Localization of photon bunching with thermal light

We propose an experimental scheme in which two orthogonally polarized thermal light beams with antisymmetrical wavefronts are overlapped. The experimental results demonstrate that this setup can focus the beam in two-photon and multiphoton correlation measurements. The focused “two-photon” spot possesses subwavelength resolution, surpassing the classical diffraction limit. Since the experimental setup consists of only two right-angle-mirror devices without the help of lenses, the two-photon focusing effect does not apparently rely on the beam focusing. Physically, the phenomenon signifies that the photon bunching can be localized within a very small region through two-photon interference in contrast to the conventional Hanbury Brown–Twiss effect of thermal light. In the higher-order intensity correlation measurement, the multiphoton bunching can be limited within a very small central region while the background is greatly suppressed.

Figure 1

Schematic diagram of the experimental setup. G.G. is a ground glass plate and BS is a beam splitter. M1 and M2 are two right-angle mirrors. Polarizers P1 and P2 set two beams orthogonal. PBS is a polarizing beamsplitter. D1 and D2 are two CCD cameras, and C.M. indicates the intensity correlation measurement.

Figure 2

Distributions of normalized intensity correlation $\frac{\langle I_H\left(x_1\right)I_V\left(x\right)\rangle }{\langle I_H\left(x_1\right)\rangle \langle I_V\left(x\right)\rangle }$ for both the wavefronts not reversed and reversed cases, when the fixed detector is located at (a) $x_1=0.0$ and (b) $x_1=0.091$ mm. The propagation distance from source to detectors is $z=460$ mm (the same $z$ in Figs. 3 and 5).

Figure 3

Distributions of normalized intensity for the cases of (a) the wavefronts not reversed and (b) the wavefronts reversed. Open circles and squares are the experimental results of the normalized two-photon intensity distributions for the polarization-dependent and polarization-independent measurements, respectively. Open diamonds are the total intensity distributions $\langle I_{\mathrm{sp}}\left(x\right)\rangle$ normalized by its average value ${\overline{I}}_{\mathrm{sp}}$.

Figure 4

Near-field two-photon Airy disk propagates along $z$ direction, where the Airy spot patterns are obtained by the experimental data, and the enclosed curves are theoretical simulation.

Figure 5

Normalized higher-order intensity correlation functions for (a) polarization-independent measurements and (b) polarization-dependent measurements. (c) Visibility $V_{\mathrm{pi}}$ (circles) and $V_{\mathrm{pd}}$ (squares) versus order $N(=2n)$.