at the pump wavelength 1064 nm and anti-reflecting at the signal wavelength, dumping the pump pulse into the beam dump (BD).
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spectrally filtered signal pulse width in a 25 GHz-bandwidth real-time oscilloscope. The measured signal intensity profile is a convolution of the incident signal pulse intensity and the measurement system’s impulse response. To calibrate the system, we first sent a known 50 fs mode-locked Ti:sapphire laser pulse onto the PD and measured a broadened 65 ps pulse width in the oscilloscope. This calibration allows us to deconvolve the actual incident signal pulse width τa from the measured pulse width τm according to τa
q τ2m − 65 ps2 :
(7)
Figure 3(a) shows the measured OPG signal spectrum (open circle) from the PPLN at 125°C, indicating a 5.8 nm bandwidth centered at 1.551 μm. The continuous line (blue color) is a theoretical fitting curve from Eq. (1) with Γ0 L 13.1. The PPLN crystal is slightly absorptive at the idler wavelength of ∼3 μm because of some O-H bonds (from residual water molecules) in the crystal [8]. Therefore the startup vacuum noise is more likely to be a signal photon at 1.5 μm. This is consistent with the assumption of no initial idler photon made for Eq. (1). Figure 3(b) shows the measured signal pulse width τm (open circle) versus the signal wavelength. The error bar is the variation range of a measured pulse width over five measurements. On the same plot, the solid dots are the actual
160
calculated measured deduced
(b)
time (ps)
140
signal pulse widths τa deduced from Eq. (7); the continuous line (red color) is a theoretical curve calculated from Eq. (1) with Γ0 L 13.1. The deconvolved signal pulse width τa at the spectral center is about 124 ps, a factor of 4.5 reduced from the pump pulse width of 560 ps. As expected, the signal pulse width decreases when measured away from the spectral center. At 1546 nm, the deconvolved signal pulse width is 80 ps, a factor of 7 reduced from the pump pulse width. In Fig. 3(b), the output signal pulse width is slightly longer than that predicted by Eq. (1). The discrepancy is attributable to pump-depletion caused pulse broadening in the OPG process [7]. The monochromator as a spectral filter needs to have a large enough bandwidth to ensure a temporal resolution of the pulse measurement. The linear dispersion of our monochromator is 1.6 nm/mm. During the measurement, the slit opening of the monochromator was 80 μm, which corresponds to a temporal resolution of 9, 19, and 27 ps for Lorentzian, hyperbolic secant, and Gaussian pulses, respectively. This 9–27 ps temporal resolution may account for the slightly longer pulse widths measured in the experiment. To demonstrate parametric pulse shortening without significantly changing the pump wavelength, we further performed noncollinearly phase matched OPG in a 44 mm long magnesium-doped LN crystal, as shown in Fig. 4. Both end faces of the LN crystal were optically polished without any anti-reflection coating. The pump laser at 1064 nm is again polarized along the crystallographic z direction, propagating along the x direction. In this experiment the signal pulse propagates at ∼1.2° with respect to the pump beam direction with a wavelength of about 1070 nm [9], whereas the idler at 150 μm emits at ∼65° from the pump beam direction is quickly absorbed by the crystal. As can be seen from the two bright off-center spots in the downstream phosphor screen in Fig. 4, the signal beam is spatially separated from the centered pump beam at the output of the crystal. The small green dots near the screen center result from angle phase matched second-harmonic generation under a strong pump at 1064 nm. In a noncollinearly phase matched optical parametric mixing process, the parametric gain is reduced because of the angular walkoff of the mixing pulses. The absorption of the idler wave in the gain crystal also suppresses the OPG gain. To achieve a high enough gain, we first
120 100 80 1545
1550 1555 Wavelength (nm)
1560
Fig. 3. (a) Measured OPG signal spectrum (open dot). The theoretical fitting curve (continuous line) is plotted by using Eq. (1) with Γ0 L 13.1. (b) Measured (open dot) and deconvolved (solid dot) signal pulse width versus wavelength. The theoretical curve (continuous line) is also plotted from Eq. (1) with Γ0 L 13.1.
Fig. 4. Experimental setup for noncollinearly phase matched OPG. The pump laser at 1064 nm is first amplified by a flashlamp Nd:YAG amplifier and focused into a lithium niobate crystal. The signal wave at 1070 nm is generated at ∼ 1.2° from the pump beam direction, as shown by the off-center bright dots on a downstream phosphor screen.
August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS
Intensity (a.u.)
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220
1.0
0.016
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0.012
180
0.008
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0.004
140
0.000
120
Pulsewidth (ps)
0.020
spectrum measured deduced
Intensity (a.u.)
0.024
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Gaussian fitting experimental data
0.8 0.6 0.4 0.2 0.0
1066 1068 1070 1072 1074 Wavelength (nm)
Fig. 5. Measured signal spectrum (continuous line) overlaid with data points of measured signal pulse widths (open dot, with reference to the right vertical axis). The actual signal pulse widths, deduced from Eq. (7), are shown with solid dots. Again, the signal pulse width decreases when the signal wavelength is away from the spectral center.
increased the pulse energy of the passively Q-switched Nd:YAG laser from 60 μJ to about 3.15 mJ in a flash-lamp pumped Nd:YAG laser amplifier. We achieved a 15% energy conversion efficiency for the OPG when focusing the pump laser to an intensity of 700 MW∕cm2 at the center of the LN crystal. The separated signal pulse at the output is again directed into the 0.5 m grating monochromator for spectral filtering. During the measurement, the slit opening of the monochromator was 60 μm, corresponding to a spectral resolution of 0.1 nm for the measurement. Figure 5 shows the measured signal spectrum overlaid with data points of measured pulse widths τm (open dots). Each error bar indicates the pulse width variation range of the data point measured over five times. In the same plot, the deconvolved pulse widths τs are shown with solid dots. It is seen from Fig. 5 that the spectrum is peaked at 1069.5 nm, about 5% different from the pump wavelength. Similar to the collinear phase matched OPG, the measured signal pulse width becomes shorter as the signal wavelength moves away from the spectral peak. Figure 6 shows a measured temporal profile of the signal pulse at 1072 nm, indicating a smooth pulse envelope with a FWHM width of 169 ps. By using Eq. (7), the actual pulse width deconvolved from the measured one is 156 ps, a factor of 3.6 reduced from the pump pulse width. In conclusion, we reported the theory and experiment of a laser pulse shortening technique utilizing the exponential gain and spectral-temporal correlation in an OPG process. The exponential gain in an OPG process quickly converts a pump pulse into a much shorter signal pulse at a different wavelength. Furthermore, the off-peak spectral energy of the signal pulse is primarily contributed from a small temporal window near the peak of the pump pulse. By spectrally filtering the energy off the spectral peak of the output signal pulse, we demonstrated 7 and 3.6 time laser-pulse-width reduction from collinear and noncollinear phase matched OPG in PPLN and LN crystals, respectively, pumped by a passively Q-switched
-400
-200
0
200
400
Time (ps) Fig. 6. Shortest measured signal pulse profile at 1072 nm from the noncollinearly phase matched OPG, indicating a smooth pulse envelope with a FWHM of 160 ps. The actual signal pulse width is 146 ps, deduced from Eq. (7).
Nd:YAG laser with a 560-s pulse width. The shortened laser pulse has a smooth temporal envelope and contains no satellite pulses. Power efficiency is important in most applications. The exponential-gain shortened laser pulse contains the whole output energy, generated from a typical OPG with conversion efficiency of 10–20% using a PPLN crystal [7]. On the other hand, the power efficiency of the spectrally filtered short output pulse is on the order of ∼1% because of removal of long-pulse energy. If necessary, a downstream laser amplifier or parametric amplifier can be built to increase the laser pulse energy. For example, the spectrally filtered signal pulse at 1.55 μm from our first OPG experiment can be amplified in an Erbium-doped fiber amplifier or a similar Nd:YAG laser pumped PPLN optical parametric amplifier. If efficiency is a concern, the undepleted pump energy from the first stage OPG can be recycled to pump a downstream optical parametric amplifier for the spectrally filtered short pulse. In all cases, pulse broadening from amplifier saturation should be avoided. This work is supported by the Ministry of Science and Technology under Grant MOST 103-2221-E-007-062-MY2. References 1. T. Taira, Opt. Mater. Express 1, 1040 (2011). 2. R. Lehneis, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, Opt. Lett. 37, 4401 (2012). 3. F. Seifert, V. Petrov, and F. Noack, Opt. Lett. 19, 837 (1994). 4. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, E. W. Van Stryland, and H. Vanherzeele, Opt. Lett. 17, 28 (1992). 5. A. Fendt, W. kranitzky, A. Laubereau, and W. Kaiser, Opt. Commun. 28, 142 (1979). 6. W. Kranitzky, K. Ding, A. Seilmeier, and W. Kaiser, Opt. Commun. 34, 483 (1980). 7. A. C. Chiang, T. D. Wang, Y. Y. Lin, C. W. Liu, Y. H. Chen, B. C. Wong, Y. C. Huang, J. T. Shy, Y. P. Lan, Y. F. Chen, and P. H. Tsao, IEEE J. Quantum Electron. 40, 791 (2004). 8. Y. F. Kong, W. L. Zhang, X. J. Chen, J. J. Xu, and G. Y. Zhang, J. Phys. Condens. Matter 11, 2139 (1999). 9. A. C. Chiang, T. D. Wang, Y. Y. Lin, S. T. Lin, H. H. Lee, Y. C. Huang, and Y. H. Chen, Opt. Lett. 30, 3392 (2005).
OPTICS LETTERS / Vol. 39, No. 16 / August 15, 2014
Parametric laser pulse shortening Yu-Chung Chiu, Yen-Chieh Huang,* and Chia-Hsiang Chen HOPE Laboratory, Institute of Photonics Technologies, Department of Electrical Engineering, National Tsinghua University, Hsinchu 30013, Taiwan *Corresponding author: [email protected] Received May 9, 2014; revised June 24, 2014; accepted July 7, 2014; posted July 16, 2014 (Doc. ID 211667); published August 8, 2014 We report simultaneous laser pulse shortening and wavelength conversion based on spectral-temporal correlation in high-gain optical parametric generation (OPG). By spectrally filtering the off-peak signal energy, we shortened a 560 ps pump pulse at 1064 nm to an 80 ps signal pulse at 1.5 μm from a 45 mm long PPLN optical parametric generator with 60 μJ pump energy from a passively Q-switched Nd:YAG laser. Using the same technique, we further demonstrated a 3.6 time shortened laser pulse at 1072 nm from noncollinearly phase matched OPG in a 44 mm long lithium niobate crystal with 3 mJ amplified pump energy from the same Nd:YAG laser. © 2014 Optical Society of America OCIS codes: (190.4410) Nonlinear optics, parametric processes; (190.4975) Parametric processes; (140.3540) Lasers, Q-switched. http://dx.doi.org/10.1364/OL.39.004792
Pulse lasers offer high peak power and time resolution for numerous applications. Mode-locked and Q-switched lasers are the most popular pulsed lasers to date. A modelocked laser often generates a laser pulse in the fs-ps regime, whereas a Q-switched laser can generate a laser pulse in the ns regime. The former is apparently more delicate and costly than the latter. The energy in a Qswitched laser can be transferred to that of a modelocked laser pulse through some amplification process. For example, a GW fs laser is often realized by pumping Q-switched laser energy to a regenerative or multipass amplifier seeded by a mode-locked laser oscillator. During the development of a solid state laser source, there has been a sub-ns pulse gap between the Q-switched and the mode-locked lasers [1]. The demand for lasers having a pulse width in the sub-ns pulse gap has increased considerably in industrial and scientific applications. Recently Lehneis et al. [2] demonstrated a 3.7 time pulse shortening for a 118 ps passively Q-switched laser with 11% energy efficiency by spectrally filtering the selfphase modulated laser pulse in an optical fiber. This group further demonstrated sub-ps laser pulse generation by first performing chirped pulse compression of a passively Q-switched laser in a grating compressor and spectrally filtering the self-phase-modulated laser pulse from an optical fiber. However self-phase modulation introduces an asymmetric frequency shift around the temporal peak of an input laser pulse, resulting in satellite pulses in the spectrally filtered output. Here we suggest an optical parametric scheme, which takes advantage of the exponential gain and phase modulation in optical parametric generation (OPG) to produce an output laser that is significantly shorter than the pump pulse and contains no satellite pulses. As the following two experiments will show, this technique also offers additional flexibility for generating a pulse-shortened laser output near or far away from the pump laser wavelength. Laser pulse width variation in an optical parametric process with strong material dispersion and pulse walkoff has been studied in the past [3–6]. The work in this Letter focuses on laser pulse widths of the order of 100 ps, at which group-velocity mismatch and groupvelocity dispersion are not important in most nonlinear 0146-9592/14/164792-04$15.00/0
optical materials. In such a quasi-static or long-pulse regime, without pump depletion and idler seeding, the signal-gain expression in a pulsed OPG process can be obtained by inserting a time-varying pump field into the continuous-wave gain expression, given by [7] Gs λs ; t
I s t sinh2 gλs ; tL − 1 Γ2 λs ; tL2 ; I s0 gλs ; tL2
(1)
where Is0 is the seed signal intensity, λs is the signal wavelength, t is the time variable for a pulsed pump, L is the nonlinear crystal length, and gλs ; t is the parametric gain coefficient, given by gλs ; t
q Γ2 λs ; t − Δk∕22 ;
(2)
where Γλs ; t is the phase matched parametric gain coefficient and Δk is the wave number mismatch of the mixing waves. Assume the temporal profile of the pump field is Gaussian, expressed by jE p tj E p0 × exp−2 ln 2 × t2 ∕τ2p , where E p0 is the peak field amplitude and τp is the full width at half-maximum (FWHM) of the pump intensity. The specific expression of Γλs ; t as a function of time is therefore s 4π 2 d2eff 2 2 2 2 Γλs ; t E e−2 ln 2×t ∕τp Γ0 e−2 ln 2×t ∕τp ; (3) ni ns λs λi p0 where Γ0 is the peak gain coefficient, deff is the effective nonlinear coefficient, λi 1∕λp − 1∕λs −1 is the idler wavelength with λp being the pump wavelength, and ns and ni are the refractive indices of the signal and idler waves, respectively. In the high gain regime, Γ ≫ Δk, Eq. (1) reduces to Gs λs ; t ∼
I s t e2Γλs ;tL 1 2 2 exp2Γ0 L × e−2 ln 2×t ∕τp ; ∼ 4 I s0 4 (4)
which yields a signal pulse width of © 2014 Optical Society of America
August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS
τp τs p : Γ0 L
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(5)
The assumption to derive Eq. (5) from Eq. (4) is Γ0 L ≫ ln 2∕2 ∼ 0.35, which is certainly valid for most OPG having Γ0 L > 10. Equation (5) clearly shows a laser pulse shortening from the exponential gain of an OPG process. The signal gain bandwidth is determined from the wave-number mismatch term Δk kp − ks − ki 2πnp ∕λp − ns ∕λs − ny ∕λi , where np is the refractive index at the pump wavelength λp . Given a pump wavelength λp and the relationship λi 1∕λp − 1∕λs −1 , the wave-number mismatch is a function of the signal wavelength, denoted by Δkλs . For example, in the high-gain regime, the signal gain bandwidth is given by [7] ΔkB λs
p 4Γλs ; t ln 2∕L;
(6)
which, according to (3), is proportional to the square root of the pump field. Equation (6) indicates a spectraltemporal correlation in the output signal pulse produced by a pulsed optical parametric generator. First of all, the larger the pump intensity I P , the broader the signal bandwidth. The phase mismatched component needs a larger pump intensity to build up. The temporal peak of a pump pulse is therefore correlated to the off-peak spectral energy of the OPG output spectrum. Figure 1(a) shows the mesh plot of the signal intensity profile as a function of the normalized time t∕τp and phase mismatch Δkλs L with Γ0 L 13.4 for a peak parametric gain of 1011 . The 1011 parametric gain is sufficient to amplify a vacuum noise photon at 1.5 μm to 10 nJ energy. It is seen from Fig. 1(b) that the sliced signal pulse width varies with Δkλs L or signal wavelength λs . In particular, the pulse width decreases as the phase mismatch jΔkλs Lj increases. Even at the spectral center Δkλs L 0, the signal pulse width is already significantly shorter than the pump pulse width or τs ∕τp < 1 because of the exponential gain in an OPG process. Therefore, the idea in this Letter is to spectrally filter the off-peak spectrum of an OPG output signal to generate a laser pulse that is significantly shorter than the pump pulse. Two experiments are presented below, one with ∼50% wavelength shifted signal and the other with 6% wavelength shifted signal from the pump one. In our experiment, the pump laser is a passively Qswitched Nd:YAG laser at 1064 nm with a pulse width of 560 ps and a maximum pulse energy of 60 μJ. Figure 2 depicts the setup of our first experiment, wherein the pump laser is focused into a 45 mm long, 1 mm thick periodically poled lithium niobate (PPLN) crystal to perform type-0 phase matched OPG. To satisfy the phase matching condition in the crystal, we first aligned the pump laser polarization along the crystallographic z direction of the PPLN crystal by using a half-wave plate (HWP). The PPLN crystal has a domain period of 29.6 μm, permitting a quasi-phase match of the OPG process for a signal wavelength near 1.550 μm at 125°C. The dichroic mirror after the PPLN, which is highly reflecting (HR) at 1064 nm and anti-reflecting (AR) at the signal wavelength, dumps the pump laser to a beam dump (BD)
Fig. 1. (a) Theoretically calculated OPG gain versus time and signal wavelength and (b) pulse width variation versus signal wavelength. The time axis is normalized to the pump pulse width τp and the signal wavelength λs is embedded in the phase mismatch ΔkL for a given pump wavelength λp . The signal pulse width decreases as the signal wavelength deviates from the phase matched one.
and transmits the OPG signal to a 0.5 m grating monochromator. The monochromator serves as a spectral filter for the OPG output signal. We employed a fast photodiode (PD) with a 35 ps rise time to measure the
Fig. 2. Schematic of the first experiment to demonstrate parametric pulse shortening in a collinear phase matched OPG. A passively Q-switched Nd:YAG laser is focused into a PPLN optical parametric generator, from which the output signal pulse near 1.5 μm is spectrally filtered in a grating monochromator and measured by a fast photodiode (PD). The dichroic mirror after the PPLN crystal is highly reflective at the pump wavelength 1064 nm and anti-reflecting at the signal wavelength, dumping the pump pulse into the beam dump (BD).
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spectrally filtered signal pulse width in a 25 GHz-bandwidth real-time oscilloscope. The measured signal intensity profile is a convolution of the incident signal pulse intensity and the measurement system’s impulse response. To calibrate the system, we first sent a known 50 fs mode-locked Ti:sapphire laser pulse onto the PD and measured a broadened 65 ps pulse width in the oscilloscope. This calibration allows us to deconvolve the actual incident signal pulse width τa from the measured pulse width τm according to τa
q τ2m − 65 ps2 :
(7)
Figure 3(a) shows the measured OPG signal spectrum (open circle) from the PPLN at 125°C, indicating a 5.8 nm bandwidth centered at 1.551 μm. The continuous line (blue color) is a theoretical fitting curve from Eq. (1) with Γ0 L 13.1. The PPLN crystal is slightly absorptive at the idler wavelength of ∼3 μm because of some O-H bonds (from residual water molecules) in the crystal [8]. Therefore the startup vacuum noise is more likely to be a signal photon at 1.5 μm. This is consistent with the assumption of no initial idler photon made for Eq. (1). Figure 3(b) shows the measured signal pulse width τm (open circle) versus the signal wavelength. The error bar is the variation range of a measured pulse width over five measurements. On the same plot, the solid dots are the actual
160
calculated measured deduced
(b)
time (ps)
140
signal pulse widths τa deduced from Eq. (7); the continuous line (red color) is a theoretical curve calculated from Eq. (1) with Γ0 L 13.1. The deconvolved signal pulse width τa at the spectral center is about 124 ps, a factor of 4.5 reduced from the pump pulse width of 560 ps. As expected, the signal pulse width decreases when measured away from the spectral center. At 1546 nm, the deconvolved signal pulse width is 80 ps, a factor of 7 reduced from the pump pulse width. In Fig. 3(b), the output signal pulse width is slightly longer than that predicted by Eq. (1). The discrepancy is attributable to pump-depletion caused pulse broadening in the OPG process [7]. The monochromator as a spectral filter needs to have a large enough bandwidth to ensure a temporal resolution of the pulse measurement. The linear dispersion of our monochromator is 1.6 nm/mm. During the measurement, the slit opening of the monochromator was 80 μm, which corresponds to a temporal resolution of 9, 19, and 27 ps for Lorentzian, hyperbolic secant, and Gaussian pulses, respectively. This 9–27 ps temporal resolution may account for the slightly longer pulse widths measured in the experiment. To demonstrate parametric pulse shortening without significantly changing the pump wavelength, we further performed noncollinearly phase matched OPG in a 44 mm long magnesium-doped LN crystal, as shown in Fig. 4. Both end faces of the LN crystal were optically polished without any anti-reflection coating. The pump laser at 1064 nm is again polarized along the crystallographic z direction, propagating along the x direction. In this experiment the signal pulse propagates at ∼1.2° with respect to the pump beam direction with a wavelength of about 1070 nm [9], whereas the idler at 150 μm emits at ∼65° from the pump beam direction is quickly absorbed by the crystal. As can be seen from the two bright off-center spots in the downstream phosphor screen in Fig. 4, the signal beam is spatially separated from the centered pump beam at the output of the crystal. The small green dots near the screen center result from angle phase matched second-harmonic generation under a strong pump at 1064 nm. In a noncollinearly phase matched optical parametric mixing process, the parametric gain is reduced because of the angular walkoff of the mixing pulses. The absorption of the idler wave in the gain crystal also suppresses the OPG gain. To achieve a high enough gain, we first
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Fig. 3. (a) Measured OPG signal spectrum (open dot). The theoretical fitting curve (continuous line) is plotted by using Eq. (1) with Γ0 L 13.1. (b) Measured (open dot) and deconvolved (solid dot) signal pulse width versus wavelength. The theoretical curve (continuous line) is also plotted from Eq. (1) with Γ0 L 13.1.
Fig. 4. Experimental setup for noncollinearly phase matched OPG. The pump laser at 1064 nm is first amplified by a flashlamp Nd:YAG amplifier and focused into a lithium niobate crystal. The signal wave at 1070 nm is generated at ∼ 1.2° from the pump beam direction, as shown by the off-center bright dots on a downstream phosphor screen.
August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS
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Fig. 5. Measured signal spectrum (continuous line) overlaid with data points of measured signal pulse widths (open dot, with reference to the right vertical axis). The actual signal pulse widths, deduced from Eq. (7), are shown with solid dots. Again, the signal pulse width decreases when the signal wavelength is away from the spectral center.
increased the pulse energy of the passively Q-switched Nd:YAG laser from 60 μJ to about 3.15 mJ in a flash-lamp pumped Nd:YAG laser amplifier. We achieved a 15% energy conversion efficiency for the OPG when focusing the pump laser to an intensity of 700 MW∕cm2 at the center of the LN crystal. The separated signal pulse at the output is again directed into the 0.5 m grating monochromator for spectral filtering. During the measurement, the slit opening of the monochromator was 60 μm, corresponding to a spectral resolution of 0.1 nm for the measurement. Figure 5 shows the measured signal spectrum overlaid with data points of measured pulse widths τm (open dots). Each error bar indicates the pulse width variation range of the data point measured over five times. In the same plot, the deconvolved pulse widths τs are shown with solid dots. It is seen from Fig. 5 that the spectrum is peaked at 1069.5 nm, about 5% different from the pump wavelength. Similar to the collinear phase matched OPG, the measured signal pulse width becomes shorter as the signal wavelength moves away from the spectral peak. Figure 6 shows a measured temporal profile of the signal pulse at 1072 nm, indicating a smooth pulse envelope with a FWHM width of 169 ps. By using Eq. (7), the actual pulse width deconvolved from the measured one is 156 ps, a factor of 3.6 reduced from the pump pulse width. In conclusion, we reported the theory and experiment of a laser pulse shortening technique utilizing the exponential gain and spectral-temporal correlation in an OPG process. The exponential gain in an OPG process quickly converts a pump pulse into a much shorter signal pulse at a different wavelength. Furthermore, the off-peak spectral energy of the signal pulse is primarily contributed from a small temporal window near the peak of the pump pulse. By spectrally filtering the energy off the spectral peak of the output signal pulse, we demonstrated 7 and 3.6 time laser-pulse-width reduction from collinear and noncollinear phase matched OPG in PPLN and LN crystals, respectively, pumped by a passively Q-switched
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Time (ps) Fig. 6. Shortest measured signal pulse profile at 1072 nm from the noncollinearly phase matched OPG, indicating a smooth pulse envelope with a FWHM of 160 ps. The actual signal pulse width is 146 ps, deduced from Eq. (7).
Nd:YAG laser with a 560-s pulse width. The shortened laser pulse has a smooth temporal envelope and contains no satellite pulses. Power efficiency is important in most applications. The exponential-gain shortened laser pulse contains the whole output energy, generated from a typical OPG with conversion efficiency of 10–20% using a PPLN crystal [7]. On the other hand, the power efficiency of the spectrally filtered short output pulse is on the order of ∼1% because of removal of long-pulse energy. If necessary, a downstream laser amplifier or parametric amplifier can be built to increase the laser pulse energy. For example, the spectrally filtered signal pulse at 1.55 μm from our first OPG experiment can be amplified in an Erbium-doped fiber amplifier or a similar Nd:YAG laser pumped PPLN optical parametric amplifier. If efficiency is a concern, the undepleted pump energy from the first stage OPG can be recycled to pump a downstream optical parametric amplifier for the spectrally filtered short pulse. In all cases, pulse broadening from amplifier saturation should be avoided. This work is supported by the Ministry of Science and Technology under Grant MOST 103-2221-E-007-062-MY2. References 1. T. Taira, Opt. Mater. Express 1, 1040 (2011). 2. R. Lehneis, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, Opt. Lett. 37, 4401 (2012). 3. F. Seifert, V. Petrov, and F. Noack, Opt. Lett. 19, 837 (1994). 4. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, E. W. Van Stryland, and H. Vanherzeele, Opt. Lett. 17, 28 (1992). 5. A. Fendt, W. kranitzky, A. Laubereau, and W. Kaiser, Opt. Commun. 28, 142 (1979). 6. W. Kranitzky, K. Ding, A. Seilmeier, and W. Kaiser, Opt. Commun. 34, 483 (1980). 7. A. C. Chiang, T. D. Wang, Y. Y. Lin, C. W. Liu, Y. H. Chen, B. C. Wong, Y. C. Huang, J. T. Shy, Y. P. Lan, Y. F. Chen, and P. H. Tsao, IEEE J. Quantum Electron. 40, 791 (2004). 8. Y. F. Kong, W. L. Zhang, X. J. Chen, J. J. Xu, and G. Y. Zhang, J. Phys. Condens. Matter 11, 2139 (1999). 9. A. C. Chiang, T. D. Wang, Y. Y. Lin, S. T. Lin, H. H. Lee, Y. C. Huang, and Y. H. Chen, Opt. Lett. 30, 3392 (2005).
