J. Eur. Opt. Society-Rapid Publ. 22, 4( 2026) 37
Figure 8. Signal and idler spectra of the NRO with the 3-mm thick PPLN at maximum pump level at 20 kHz recorded with a resolution of ~ 0.5 nm( FWHM indicated) for broadband( a) and narrowband( b) operation.
Figure 9. Idler beam caustics in the narrowband regime of the NRO with the 3-mm thick PPLN at maximum pump level at 20 kHz: experimental data( symbols) recorded with a Pyrocam PY-III-C-B camera( Ophir-Spiricon) using a 30-mm CaF 2 lens and fits( lines). The inset shows a far-field idler beam profile recorded at 1 m from the VBG.
Figure
10. Pump, signal, and idler temporal profiles of the NRO with the 3-mm thick PPLN at maximum pump level at 20 kHz recorded with a 200-ps, extended InGaAs photodetector( FWHM indicated).
walk-off as a result of the group velocity mismatch( GVM) and the effect of group velocity dispersion( GVD) in the frequency domain. The actual spectral transmission and reflectivity of each mirror and the VBG are accounted for in a similar manner also in the frequency domain.
The plane-wave model ignores diffraction but back conversion and pump depletion are its inherent features. No spatial walk-off effects are considered for QPM. The code starts with quantum noise generated in the standard way, i. e., by one half photon( signal, idler) energy per frequency interval on the average( electric field with random phase and Gaussian amplitude distribution with zero mean and corresponding variance).
For the 5 mol % MgO-doped LiNbO 3, the temperaturedependent Sellmeier relations from [ 21 ] areused. Adirect evaluation of the effective nonlinearity of PPLN( d eff = 14 pm / V) can be found in [ 22 ] and this value is widely quoted by manufacturers, including the present provider. It takes into account the imperfect poling quality of PPLN. According to [ 22 ] this value is considered to be 78 % of the ideal value for a first order grating derived from d 33 = 28.2 pm / V. The latter value for the diagonal tensor element agrees well with the d 33 = 25 pm / V value reported for 5 % MgO-doped congruent LiNbO 3 by non-phase-matched methods [ 23 ]. For our experimental conditions, we only converted the d eff = 14 pm / V value valid for second-harmonic generation of 1064 nm fundamental to our three-wave parametric process using Miller’ s rule and the calculated refractive indices, which gave d eff = 11.8pm / Vforuseinthe code.
When broadband radiation is considered, dispersion has to be accounted for in a similar way as for femtosecond pulse durations. The lowest order dispersion effect is equivalent to temporal walk-off between the signal and idler pulses in the time domain and this is an underlying mechanism in the code. The walk-off time between the signal and idler pulses is defined as usual in terms of the corresponding group velocities v s and v i given by ¼ c n g
, withthegroup refractive indices n g ¼ n þ x dn: dx 1
s s; i ¼ L c � 1 v s v: ð1Þ i
Here L c denotes the crystal length. Temporal features with time scales shorter than s s; i are smoothed out by the GVM and cannot be correctly predicted by the model and this approximation is justified for spectral widths not exceeding s �1 s; i
[ 23 ]. For yet larger spectral widths, the GVD terms in the coupled wave equations have to be retained.