The concept of chirped pulse amplification (CPA) has made possible the development of amplified femtosecond systems as well as the remarkable evolution of highly nonlinear optics [1]. A CPA system generally consists in a tunable femtosecond laser oscillator, a stretcher which stretches the femtosecond pulses up to a few nanoseconds, amplifiers, often a combination of regenerative and multiple pass amplifiers, and finally a compressor which brings back the amplified pulse to its initial duration. However, the generated and amplified pulses have usually a spectrum limited by the amplifying bandwidth of the used amplifiers. This obviously restricts the spectral range covered by the laser pulses and also limits the minimum achievable pulses duration. Moreover, during pulse amplification, the spectral gain narrowing effect results in a narrowing of the spectral bandwidth of the amplified pulse. In order to compensate for the gain narrowing and therefore to obtain broadband pulse amplification, spectral shaping technique has been used in CPA laser systems [2]. Generally, it consists in the introduction of a band-pass filter in the used regenerative amplifier cavity. In their pioneer works, Dubietis et al. [3–5] have demonstrated that optical parametric (OP) CPA (OPCPA) offers the possibility for the generation of ultrashort laser pulses with high power. OPCPA has many advantages such as high gain without spectral narrowing as well as a high contrast ratio. It can efficiently replace conventional regenerative amplifiers in chirped pulse amplification systems. Moreover, in an OPCPA, the spectral gain is not fixed by the material but by the interaction geometry.

Hereafter, we present some results on the evolution of the amplified spectrum versus the interaction geometry. We take advantage of the broadened spectrum generated during the propagation of a nanojoule 120 fs Ti:Sapphire femtosecond pulse through a photonic bandgap optical fiber [6]. This broadened spectrum and spatially TEM₀₀ mode is stretched up to 350 ps and then amplified in a 1 cm BBO crystal pumped by a 20 mJ and 6 ns, injected and frequency doubled, Nd:YAG laser. We show that in a collinear geometry, the change of the phase matching condition, makes it possible to tune the central frequency of the amplified pulse while maintaining its spectral bandwidth constant. Furthermore, we also investigate the evolution of the amplified spectrum in non-collinear geometry. It is shown and confirmed that broadband laser pulses can be generated and amplified. Experimental and theoretical results are compared. Then, in good agreement with our spectral measurement, we show that the compression of amplified pulses depends on the interaction geometry. Finally, we illustrate spectral shaping of amplified laser pulses using OPCPA. In a collinear geometry, we demonstrate that spectral shaping of amplified pulse is possible by cascading two BBO crystals working under slightly different phase matching conditions.

In optical parametric amplification, photons contained in the short wavelength λ_p pump beam are split into signal photons at λ_s and idler photons at longer wavelength λ_i. The energy conservation implies:

To be efficient this nonlinear optical process implies a momentum conservation of the involved photons. This yields the well-known phase matching condition:

where k_p ⃗, k⃗ _s and k⃗ _i are the wave vector of the pump, signal and idler beams.

The phase-matching vector diagram for the general non-collinear geometry is shown in Fig 1. The geometric parameters for interaction are the phase-matching angle θ between the pump and the optic axis and the non-collinear angle α between the signal and the pump in the crystal.

 

Fig. 1. Phase-matching k-vector triangle for non-collinear optical parametric amplification.

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If there is no significant pump depletion, the intensity gain G of the amplified signal beam can be obtained by solving the coupled wave equations. This yields [7]:

where L is the crystal length, I_s is the signal intensity and $g=\sqrt{{\Gamma }^2-{(\Delta k⁄2)}^2}$. In the latter expression of g, Δk is the phase mismatch between the wavevector of the pump, signal and idler wave and Γ²=8π ² $d_{\mathit{\text{eff}}}^2$ I_p /ε₀ cn_p n_sn_iλ_sλ_i where d_eff is the effective nonlinear coefficient, I_p is the pump intensity, c is the speed of light in vacuum, ε₀ the permitivitty of vacuum and n_j and λ_j (with j=p,s,i) are the index of refraction and wavelength of the j’s wave. In an uniaxial crystal and for type I interaction, the indexes of refraction for the pump, signal and idler beams, n_p , n_s and n_i , are determined by the following equations:

where n_so , n_io , n_po and n_pe are respectively the ordinary indexes of refraction for signal, idler and pump wavelength and extraordinary index for the pump wavelength.

In a non-collinear interaction geometry when Δk=0, we have:

Usually for spectrally broadband laser pulses, the central frequency λ_c is the only spectral component for which Δk(λ_c)=0. Therefore, during their propagation in the crystal, the different spectral components of the laser pulse experience different amplification. To compute the evolution of the gain versus the wavelength, we fixed θ and α (i.e. the phase matched wavelength λ_c) and compute the parametric gain around the wavelength λ_c solving numerically the set of equations 3-5. Typical spectral gain curves versus the angle when the angle between the pump and the optic axis is θ~22° and for a 10mm long BBO crystal seeded by a spectrally broadband laser pulse and pumped by a 532 nm pulse with I_p=500 MW/cm² are shown on the Fig. 2(a).

These results clearly show that whatever the interaction geometry, it is possible to produce tunable amplified pulses on a given spectral range by slightly tuning the phase-matching angle. Moreover, the full width maximum of the amplified spectrum remains almost constant. As can be seen in Fig. 3(a), in a non-collinear geometry, the spectral acceptance is broader compared to the collinear geometry. The spectral width can be made as large as 130 nm when the internal non-collinear angle is α=2.3° [8].

 

Fig. 2. Theoretical spectral gain (a) and experimental spectra of amplified pulses (b) for different phase matching angles in a collinear geometry

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Fig. 3. Theoretical spectral gain (a) and experimental spectra of amplified pulses (b) for two different non collinear angles. The phase-matching angle is set to obtain a spectral gain centered at 810 nm.

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The experimental set-up used to demonstrate the spectral gain geometry dependence is sketched in Fig. 4. The 125 fs, 2 nJ and λ_s=810 nm pulses issued from a 76 MHz Ti:sapphire oscillator are injected in a 15 cm long photonic band gap optical fiber (the zero dispersion wavelength of the fiber is 1.065 µm and its core diameter is 5.0 µm). At the exit of the fiber, the spectrum extends from 770 nm up to 850 nm. The laser pulses are then sent in a 4 passes grating stretcher system. In the stretcher the spectrum is clipped and only 30 nm are transmitted. Therefore the rotation of the grating makes it possible to adjust the central frequency of the transmitted pulses. The pulses duration at the exit of the stretcher, measured by a streak camera, is 350 ps. The pulses are then sent in a 10 mm long BBO crystal pumped by an injected and frequency doubled Q-switched Nd:YAG laser. Only 20 mJ of the pump beam (λ_p=532 nm, τ_p=6ns) are used to pump the BBO crystal cut for type I phase matching (θ_cut=23°, φ_cut=90°). In the crystal, the pump and seed beams are ~1 mm in diameter and are spatially overlapped. The noncollinear angle α between the signal and the pump in the crystal is adjustable and the phase matching condition is achieved by tuning the angle θ between the pump beam and the optic axis of the crystal.

To synchronize the pump and signal pulses, we use an electronic home made system. A 10 Hz clock driving the ignition of both the flash lamp and the Q-switch of the Nd:YAG laser is build through a division a 76 MHz clock. This 76 MHz clock, synchronized on the repetition rate of the Ti:sapphire laser, is driven by a fast photodiode shined by a small leak of the laser oscillator. The spectrum of the amplified pulse is measured using a monochromator. At the exit of the monochromator, a fast photodiode, connected to a time gated integrator, records the evolution of the intensity versus the wavelength.

 

Fig. 4. Experimental set-up.

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Firstly, we work in a collinear geometry (α=0°) and we change the phase-matching angle θ. Typical spectra of amplified pulses are presented in Fig. 2(b). The recorded amplification for the central frequency of the seeded pulse was ~250 on the whole scanned spectral range in accordance with theoretical gain achieved accounting that the pump power density is ~500 MW.cm^-2. In Fig 3(b), we can clearly note that the experimental and theoretical tuning curves are in good agreement.

In Fig. 5(a), we report the theoretical internal phase matching angle versus the central amplified wavelength. In order to compare this curve with experimental data, external phase matching angle is measured for different amplified wavelength and experimental internal phase matching angle θ is deduced from crystal cut angle θ_cut. Again a very good agreement between experimental data and theoretical curve provided that we fixed θ_cut=23.1°, value which is very close to manufactured crystal cut angle θ_cut=23°.

 

Fig. 5. Internal phase matching angle (a) and FWHM spectral width (b) of amplified pulses versus wavelength for collinear geometry.

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In Fig. 5(b), we report the FWHM spectral width of the amplified pulses. It is important to note that such a pulse width (~12 nm) is smaller than the injected seeding pulse but remains almost constant on the whole studied spectral range. This phenomena is related to the small spectral acceptance of the BBO crystal in the pump-signal collinear geometry we used. However we found that the experimental data are larger than the theoretical expected values.

We have also recorded the amplified spectra in a non collinear geometry of the pump-seed beam interaction in the BBO crystal (Fig 3(b)). The phase matching angle is chosen to obtain an amplified spectrum centered at 810 nm. As previously reported [9], we clearly note that the amplified spectra can be made wider in such a non collinear geometry.

 

Fig. 6. FWHM spectral bandwidth versus non-collinear angle (a) and non-collinear angle versus phase matching angle (b) for an amplified pulse centered at 810 nm.

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In Fig 6(a), we report the spectral bandwidth versus the non-collinear angle. For α=2.4°, we can noticed in contrary with theoretical computation the spectral bandwidth of amplified pulse is ~30 nm. In fact, in this case and under our experimental conditions, the amplified spectrum is limited by the spectrum of the seeding pulse which is ~30 nm. We also compare the experimental data and theoretical relationship between the phase-matching angle and the non-collinear angle for a signal wave centered at 810 nm. As we can see in Fig 6(b), a good agreement is found.

We recompress the amplified pulses at the exit of the BBO crystal by using a grating compressor. The compressor is made using matching groove density (1200 lines/mm) working close to the angle of incidence set in the stretcher. The distance between the two prisms is adjusted by a right angle prism placed on a micrometric translation stage. The temporal pulse duration of the compressed pulses is measured with a 2^nd order auto-correlator using a thin BBO crystal. The photodiode recording the auto-correlation signal is connected to a time gated integrator. First, we optimize the compressor in order to minimize the recompressed pulse duration without amplification. At 810 nm, we find that the optimal compression for the FWHM 30 nm spectrum gives a FWHM temporal width of 125 fs. It is clear that such a pulse is not temporally Fourier transform. In fact, under our experimental conditions, the compressor we use cannot correct for the spectral dispersion introduced during the laser pulse propagation in the used photonic band gap fiber. Whatever, we measure the auto-correlation of the amplified pulse versus the amplification geometry in the BBO crystal. Obviously, if parametric amplification introduces important spectral modifications in either the amplitude or the phase of the amplified spectral components, this should impact the amplified pulse duration. For collinear and non-collinear phase matching conditions, we find a pulse duration at FWHM of respectively 230 fs and 120 fs. This result is in good agreement with the spectral measurements presented in Fig 3(b). Clearly, in non collinear geometry, when the spectral acceptance of the BBO crystal is larger compared to the spectrum, the amplified pulse duration remains almost unaffected. On the contrary, when the spectral acceptance of the used crystal is smaller than the spectrum of laser pulse to amplify, the amplified pulse duration is strongly modified. It is again important to notice that due to the propagation within the photonic band-gap fiber, the amplified pulses are not Fourier transform. However, it has been recently shown that further pulse compression can be achieved [6].

 

Fig. 7. Measured autocorrelations of the recompressed and amplified signal in collinear (solid line) and non collinear (dotted line) geometry.

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The geometry dependence of the OPCPA provides a very simple way to achieve spectral pulse shaping. For this purpose, two BBO crystals (L=10 mm and L=15 mm, θ_cut=23°, φ_cut=90°) are used in a walk-off compensation scheme and are pumped, in collinear geometry, by the same Nd:YAG pulse. As we have shown in Fig. 2(a), the central wavelength amplified in the parametric process depends on the phase-matching angle. Then, if one tunes independently the two different crystals, one can amplify two different parts of the input spectrum. This effect is shown in Fig 8. The two parts of the spectrum have approximately the same amplitude. This is obtained by slightly detuning one of the two crystal. In fact, by changing the experimental conditions, it is possible to change both the amplitude and the position of the maximum and minimum of the spectrally shaped amplified pulse.

 

Fig. 8. Spectral shaping of amplified pulses in a two BBO OPCPA.

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In conclusion we have experimentally explored some aspects of the interaction geometry dependence offered by an OPCPA. The efficiency of our system is limited by the temporal overlapping of signal and pump pulses but it could be improved by stretching the signal pulse up to the pump duration [8]. However, we have theoretically and experimentally demonstrated that laser pulses geometry and angles are the key factors in the OPCPA process. In particular, the spectral tunability of the amplified pulses and the possibility to achieve broad spectral range amplification are shown. Moreover, we demonstrate that the combination of two BBO crystals makes it possible to spectrally shape the amplified pulses.