Phonon-assisted nonlinear optical processes in ultrashort-pulse pumped optical parametric amplifiers

Optically active phonon modes in ferroelectrics such as potassium titanyl phosphate (KTP) and potassium titanyl arsenate (KTA) in the ~7–20 THz range play an important role in applications of these materials in Raman lasing and terahertz wave generation. Previous studies with picosecond pulse excitation demonstrated that the interaction of pump pulses with phonons can lead to efficient stimulated Raman scattering (SRS) accompanying optical parametric oscillation or amplification processes (OPO/OPA), and to efficient polariton-phonon scattering. In this work, we investigate the behavior of infrared OPAs employing KTP or KTA crystals when pumped with ~800-nm ultrashort pulses of duration comparable to the oscillation period of the optical phonons. We demonstrate that under conditions of coherent impulsive Raman excitation of the phonons, when the effective χ(2) nonlinearity cannot be considered instantaneous, the parametrically amplified waves (most notably, signal) undergo significant spectral modulations leading to an overall redshift of the OPA output. The pump intensity dependence of the redshifted OPA output, the temporal evolution of the parametric gain, as well as the pump spectral modulations suggest the presence of coupling between the nonlinear optical polarizations PNL of the impulsively excited phonons and those of parametrically amplified waves.


Figure SCalibration verification of visible and near-IR spectrometers.
HeNe laser (632.8 nm line) spectra measured by the visible-CCD and near-IR InGaAs spectrometers. The central wavelength (λ 0 ) and full-width at half-maximum (Δλ) values are the results of Gaussian fits. Based on the resolution of the InGaAs spectrometer, we calculate the error in determination of the spectral positions of signal spectra from the OPA (and thus the redshift value Δ) to be ≈±78 cm -1 , corresponding to ±2.34 THz (±9.67 meV).

Figure SDependence of the overall redshift Δ in KTP-OPA as a function of the pump pulse bandwidth.
The redshift values were measured at ~25-28 µJ pump pulse energy at the crystal in all cases. The top horizontal axis displays the respective transform-limit pulse-widths (assuming Gaussian pulse shape). The vertical dashed line indicates the oscillation period of the δ 2~2 1 THz phonon mode. The oscillation period of the δ 2~6 .9 THz phonon mode (~145 fs) is outside the range of the horizontal axes.
3.1. Table S1. Individual signal/idler spectra. Envelope mode spectra are shown as well (blue), as well as the expected "intrinsic signal" wavelength (dashed line).

2.3.
The electric field amplitudes E for the pump wave were calculated based on 1 2 , where n(KTP)=1.8, ε 0 =8.854 . 10 -12 C/(V . m), c=3 . 10 8 m/s; I is the pulse peak intensity calculated based on the 50-fs pump pulsewidth and the ~300-micron diameter of the beam at the nonlinear optical crystal in the OPA. Figure S4. Pump energy dependence of individual signal (a) and idler (b) outputs separated by their polarizations. The similar results of the fits to Eqn. 4 demonstrate that both signal and idler are generated from the same effective nonlinearity. The large errors in parameter A values are due to the fact that we artificially assign the zero output value at the zero pump power (see discussion below for Table S3). Table S3. Fit parameters of pump energy and pump electric field dependencies of the total OPA output and various modes from KTP-OPA, Fig. 4 of the main text, and Fig. S3. The parameter is fixed to the indicated value wherever the error is not indicated.

2.5.
The large error in the fit parameter A values is explained by the fact that we artificially assigned the zero power value at the zero pump intensity. However the OPA output at the zero pump power is essentially the seed power within the amplified bandwidth which may vary in the range ~10 -4 -10 -3 µJ. For this reason we tested the fit results for a few values of parameter A. While the values of A change by ~two orders of magnitude, the values of the B and C parameters do not change drastically. In the main text ( Fig. 4 and Table 1), we report the values of A, B and C that provide the best fit curves for each given data set. Indices: "1": envelope mode (blue lines in Table S.1); "2": mode [0] (at intrinsic signal wavelength); "3": mode at ν[0]-δ 1 ; "4": mode at frequencies between ν[0]-2δ 1 and ν[0]-δ 2 . Figure S5. KTA-OPA pump pulse energy (and pump electric field) dependences of the total OPA output (a), the envelope mode (b) and the sum of partial modes at frequencies ν[0] and ν[0] -δ 1 (c) together with fits to Eqns. 4 and 5. Corresponding values of the fit parameter A are indicated.

4.3.
The electric field amplitudes E for the pump wave were calculated based on 1 2 , where n(KTA)=1.8, ε 0 =8.854 . 10 -12 C/(V . m), c=3 . 10 8 m/s; I is the pulse peak intensity calculated based on the 50fs pump pulsewidth and the ~300-micron diameter of the beam at the nonlinear optical crystal in the OPA. Table S6. Fit parameters of pump energy and pump electric field dependencies of the total OPA output and various modes from KTA-OPA, Fig. S5.

3.4.
The parameter is fixed to the indicated value wherever the error is not indicated.  Figure S6. Temporal evolution of the parametric gain in KTA crystal when pumped by ~50-fs 800-nm pulses.
The FWHM width of the instantaneous component (fit to a Gaussian, dashed line) is ~71 fs (indicated with arrows), corresponding to ~50.4-fs pump pulsewidth as the longest estimated value. The ZnSe plate was removed from the white-light continuum seed beam path for this measurement. The KTA crystal was tuned to select the signal wavelength at ~1500 nm where the group-velocity dispersion imposed on the near-IR portion of the continuum seed pulses by routing optics is minimized. The front (trailing) edge of the pump pulse is at the positive (negative) delay values.
The spectrum was measured with the InGaAs array spectrometer in the absence of pump. The vertical dashed line shows the transmission edge of the 900-nm long-pass filter. The 2 nd -order diffraction of the grating did not allow to measure the spectrum beyond ~1750-1800 nm, however the non-zero WLC spectral intensity at ~1750 nm indicates that the seed contained spectral components at λ>1750 nm available for optical parametric amplification (OPA). The latter was demonstrated by direct OPA of horizontally-polarized signal beyond the degeneracy point (e.g., Fig. 1a).