We study the three-dimensional (3D) spatially-resolved distribution of the energy density of light in a 3D scattering medium upon the excitation of open transmission channels. The open transmission channels are excited by spatially shaping the incident optical wavefronts. To probe the local energy density, we excite isolated fluorescent nanospheres distributed inside the medium. From the spatial fluorescent intensity pattern we obtain the position of each nanosphere, while the total fluorescent intensity gauges the energy density. Our 3D spatially-resolved measurements reveal that the local energy density versus depth (z) is enhanced up to 26× at the back surface of the medium, while it strongly depends on the transverse (x, y) position. We successfully interpret our results with a newly developed 3D model that considers the time-reversed diffusion starting from a point source at the back surface. Our results are relevant for white LEDs, random lasers, solar cells, and biomedical optics.

We propose a novel scheme to achieve two-photon super bunching of thermal light through multiple two-photon-path interference, in which two mutually first-order incoherent optical channels are introduced by inserting a modified Michelson interferometer into a traditional two-photon HBT interferometer, and the bunching peak-to-background ratio can reach 3 theoretically. Experimentally, the super bunching peak-to-background ratio was measured to be 2.4, much larger than the ratio 1.7 measured with the same thermal source in a traditional HBT interferometer. The peak-tobackground ratio of two-photon super bunching of thermal light can be increased up to 2 × 1.5 n by inserting cascadingly n pairs of mutually first-order incoherent optical channels into the traditional two-photon HBT interferometer. The two-photon super bunching of thermal light should be of great significance in improving the visibility of classical ghost imaging.Two-photon bunching of thermal light was first observed by Hanbury Brown and Twiss (HBT) in 1956 [1], where the maximum bunching peak-to-background ratio for thermal light is 2. One of the prospective applications of two-photon bunching effect is ghost imaging, and extensive studies have been carried out by using various light sources [2][3][4][5][6][7]. However, the imaging visibility of the classical ghost imaging, especially with complicated imaging structures, is relatively low based on the traditional two-photon HBT interference of thermal light. To overcome this limitation, spatial super bunching of thermal light with a bunching peak-to-background ratio larger than 2 has attracted a lot of interests, and great progresses have been made recently to enhance the visibility of classical ghost imaging [8][9][10][11][12][13]. It was demonstrated that the visibility of classical ghost imaging is improved by employing nth-order (n > 2) coherence of thermal light, in which the bunching peak-to-background ratio reaches n! [11][12][13]. For the two-photon case, super bunching effect was observed with laser beam scattered by a dynamic deep random phase screen with nonGaussian statistics [14,15]. Recently, two-photon super bunching effect was also observed for thermal-like photons with attractive interaction between photons propagating in a nonlinear medium with a focusing nonlinearity [16]. In this Letter, we report on the two-photon super bunching effect of thermal light by employing multiple two-photon-path interference, which would be of great significance in improving the visibility of classical ghost imaging.Figure 1(a) shows a schematic diagram for a traditional two-photon HBT interferometer. It is well known that the key of the two-photon bunching effect is the existence of two different but indistinguishable two-photon paths to trigger a coincidence count, i.e., A1B2 and A2B1, where A and B denote two different photons, and 1 and 2 denote two different detectors, respectively [5,13,[17][18][19]. Generally, in the nth-order coherence with n detectors, the number of different but indistingu...

Two-photon interference with independent classical sources, in which superposition of two indistinguishable two-photon paths plays a key role, is of limited visibility of interference fringes with a maximum value of 50%. By using a random-phase grating to modulate the wavefront of a coherent light, we introduce superposition of multiple indistinguishable two-photon paths, which enhances the two-photon interference effect with a signature of visibility exceeding 50%. The result shows the importance of phase control in the control of high-order coherence of classical light.

We propose a two-photon subwavelength interference scheme for classical light in which multiple quantum-like entangled two-photon paths play an essential role. These entangled two-photon paths are introduced through a specially designed source composed of many point sources j with j 's complex amplitude being a superposition of modes e iφ j and e iφ (1) j , where φ j and φ (1) j are temporally random phases but satisfying φ j + φ (1) j = φ 0 , with φ 0 being either a constant or a random phase in time. Interference between the entangled two-photon paths could lead to second-order subwavelength interference of an object put in front of the source plane. In a proof-of-principle experiment, by using a spatial light modulator to modulate the wave front of a coherent light, we have generated such a source and observed subwavelength interference of a double-slit mask via two-photon measurement.

We propose a N-photon imaging scheme with the resolution reaching the fundamental Heisenberg limit. The key imaging element is a phase-controlled screen which introduces synchronous-position N-photon interference, giving rise to enhanced resolution that exceeds the well-known Rayleigh resolution limit by a factor of N. In the standard wide-field illumination situation, our imaging scheme requires an entangled source to illuminate the object. Besides, we show that classical light is also applicable to realize this Heisenberg-resolution imaging if a scanning-focused-beam illumination is used. Our N-photon imaging scheme is practically realizable by using current well-developed technology.