JEOS RP ISSN01 | Seite 32

J. Eur. Opt. Society-Rapid Publ. 21, 3( 2025) 27

Figure 2. The Schmidt modes distributions with( a) r p = 2pGHz and f = 56mm �2;( b) r p = 20pGHz and f = 56mm �2;( c) r p = 2pGHz and f = 56mm �2. Most modes show the FFRP structures of spectral distribution except n = 1.

are filled with full frequency response points( FFRP) distribution. The FFRP distribution represents the response point corresponding to each frequency, but the response amplitude of each point is different, and the amplitude values oscillate between 0 and the maximum value. With some specific conditions, such as when the pumping bandwidth is GHz shown in this paper, the similar structure spectral distribution can be detected in some special Schmidt modes which has been described in Refs. [ 28, 30 ].

From Figure 2, it can be found that the distribution of the first mode is clearer and more symmetrical, and its frequency response range Dx is mainly depended on the chirp rate of the QPM crystal. The chirp rate increase can effectively expand the frequency response range Dx for the reason of the chirped poled grating periods can effectively compensate the phase mismatching of biphoton with more frequency. By comparison, when the pumping optical bandwidth r p = 2pGHz and 20pGHz, its impact on the frequency response range Dx is not obvious, the main reason is that the center frequency of the pumping optical reaches the THz level, the pumping bandwidth of GHz and 10 GHz is extremely narrow compared with THz, the difference is not particularly obvious, so the impact on the frequency response Dx is also relatively limited. However, the difference in pumping optical bandwidth will cause the distribution of spectral power in different modes. The main reason is that the bandwidth of the pump laser can affect the frequency relationship between the pump, signal and idler lights. For example, the mode distribution of n = 1 in Figure 2 is a very obvious difference. It means that the corresponding amplitudes are larger, with a higher response probability. In particular, when the pumping optical bandwidth r p = 2pGHz, the pumping light is closer to the monochromatic light than that at r p = 20pGHz. The spectral frequency distribution in this mode is also closer to the biphoton spectral distribution obtained by SPDC with the monochromatic pump light as described in Refs. [ 28, 30 ]. The spectrum distribution in the first mode cannot be clearly defined if the pumping bandwidth is too narrow or too wide, and the appropriate pumping bandwidth can be used as an approximation of the monochromatic light, such as r p is GHz or 10 GHz levels in the paper. Through the two comparisons, it can be found that when the pumping bandwidth r p = 20pGHz, the spectral amplitude of the left and

Table 1. The frequency response bandwidth per central frequency of pump light signed as Dx / x p in some Schmidt modes

f( mm �2) 5.6 56 r p( GHz) 2p 2p 20p

right sides of the generated biphoton with a frequency of x p / 2 is slightly higher, and the middle of the original double-rectangular distribution is improved.

With the increase of the modulus index n, the distribution of each mode shows less different, and the frequency response range Dx is almost consistent, and all of them fill the entire spectral frequency space. By comparing different Schmidt modes with different pump bandwidths and different chirp rates, it can be found that the main spectral form is FFRP distribution, and the spectral distribution described in Refs. [ 28, 30 ] can be obtained only in some specificmodes with modulus index n = 1 mode, and the other modes are basically FFRP distribution. The frequency response range Dx is consistent in different modes with the same chirp rate and pump bandwidth. Therefore, a basic conclusion can be drawn that the chirp rate is the main factor affecting the frequency response range in the SPDC of chirped QPM crystals when the pump light is determined.

Table 1 specifically describes the variation of the ratio of spectral response range Dx to the center frequency of the pump light in different modes with different chirp rates and pumping bandwidth. By comparison, it can be found that the chirp rate of the QPM crystal is the main decisive factor. When the chirp rate is small, the frequency response range Dx is also narrower, narrower than the center frequency of the pump light. As the chirp rate increases, the frequency response range Dx becomes wider, even wider than the center frequency of the pump light. Meanwhile,