Direct measurement of the parameters of a femtosecond pulse train with a THz repetition rate generated by the interference of two phasemodulated femtosecond pulses Anton N. Tsypkin,* Yulia A. Komarova, Sergey E. Putilin, Andrey V. Okishev, and Sergey A. Kozlov Department of Photonics and Optical Informatics, ITMO University Kronverkskiy pr, 49, St. Petersburg 197101, Russia *Corresponding author: [email protected] Received 16 September 2014; revised 26 January 2015; accepted 30 January 2015; posted 2 February 2015 (Doc. ID 223239); published 10 March 2015

A femtosecond pulse train with THz repetition rate generated by the interference of two phasemodulated pulses has been recorded experimentally. Pulse repetition rates and their duration have been measured. It has been shown that at the 50-fs time delay between phase-modulated pulses the repetition rate is 3.1 THz with a pulse width of 200 fs, while at the 120-fs time delay the repetition rate is 7.1 THz with a pulse width of 67 fs. © 2015 Optical Society of America OCIS codes: (320.2250) Femtosecond phenomena; (320.7090) Ultrafast lasers; (320.7120) Ultrafast phenomena; (230.4110) Modulators. http://dx.doi.org/10.1364/AO.54.002113

1. Introduction

Laser radiation in the form of an ultrashort pulse train is important for many applications. Such pulse trains are used for the detection of fast chemical processes [1], to generate tunable narrowband THz radiation [2], in investigations of molecular movement in solid state media [3]. Pulse trains with a THz repetition rate are also used in ultrafast information transfer systems [4]. At the present time existing techniques for the generation of ultrashort optical pulse trains allow a repetition rate in the 100-GHz–1-THz range to be achieved. In [5] the possibility of transforming cw laser radiation into periodic pulse trains in microresonators made of MgF2 crystal is shown. 1559-128X/15/082113-05$15.00/0 © 2015 Optical Society of America

The maximum pulse repetition rate in these systems reaches 200 GHz. Generation of optical pulse trains with a repetition rate up to 100 GHz is possible by spectral filtering with the shaper described in [6]. With the increase of the repetition rate, in this case the pulse contrast is degraded due to the overlapping of the neighboring pulses. Generation of the optical pulse trains with improved contrast is possible with the use of the matrix of birefringent crystals [7–9] and Bragg fiber gratings [10]. In [11] the simple method of high-contrast pulse train generation is described that uses a stretcher and multiple-order phase plate. The pulse repetition rate in these systems depends on stretcher base and phase plate thickness and can be higher than 100 GHz. The simpler method of obtaining pulse trains with tunable periods uses a matrix of Michelson interferometers [12]. Pulse train generation with a tunable period is demonstrated in [13], where the phase of the 10 March 2015 / Vol. 54, No. 8 / APPLIED OPTICS

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chirped pulse at the stretcher output is controlled by a programmed acousto-optic dispersion filter. In this system the pulse repetition rate can reach 1 THz. A further increase of the pulse repetition rate is limited by the design of experimental setups and systems. Such an increase and pulse width reduction allow increasing the precision and record speed [1,2]. The possibility of the generation of pulse trains with a THz repetition rate is theoretically proven in [14,15]. Such a pulse train is generated when two femtosecond light pulses with different spectral content interact in a nonlinear dielectric medium with a normal group velocity dispersion. In [15–17] it is theoretically shown that as a result of the interference of two femtosecond pulses with an ultrabroadband spectrum and linear phase modulation, when time delay between pulses are less than their width, a quasi-discrete spectral continuum with a corresponding femtosecond pulse train with a THz repetition rate is generated. In [17,18] this technique is demonstrated experimentally. It is shown that a femtosecond pulse width in the train and the pulse repetition rate depend on the time delay between incoming pulses. In this paper, the THz repetition rate and pulse width of the femtosecond pulse train generated as a result of the interference of two phase-modulated pulses are measured experimentally. It is shown that at the 50 fs of time delay between the pulses the repetition rate is 3.1 THz and the pulse width is 200 fs, while at the 120 fs time delay the repetition rate is 7.1 THz with a 67-fs pulse width. 2. Experimental Setup

Experimental setup for the interferometric generation of THz pulse trains is shown in Fig. 1. It is based on a femtosecond Ti:sapphire laser that produces 30 fs pulses at the central wavelength of 820 nm, with the spectral width of 54 nm FWHM. The laser system repetition rate is 100 MHz, with an average power 330 mW. An external dispersion compensator is used for laser chirp compensation. We used a Faraday isolator at the output of the Ti:sapphire laser to prevent any feedback from the rest of the experimental setup.

Fig. 1. Block diagram of the experimental setup for the generation of a fs pulse train with a THz repetition rate. 2114

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The laser pulse is divided in two, one of which is going into Michelson interferometer and the second one into the delay line. The translation of the one of the Michelson interferometer mirrors provides the control of the delay between pulses inside interferometer. At the interferometer output the femtosecond pulse train is generated as a result of the spatial interference with the quasi-discrete spectrum that forms as a result of spectral interference. Then pulses are combined by parabolic mirror in a noncollinear BBO second harmonic generator (SHG). The SHG spectrum is measured by an ASP100 spectrometer in the 190–1100 nm wavelength range. Experimental setup X-FROG [19] is used to register the output pulse train. 3. Experimental Results

Figure 2 shows the results of the experimental measurement of the spatial interferometric structure of two pulses for different time delays in the interferometer (1), and separately temporal (2) and spectral (3) structures. In (4) a quasi-discrete spectrum that formed as a result of spectral interference is shown. The discrete spectral structure at the interferometer output is described as follows [20]: jGint ωj2  j1∕2Gωe−iωΔτ j2  1∕2jGωj2 1  cosωΔτ;

(1)

where Δτ is the temporal delay between the pulses in the interferometer. The spatial interferometric structure of the two pulses at different time delays between pulses in the interferometer presents the dependence of the time delay in the base arm of the X-FROG setup on SHG spectrum in noncollinear BBO SHG. Figure 2 (a) shows that the pulse width increases and output pulse has linear chirp that is defined by the inclination of spatial structure. It also can be seen that as a result of spatial interference [Figs. 2(b)–2(d), (2)] the temporal structure consists of the periodic subpulse train, and which repetition rate increases and pulse width decreases with time delay increase. It is measured that at a 50 fs delay the repetition rate is 3.1 THz with a pulse width of 200 fs, while at 120 fs delay the repetition rate is 7.1 THz with a 67 fs subpulse width. The quasi-discrete spectrum is formed as a result of spectral interference [Fig. 2, (4)]. It is important that the number of maxima in a quasidiscrete spectrum of subpulses is equal to their number in the subpulse train. This is due to the fact that each subpulse in the temporal sequence of the interference pattern has a center frequency slightly different from the previous subpulse. That difference corresponds to the central frequency of spectral lines in the quasi-discrete structure. This fact allows the encoding of information using a sequence similar to that presented in [17], by removing spectral lines in the quasi-discrete emission spectrum that correspond to select subpulses using a spectral filter.

Fig. 2. Interference structure for two pulses (1), temporal (2) and spectral (3) structure, quasi-discrete spectrum formed as a result of spectral interference (4). Time delay is: (a) 0 fs, (b) 50 fs, (c) 100 fs, and (d) 120 fs.

There is no relationship between the repetition rate of the laser and the THz repetition rate within each pulse. From each pulse of a Ti:sapphire laser (that has a repetition rate of 100 MHz) we obtain a sequence of subpulses with a THz repetition rate using a Michelson interferometer. The number of subpulses is defined by the quadratic phase modulation of the pulse and the time delay between the mirrors of the Michelson interferometer. 4. Theoretical Study of the Registration of the Interferometrically Generated Subpulse Train

The changes of laser pulse temporal structure in a Michelson interferometer silica beam splitter cube can be easily calculated:

1 Ez; t  2π

Z

∞ −∞

Gωeiωt−kωz dω;

(2)

where Ez; t is the laser pulse electric field strength as a function of coordinate direction) R ∞ z (propagation and time t; Gω  −∞ E0; te−iωt dt is the pulse spectrum at the beam splitter cube entrance surface (z  0); kω  nω ωc is the wavenumber; nω is the dependence of the linear refractive index on light frequency ω; and c is the speed of light in a vacuum. For example, Fig. 3 shows the results of the laser pulse shape and its phase modulation calculations t for the boundary condition E0; t  E0 · e−2τ2 · sinω0 t. The parameters of the laser pulse and splitter materials are: τ  30 fs, λ0  2πc∕ω0  820 nm; 10 March 2015 / Vol. 54, No. 8 / APPLIED OPTICS

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material. Figure 3(b) shows the calculated frequency modulation at the beam splitter output. Figure 3(b) shows that frequency modulation can be described by the linear dependence ωt  ω0 · 1  α · ω0 t − t0 ;

Fig. 3. (a) Optical pulse envelope at the input (dashed line) and output (solid line) of the interferometer beam splitter; (b) frequency modulation of the output pulse.

and n0 ω  N 0  acω2 − bcω−2 , where the dispersion parameters are [21]: N 0  1.45, a  2.74× 10−44 c3 ∕cm, b  3.94 × 1017 c−1 . The beam splitter thickness is 4 cm. Let us analyze the field on the beam axis and neglect diffraction. Figure 3(a) shows, for convenience, the envelope of a femtosecond pulse at the beam splitter input (dashed line) and its output (solid line). The pulse width, as numerical simulations and experiment show, increases from 30 to 400 fs due to dispersion of the beam splitter

(3)

where the frequency modulation coefficient is α  3.5 × 10−4 . The presence of linear frequency modulation allows for the forming of trains of shorter pulses after their interference [15,16]. Figure 4 shows theoretical results of two femtosecond pulse interference. Pulse parameters are calculated using Eq. (1) and correspond well to experimentally obtained pulses shown in Fig. 3. Figure 4 shows that the result of the interference of two 400-fs pulses with time delay between them of 50 fs is the pulse train of two 250-fs subpulses [Fig. 4(b)] with overall width of τtrain  740 fs and repetition rate ν  N∕τtrain  2.7 THz. This repetition rate is defined by the time delay between the pulses and frequency modulation coefficient of a pulse [16]. When the time delay is increased from 50 to 120 fs [Figs. 4(b)–4(d)] the subpulse repetition rate increases from 2.7 to 7.3 THz. The calculated subpulse repetition rate and width correspond very well to the experiment. 5. Conclusion

A fs pulse train with a THz repetition rate that is formed as a result of the two phase-modulated pulse interference has been experimentally characterized. Subpulse repetition rate and width have been measured. Numerical modeling of the interference process of two phase-modulated pulses has been performed, with results corresponding very well to experimental measurements. The number of spectral peaks in a fs pulse quasi-discrete spectrum is equal to the number of subpulses in the formed train. References

Fig. 4. Results of the interference of two fs pulses with frequency modulation with different time delays between them: (a) 0 fs, (b) 50 fs, (c) 100 fs, and (d) 120 fs. 2116

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Direct measurement of the parameters of a femtosecond pulse train with a THz repetition rate generated by the interference of two phase-modulated femtosecond pulses.

A femtosecond pulse train with THz repetition rate generated by the interference of two phase-modulated pulses has been recorded experimentally. Pulse...
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