Temporal compression and shaping of chirped biphotons using Fresnel-inspired binary phase shaping

Chirped biphotons generated via spontaneous parametric down-conversion in chirped quasi-phase-matched nonlinear crystals have ultrabroadband frequency spectra, while their correlation times are not ultranarrow, due to the nonlinear frequency dependence of the phase factor. Based on the idea of Fresnel zone lenses, we propose a Fresnel-inspired binary phase-shaping scheme for tailoring broadband biphoton spectra. By applying binary phase masks to the biphoton spectrum, a Fresnel zone lens was produced in the frequency domain, compressing the broadband temporal wave packets of the chirped biphotons to the Fourier-transform limit due to the effective removal of the quadratic phase. Furthermore, biphoton correlation trains can also be generated by properly shaping the biphoton spectrum with this scheme. This provides a method for biphoton compression and shaping, which avoids the length dependence and the impact of higher-order dispersion in a dispersive medium by using the phase compensation method. Our results could prove useful in quantum metrology, lithography, and coding of entangled photons.

Figure 1

Plot of the Fresnel cosine and sine functions. The two functions intersect when $n$ is zero or a positive integer, as shown by the open (even $n)$ and solid (odd $n)$ circles.

Figure 2

(a) Broadband spectrum of chirped biphotons. The spectrum is nearly flat over the whole frequency range over which the pulse shaper operates. The bold red line schematically represents the wide slit based on an analogy with Fresnel diffraction from a slit. (b) Plot illustrating the extremum conditions of $G^2\left(\tau \right)$ expressed by the Fresnel cosine (blue line) and Fresnel sine (dashed red line) functions versus bandwidth $\Delta \Omega$ at $\tau =0$. The open and solid circles on the horizontal axis correspond to the maximal and minimal values of $G^2\left(\tau \right)$, respectively. (c) Corresponding spectral tailoring scheme for biphoton compression and shaping.

Figure 3

Temporal compression of chirped biphotons. The blue and red square lines represent the compressed results with Fresnel-inspired BAS and Fresnel-inspired BPS, respectively. (a) Plot of the original result with the quadratic phase factor (bold black line). (b) Fourier-transform-limited result (bold black line).

Figure 4

Temporal shaping of chirped biphotons. Double-peak (a) and triple-peak (b) biphoton correlation trains by modulating the biphoton spectrum with Fresnel-inspired BAS. The bold blue lines schematically represent the shaping scheme for a biphoton spectrum based on an analogy with Fresnel diffraction from a slit.