Superbunching effect of classical light with a digitally designed spatially phase-correlated wave front

Superposition of multiple indistinguishable two-photon paths is introduced by means of a digital wave front encoding technique to design a spatially phase-correlated wave front of a light field, which could result in a superbunching effect with a bunching peak much larger than 2, the theoretical bunching peak of thermal light. Experimentally, we demonstrated a bunching peak of $11.72\pm 0.05$ with the digitally designed phase-correlated wave front of classical light, which can be improved further on. A significant improvement of the visibility of the second-order interference fringes and ghost imaging was also experimentally demonstrated. Our method provides a convenient digitally controllable way to implement superposition of multiple different but indistinguishable two-photon paths, and therefore to modify the optical coherence properties of photons. Such a superbunching effect may have potential applications in improving the visibility of correlation interference and imaging, and enhancing the efficiency of two-photon nonlinear effects such as two-photon absorption effect.

Figure 1

(a) Schematic diagram of the two-photon paths for thermal light in the traditional HBT interferometer. The solid and dashed arrows denote respectively the two different but indistinguishable two-photon paths. (b) Schematic diagram of the two-photon paths with the designed spatially phase-correlated wave front of classical light, where multiple different two-photon paths are indistinguishable when they are of the same encoded random phase $l\varphi =(m+n)\varphi =(i+j)\varphi$, and $\varphi$ changes randomly with time.

Figure 2

The $N$ dependence of the superbunching peak value $g_N^{\left(2\right)}\left(0\right)$.

Figure 3

Schematic diagram of the experimental setup. $\lambda /2$: half-wave plate; SLM: spatial light modulator; CCD: charge coupled device. The inset in the upper left corner shows the phase pattern encoded on the wave front of the light field via SLM, where different gray scales indicate different phase values $n\varphi$ with $\varphi$ changing randomly with time within $[0,2\pi )$. The double-slit mask can be inserted into the optical path when one studies the second-order interference pattern or ghost images of the double slit.

Figure 4

The measured superbunching curves with $R=8$ mm (a) and 5 mm (b). The black solid curves, the blue dotted curves, the green dot-dashed curves, and the red dashed curves are for the bunching effect of pseudothermal light and for superbunching with $N=4,16,64$, respectively.

Figure 5

The measured second-order interference patterns of the double slit with $R=2.5$ mm. The black solid, the blue dotted, the green dot-dashed, and the red dashed curves are the second-order interference fringes for pseudothermal light and for superbunching sources with $N=4,16,64$, respectively.

Figure 6

The experimental ghost images of a double-slit with a slit width of $200\mu \mathrm{m}$, a slit separation distance of $400\mu \mathrm{m}$, and a slit height of 1400 $\mu \mathrm{m}$. Here (a), (b), (c), and (d) are the reconstructed ghost images with pseudothermal light and the superbunching sources with $N=4,8,16$, respectively. Statistical averages are taken over 10 000 frames.