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Boosting the photon bunching of classical light via a modified Fabry-Pérot cavity

This paper proposes and experimentally demonstrates a modified Fabry-Pérot cavity utilizing cascaded spatial light modulators to generate classical superbunching light with photon bunching peaks and ghost imaging visibility significantly enhanced by orders of magnitude compared to thermal light.

Original authors: Lu Zhang, Dongxu Zhou, Hongzhi Zhang, Guoquan Zhang

Published 2026-10-07

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CC BY 4.0

Original authors: Lu Zhang, Dongxu Zhou, Hongzhi Zhang, Guoquan Zhang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of light, photons usually behave like a polite crowd at a concert, arriving at a detector one by one in a steady, predictable stream. This is how we see the world with lasers or the sun; the light is orderly and calm. But there is another kind of light, known as thermal light, where photons have a different habit. Instead of arriving alone, they tend to clump together in small groups, a behavior scientists call "bunching." This clustering happens because the light waves are jumbled and random, causing the particles to arrive in pairs or small clusters more often than chance would predict. For decades, physicists have been fascinated by this tendency, using it to peer into the quantum nature of reality and to build special cameras that can see objects without the light ever touching them directly. However, there is a limit to how tightly these photons can huddle together in standard thermal light. To push past this limit and create light that bunches even more intensely, researchers have been searching for ways to manipulate the light waves more aggressively, hoping to unlock new levels of sensitivity for imaging and sensing.

A team of researchers at Nankai University in China has now found a way to dramatically increase this clumping effect using a clever modification to a classic optical device. They took a standard setup known as a Fabry-Pérot cavity, which is essentially a box with two mirrors that trap light to make it bounce back and forth, and replaced one of the mirrors with a special screen called a spatial light modulator. This screen acts like a programmable surface that can twist and turn the light waves as they hit it. In their experiment, the scientists sent a beam of laser light into this modified box. As the light bounced between the mirror and the screen, it hit the screen multiple times. With every single bounce, the screen applied a new, complex pattern of twists to the light's wave front. By carefully designing these patterns so that they were linked to one another, the researchers forced the photons to follow many different paths that looked identical to a detector.

The result of this cascading effect was a light field where the photons were forced to bunch together with unprecedented intensity. When the researchers measured how often two photons arrived at the same time, they found a peak value of 36.9, which is more than eighteen times higher than the natural limit for standard thermal light. They pushed the experiment even further to see what happened with groups of three photons arriving simultaneously. In this case, the bunching peak soared to a staggering 2,460, a massive leap compared to the tiny clustering seen in ordinary light. To put this in perspective, if standard thermal light is like a few people occasionally bumping into each other in a hallway, this new method creates a situation where entire groups of people are forced to walk through the door in tight, synchronized clusters. The researchers confirmed that this effect grew stronger every time they added another "bounce" or layer of modulation to the system, proving that the technique could be scaled up to create even more extreme bunching.

Beyond simply observing this strange behavior, the team demonstrated that this super-bunched light could be used to take better pictures. They used the light to perform a technique called ghost imaging, which reconstructs an image of an object by analyzing how light interacts with it, even if the camera never directly sees the object. When they used standard thermal light for this task, the resulting image was very faint and blurry, with a visibility of just 1.2 percent, making it difficult to distinguish the details. However, when they switched to their newly created super-bunched light, the image clarity improved dramatically. The visibility of the reconstructed image jumped to 32.5 percent, a thirty-fold improvement that made the features of the object sharp and clear. They repeated this success with more complex, three-photon imaging, where the visibility jumped from a mere 2.3 percent to an impressive 88.7 percent. These findings suggest that by simply arranging mirrors and programmable screens in a specific way, scientists can create classical light that behaves with a level of coordination usually reserved for exotic quantum systems, opening the door to much more sensitive imaging tools and new ways to study how light interacts with matter.

Technical Summary: Boosting the Photon Bunching of Classical Light via a Modified Fabry-Pérot Cavity

Problem Statement
The Hanbury Brown and Twiss (HBT) effect describes the tendency of thermal light photons to arrive in bunches, characterized by a normalized second-order correlation function peak of $g^{(2)}(0) = 2$ . While "superbunching" (where $g^{(2)}(0) > 2$ ) is essential for enhancing the performance of applications such as ghost imaging, ghost interference, and multi-photon nonlinear light-matter interactions, achieving high bunching peaks in the spatial domain remains challenging. Previous methods using spatial light modulators (SLMs) to encode spatially correlated phases have demonstrated superbunching, but the achievable peak values in the spatial domain have generally remained relatively low compared to temporal domain enhancements. There is a need for a method to significantly boost the spatial photon bunching of classical light to improve the visibility and efficiency of practical optical applications.

Methodology
The authors propose and experimentally verify a method to boost photon bunching by modifying a Fabry-Pérot (F-P) cavity. In this configuration, one of the cavity mirrors is replaced by a reflection-type phase-only Spatial Light Modulator (SLM).

Mechanism: The system utilizes the longitudinal propagation of light within the cavity to cascade multiple independent transverse phase modulations. Each time the light reflects off the SLM, a specific spatially correlated phase structure is encoded onto the wavefront.
Theoretical Basis: Based on Feynman's path integral theory, the bunching effect arises from the superposition of indistinguishable two-photon paths. By encoding spatially correlated phases ( $\phi, 2\phi, \dots, N\phi$ ) and cascading $M$ such phase plates (achieved via $M$ reflections in the cavity), the number of indistinguishable two-photon paths increases significantly.
Experimental Setup: A 532 nm continuous-wave laser is coupled obliquely into the modified F-P cavity. The cavity consists of the SLM and a dielectric mirror. The oblique incidence ensures that beam spots on the SLM and mirror are spatially separated, allowing for multiple reflections. The number of cascaded phase plates ( $M$ ) corresponds to the number of reflections. The output light is collected by a lens and detected by a CCD camera.
Measurement: The normalized second-order ( $g^{(2)}$ ) and third-order ( $g^{(3)}$ ) spatial correlation functions are calculated from ensemble averages of 10,000 intensity frames. Ghost imaging experiments are conducted using a double-slit object to measure image visibility.

Key Contributions

Novel Cavity Design: The introduction of a modified F-P cavity with an SLM mirror to cascade spatial phase modulations in the longitudinal direction, effectively multiplying the bunching enhancement mechanism.
Theoretical Modeling: Derivation of a generalized expression for the normalized second-order spatial correlation function, $g^{(2)}_{N,M}(x_1, x_2)$ , which predicts that the bunching peak scales as $\left(\frac{2N^2+1}{3N}\right)^M$ , where $N$ is the number of spatially correlated phases and $M$ is the number of cascaded plates.
Experimental Realization: Successful generation of classical superbunching light fields with significantly enhanced multi-photon bunching peaks compared to thermal light.

Results

Two-Photon Bunching: For a configuration with $N=64$ spatially correlated phases and $M=3$ cascaded reflections, the measured two-photon bunching peak was 36.9 ± 2.0. This represents an improvement of approximately one order of magnitude over thermal light ( $g^{(2)} \approx 2$ ) and significantly exceeds previous spatial domain results.
Three-Photon Bunching: The three-photon bunching peak for the same configuration ( $N=64, M=3$ ) was measured to be (2.46 ± 0.12) × 10³. This is a three-order-of-magnitude improvement over the theoretical limit of 6 for thermal light (experimentally measured as 3.46 ± 0.17 for pseudo-thermal light).
Scaling: The logarithmic values of the bunching peaks were observed to increase linearly with the number of cascaded plates ( $M$ ), confirming the theoretical prediction of cumulative enhancement.
Ghost Imaging: The application of these superbunching fields in ghost imaging demonstrated a substantial increase in image visibility.
- For second-order ghost imaging, visibility improved from 1.2% (pseudo-thermal light) to 32.5% (superbunching light, $N=64, M=3$ ).
- For third-order ghost imaging, visibility improved from 2.3% (pseudo-thermal light) to 88.7% (superbunching light, $N=64, M=3$ ).
- The authors note that the visibility of the second- and third-order ghost images was confirmed experimentally to be improved by ~40 times as compared to that using pseudo-thermal light fields.

Significance
The paper claims that generating classical light fields with superbunched photons is of essential importance for both fundamental physics and potential applications. The demonstrated ability to boost multi-photon bunching in the spatial domain using a modified F-P cavity provides an effective method to enhance the performance of correlated imaging, ghost interference, and nonlinear optics. The experimental results confirm that cascading spatially correlated phase modulations in a cavity is a viable strategy to overcome the limitations of traditional thermal light sources in high-order coherence applications.

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