Active control the peak value of Hanbury Brown-Twiss effect with classical light by holographic projection

TL;DR

The paper addresses active control of the Hanbury Brown–Twiss peak value $g^{(2)}(0)$ for classical light by holographic projection in a single-lens incoherent imaging system. It develops a 1D theoretical framework relating object-plane target statistics to image-plane $g_P^{(2)}(0)$ and proposes a fast single-frame estimator, then validates the model experimentally using chaotic speckle and sparse phase-only CGHs, achieving strong super-bunching ($g^{(2)}(0)$ up to 39.77). The results show that the peak can be enhanced by increasing the target coherence degree $\mathscr{D}^{(2)}$, enlarging the projection NA, or exploiting holographic noise, with the single-frame method providing a rapid predictive tool. These findings enable programmable control of photon bunching in HBT-based imaging and projection systems, with potential applications in ghost imaging and classical multi-photon interference using classical light.

Abstract

The Manipulation of g^(2)(0) peak value of Hanbury Brown-Twiss (HBT) effect is discussed with a holographic projection scheme. By the aid of target pattern artificially designed in the projection imaging system, the statistical distribution of projection pattern will be highly controllable. In this work, we theoretically point out key factors influencing the g^(2)(0) peak value of HBT effect in a single-lens incoherent imaging system. We find the peak value is not only decided by statistical property and coherence length of target pattern but also depends on the intrinsic characteristics of projection system, such as numerical aperture and projection quality. Then, we experimentally measured the g^(2)(0) peak value of HBT effect with a phase-only holographic projection scheme and demonstrate the applicability of our theoretical analysis on the holographic scheme. Here, the super-bunching effect in the projection plane has been observed, when target patterns originated from chaotic speckle or it's function transformation patterns. Moreover, we design some sparse target patterns, whose holographic reconstruction patterns show the super-bunching effect achieving g^(2)(0)=39.77. Finally, we discussed the positive influence of holographic noise on increasing the g^(2)(0) peak value. The presented work predicting the peak value of HBT effect not only is applicable for the lens imaging system but also in other projection systems, such as the holographic projection.

Figures (8)

• Figure 1: (a) Schematic diagram of the experimental setup to measure diffraction light intensity from a phase-only spatial light modulator (SLM). BE: beam expander; BS: beam splitter; CCD: charge coupled device. (b) The single-frame experimental speckle from the chaotic source. The $g^{(2)}(0)$ peak value is 1.93 evaluated by using Eq. (\ref{['EQ04']}).
• Figure 2: Target patterns of chaotic speckle (a)-(c) and holographic projection patterns (d)-(i). Plotted is the $\kappa$th power of the simulated noiseless speckle for $\kappa$ = (a) 0.5, (b) 1 and (c) 2, respectively. (d), (e) and (f) are one of 1,000 holographic projection results corresponding to target patterns in (a), (b) and (c), respectively. (g), (h) and (i) are the intensity average patterns of those 1,000 holographic projection results corresponding to target patterns in (a), (b) and (c), respectively. The evaluation of $g^{(2)}(0)$ peak value by using Eq. (\ref{['EQ04']}) is displayed below the subgraphs.
• Figure 3: Relationships between the $g^{(2)}(0)$ peak value and the chaotic source size $D_{\rm{chaotic}}$ for the cases $\kappa$ = (a) 0.5, (b) 1, and (c) 2 from top to bottom, respectively. Relationships between the $g^{(2)}(0)$ peak value and the CGH size $D_{\rm{CGH}}$ for the cases $\kappa$ = (d) 0.5, (e) 1, and (f) 2 from top to bottom, respectively. The blue solid circles are the average peak value $\overline{g^{(2)}(0)}$ according to 1,000 projection pattern sequences. The red hollow circles are the $g^{(2)}(0)$ peak value for the intensity average pattern of these 1,000 frames projection results. The red solid curves are the theoretical linear fits by using Eq. (\ref{['EQ03']}).
• Figure 4: Comparison of $g^{(2)}(0)$ peak value by two measurement methods: (a) the intensity correlation of multi-frame patterns and (b) the statistical analysis by single-frame pattern, respectively. (a) The second-order bunching effect calculated by 10,000 frames of chaotic speckles (black hollow circle) and holographic projection for the cases $\kappa$ = 0.5, 1, and 2 (blue hollow squares, red hollow triangles, and green hollow diamonds, respectively). (b) Dynamic curves of $g^{(2)}(0)$ peak value taken over 1,000 frame of chaotic speckles (black line) and holographic projections corresponding to $\kappa$ =0.5, 1, and 2 (blue line, red line, and green line, respectively).
• Figure 5: 0-1 binary sparse target patterns (a)-(c) and holographic projection patterns (d)-(i). Sparse patterns originated from an all-zero matrix by inserting randomly 1 with a proportion of $p$ = (a) 1$\%$, (b) 0.5$\%$ and (c) 0.1$\%$, respectively. (d), (e) and (f) are one of 100 holographic projection results corresponding to target patterns in (a), (b) and (c), respectively. (g), (h) and (i) are the intensity average of those 100 holographic projection results corresponding to target patterns in (a), (b) and (c), respectively. The evaluation of $g^{(2)}(0)$ peak value by using Eq. (\ref{['EQ04']}) is displayed below the subgraphs.