Femtosecond pulse amplification by a two-photon arranged photorefractive amplifier (TAPA) has been demonstrated. A gain bandwidth of 32 THz has been achieved with an extraction efficiency of 27 %.
© 2007 Optical Society of America
Photorefractive (PR) materials have been commonly used for holographic recoding, phase conjugation mirrors, and wave-mixing. These efficient wave-mixing are supported by a deeply modulated index grating. An index change in the order of 10-2 via Pockels’ effect can be easily achieved by the space-charge field due to linear  and nonlinear  light absorption. The time-response of the index grating is, however, in the order of seconds so that usually the PR materials are used for slow response applications. In contrast, femtosecond holography at an intensity region of 10–300 GW/cm2 has been reported . In this case, the main contribution of index modulation is owing to instantaneous optical Kerr effect rather than the Pockels’ effect.
In this paper, we demonstrate femtosecond pulse amplification with two-photon induced photorefractive effect. This scheme is schematically shown in Fig. 1. The input femtosecond pulses from a mode-lock oscillator are stretched and are amplified similar to the conventional chirped-pulse amplification (CPA) system. After the amplification, the seed pulse and the chirped pulse (the pump pulse) interact in a PR medium. We assume that the PR medium has perfect transmittance at the laser wavelength and has electronic and instantaneous two-photon absorption. The two-photon interaction between the TL seed pulse and the chirped pulse form a chirped index grating . The spatial phase structure of the two-photon arranged grating has the same phase structure of the chirped pulse. The first order diffraction of the pump beam appears in the same direction to the seed pulse. In photorefractive materials that operate by pure diffusion (the phase shift between the light fringe and the PR index grating is π/2), no phase coupling is produced between the seed and the pump beams [6,8]. Thus the seed pulse is amplified in the medium and its phase structure is kept constant regardless of the energy transfer. In the other words, phase modulation or distortion of the pump beam is disappeared in the output. The self-cancellation of phase information of the pump beam is actually equivalent to the regeneration of the seed pulse i.e. coherent amplification of femtosecond light pulses based on the frequency-domain phase conjugation .
2. Two-photon arranged grating
The gain bandwidth of the two-photon arranged photorefractive amplifier (TAPA) is limited by the transmissive bandwidth of the photorefractive medium that has two-photon absorption. The maximum possible gain bandwidth Δω limited by the two-photon absorption corresponds to approximately carrier frequency ω 0 (Δω = 2ω 0 - ω 0 = ω 0, ∴ Δω/ω 0 ≅ 1). Thus amplification of few-cycle light pulse is possible.
On the other hand, the PR materials have residual linear absorption due to impurity ions. The excitation via the linear absorption at laser fundamental frequency erases the two-photon arranged gratings. We have to carefully select PR materials to maximize the ratio of two-photon and linear absorptions i.e.
where α (1/cm), β (cm/W), and I (W/cm) are linear absorption coefficient at laser wavelength, two-photon absorption coefficient and laser intensity, respectively. The threshold intensity to form the two-photon arranged grating is given by the critical intensity Ic
For example, typical value of β is 1–10 cm/GW  so that the critical intensity in a commonly available crystal having α =0.01 cm-1 is in the order of MW/cm2. The two-photon arranged grating can be directly written by CW mode-lock lasers. The response time in the two-photon grating formation in the medium (βI=0.01 cm-1, with a space charge of 1019 electrons/cm3) at an average laser intensity of 1 W/cm2 is estimated to be 250 s. Faster response can be expected as a function of square of light intensity.
The maximum possible compression factor from the chirped pump to the seed is limited by the contrast ratio of two-photon fringes. The contrast as a function of the compression factor has been reported elsewhere . The contrast is given as the amplitude of electric field, the function corresponding to quartic root of the two-photon absorption, so this interaction is essentially highly sensitive. For example, a seed pulse having 1/100 fraction of the pump energy is enough for 10,000 times pulse compression. In the other words, a stage gain of 100 is possible with a 10 fs seed and 100 ps pump pulses. An index modulation of > 0.01 can be satisfied with commonly available PR crystals so that the pump to the femtosecond output conversion efficiency > 50 % is possible .
A 9 fs mode-lock Ti:Al2O3 laser operating at a repetition rate of 76 MHz was used for the few-cycle experiments. A spectra width of the laser was Δλ =115 nm (FWHM) centered at 800 nm. A Fe doped LiNbO3 crystal was selected for the first demonstration because it has broad absorption spectrum around 400 nm and has a 700 nm to IR transmission band as shown in Fig. 2. A 40 mm-thick quartz block was used to generate chirped pump pulses having a pulse duration of 400 fs (FWHM). A seed pulse and the chirped pulse interacted in a 1 cm-thick crystal with a crossing angle of F/5. The grating wave vector was parallel to the c-axis. When intensity of the chirped pulse was 250 kW/cm2, no diffraction was found over 1 hour exposure. Figure 3 is showing diffraction efficiency of two-photon arranged grating by the pump beam having 5.1 MW/cm2 as a function of time. These spectra were measured accumulatively after every 30 s exposure to the pump and seed pulses. The diffraction efficiency little bit blue shifted with time, grew up to 300 s then saturated. As an femtosecond amplifier, the extraction efficiency from the chirped pump to femtosecond output was 27 %. A gain bandwidth was measured to be 69 nm (Δν =32 THz).
Figure 4 is showing output spectra as a function of delay time between the seed and the chirped pump pulses. The chirp rate of the two-photon arranged gratins well agrees with the group-delay-dispersion of 1440 fs2 in the SiO2 block pulse-stretcher.
The spectral function in diffraction efficiency of two-photon arranged grating S(λ) is given by
where β(λ), Ip(λ), and Is(λ) are two-photon absorption coefficient, the pump and seed spectral intensity, respectively. When we assume that β(λ) is in proportion to α(λ/2), the blue shift in the diffraction efficiency is as the contribution of β(λ). The saturated-gain bandwidth of 69 nm (shown in Fig. 3) well agrees with the width of S(λ)Ip(λ) (that is 66 nm) so that the gain narrowing is mainly owing to the two-photon processes. Spectrally flat-top pump pulse is required to prevent the gain narrowing. Also strongly saturated writing extends the gain bandwidth. But heavy saturation may degrade contrast of output pulse and/or beam quality due to the phase distortion.
When this scheme is used in a CPA system, group-delay-dispersion (GDD) or phase distortion in the CPA chain (except for GDD in the PR medium itself) may be automatically compensated. The response time of PR material is in inverse proportion to average absorbed power so that this scheme is suitable to quasi-CW or high repetition rate systems rather than the single-shot machine. The fast response enables to compensate time-dependent phase distortion and/or carrier envelope phase (CEP) fluctuation due to thermal drift.
In conclusion, an amplifier having 32 THz bandwidth has been demonstrated by the two-photon induced photorefractive effect directly produced by an IR laser at the intensity of 5 MW/cm2. The extraction efficiency from the pump to output was 27 %. This scheme is based on the PR effect so that coherent pulse synthesis by accumulative multiple exposures is possible. This scheme can be used not only for the amplifier and frequency-domain phase conjugator but also for ultra-fast wave processing including waveform memory, ultra-fast pulse synthesizer, phase-sensitive cross-correlator and discriminators.
Part of this work is supported by a grant-in-aid for scientific research, and the 21st Century Center of Excellence (COE) program from the Ministry of Education, Culture, Science, Sports and Technology.
References and links
1. A. A. Ahkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. I. Levinstein, and K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74(1966). [CrossRef]
2. M. Horowitz, B. Fischer, Y. Barad, and Y. Silberberg, “Photorefractive effect in a BaTiO3 crystal at the 1.5-μm wavelength regime by two-photon absorption,” Opt. Lett. 21, 1120–1122(1996). [CrossRef]
4. Hajime Nishioka, Hitoshi Tomita, Keisuke Hayakawa, and Ken-ichi Ueda, “All-optical temporal phase correction scheme for few-cycle optical pulses using diffractive optics,” Opt. Express 14, 7447–7455(2006). [CrossRef]
5. O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and d. Psaltis, “Femtosecond time-resolved absorption processes in lithium niobate crystals,” Opt. Lett. 30, 1366–1368 (2005). [CrossRef]
7. H. Xia, X. Zeng, J. Wang, J. Zhang, J. Xu, Y. Zhang, and Q. Nie, “Optical absorption spectra of LiNbO3, and Zn:Fe:LiNbO3 single crystals grown by Bridgman method,” Cryst. Res. Technol. 39, 337–342(2004). [CrossRef]