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Compared to classical optical coherence theory based on Maxwell's electromagnetic theory and Glauber's quantum optical coherence theory based on matrix mechanics formulation of quantum mechanics, quantum optical coherence theory based on Feynman's path integral formulation of quantum mechanics provides a novel tool to study optical coherence. It has the advantage of understanding the connection between mathematical calculations and physical interpretations better. Quantum optical coherence theory based on Feynman's path integral is introduced and reviewed in this paper. Based on the results of transient first-order interference of two independent light beams, it is predicted that the classical model for electric field of thermal light introduced by classical optical textbooks may not be accurate. The physics of two-photon bunching of thermal light and Hong-Ou-Mandel dip of entangled photon pairs is the same, which can be interpreted by constructive and destructive two-photon interference, respectively. Quantum optical coherence theory based on Feynman's path integral is helpful to understand the coherence properties of light, which may eventually lead us to the answer of the question: what is a photon?, Comment: 40 pages, 35 figures

Remote heart rate measurement is an increasingly concerned research field, usually using remote photoplethysmography (rPPG) to collect heart rate information through video data collection. However, in certain specific scenarios (such as low light conditions, intense lighting, and non-line-of-sight situations), traditional imaging methods fail to capture image information effectively, that may lead to difficulty or inability in measuring heart rate. To address these limitations, this study proposes using ghost imaging as a substitute for traditional imaging in the aforementioned scenarios. The mean absolute error between experimental measurements and reference true values is 4.24 bpm.Additionally, the bucket signals obtained by the ghost imaging system can be directly processed using digital signal processing techniques, thereby enhancing personal privacy protection., Comment: 4 pages, 6 figures

Optical phased arrays (OPA) with high integration, fast speed, low power consumption, and high steering resolution are critical components in the emerging photonic integrated circuit (PIC), LiDAR, free space optical communication, 3D printing, and so on. According to the OPA working principle, its function is generally achieved by independently controlling the phase of the array elements. In practice, this presents a major challenge to overcome critical trade-offs of the element numbers, the control electronics, and the power consumption. Here, we give an alternative OPA solution to overcome this technical limitation, in the form of a cascaded periodically poled electro-optical crystal structure. Compared with the existing OPA scheme, only one control electronics is used to control the entire array elements in the current proposal, regardless of the number of array elements, implying higher integration and lower power consumption. With the help of the fast response properties of electro-optic crystal materials, a high-speed and high-resolution beam steering device is demonstrated. Simulating results show that the angular resolution can be improved by several orders of magnitude when the number of the cascaded-layer increases. An OPA prototype of a 6-layer cascaded periodically poled LiNbO$_3$ (cascaded-PPLN) was designed, fabricated, and characterized. The experiment that observed beam deflection in cascaded-PPLN OPA agrees well with the simulation results. Meantime, by demonstrating dynamic beam steering continually, its capability of continuous scanning and continually active phase tunability has been verified. Therefore, this cascaded periodically poled electro-optical crystal OPA offers a feasible direction of miniaturization and low power consumption for the optical system, such as the PIC system.

Due to the complex of mixed spectral point spread function within memory effect range, it is unreliable and slow to use speckle correlation technology for non-invasive imaging through scattering medium under broadband illumination. The contrast of the speckles will drastically drop as the light source's spectrum width increases. Here, we propose a method for producing the optical transfer function with several speckle frames within memory effect range to image under broadband illumination. The method can be applied to image amplitude and color objects under white LED illumination. Compared to other approaches of imaging under broadband illumination, such as deep learning and modified phase retrieval, our method can provide more stable results with faster convergence speed, which can be applied in high speed scattering imaging under natural light illumination.

A new type of polarization sensitive interferometer is proposed, which is named as Delta interferometer due to the geometry of the simplest interferometer looks like Greek letter, Delta. To the best of our knowledge, it is the first time that this type of interferometer is proposed. The main difference between Delta interferometer and other existed interferometer, such as Michelson interferometer, Mach-Zehnder interferometer, Young\rq{}s double-slit interferometer, is that the two interfering paths are asymmetrical in Delta interferometer, which makes it polarization sensitive. The visibility of the first-order interference pattern observed in Delta interferometer is dependent on the polarization of the incidental light. Optical coherence theory is employed to interpret the phenomenon and a single-mode continuous-wave laser is employed to verify the theoretical predictions. The theoretical and experimental results are consistent. Delta interferometer provides a perfect tool to study the reflection of electric field in different polarizations and may find applications in polarization sensitive scenarios.

Stronger light intensity fluctuations are pursued by related applications such as optical resolution, image enhancement, and beam positioning. In this paper, an Nth-order light intensity fluctuation amplifier is proposed, which was demonstrated by a four-wave mixing process with different statistical distribution coupling lights. Firstly, its amplification mechanism is revealed both theoretically and experimentally. The ratio $R$ of statistical distributions and the degree of second-order coherence ${g^{(2)}}(0)$ of beams are used to characterize the affected modulations and the increased light intensity fluctuations through the four-wave mixing process. The results show that the amplification of light intensity fluctuations is caused by not only the fluctuating light fields of incident coupling beams, but also the fluctuating nonlinear coefficient of interaction. At last, we highlight the potentiality of applying such amplifier to other N-order nonlinear optical effects.

Benefit from the promising features of second-order correlation, ghost imaging (GI) has received extensive attentions in recent years. Simultaneously, GI is affected by the poor trade-off between sampling rate and imaging quality. The traditional image reconstruction method in GI is to accumulate the action result of each speckle and the corresponding bucket signal. We found that the image reconstruction process of GI is very similar to the Recurrent Neural Network (RNN), which is one of the deep learning algorithm. In this paper, we proposed a novel method that effectively implements GI on the RNN architecture, called GI-RNN. The state of each layer in RNN is determined by the output of the previous layer and the input of this layer, and the output of the network is the sum of all previous states. Therefore, we take the speckle of each illumination and the corresponding bucket signal as the input of each layer, and the output of the network is the sum of all previous speckle and bucket signal, which is the image of the target. The testing results show that the proposed method can achieve image reconstruction at a very low sampling rate (0.38$\%$). Moreover, we compare GI-RNN with traditional GI algorithm and compressed sensing algorithm. The results of different targets show that GI-RNN is 6.61 dB higher than compressed sensing algorithm and 12.58 dB higher than traditional GI algorithm on average. In our view, the proposed method makes an important step to applications of GI.

Differing from the traditional method of achieving subwavelength interference, we have demonstrated the two-photon subwavelength interference effect of broadband chaotic light in a polarization-selective Michelson interferometer with an ultrafast two-photon absorption detector the first time, which is achieved by manipulating two-photon probability amplitudes involved in the interference. In theory, the two-photon polarization coherence matrix and probability amplitudes matrix are combined to develop polarized two-photon interference terms, which explains the experimental results well. In order to make better use of this interferometer to produce the subwavelength effect, we also make a series of error analyses to find out the relationship between the visibility and the degree of polarization error. Our experimental and theoretical results are helpful to understand the two-photon subwavelength interference, which sheds light on the development of the two-photon interference theory of vector light field based on quantum mechanics. These experimental results may help to develop future optical interferometry, optical polarimetry, and subwavelength lithography., Comment: 10 pages, 5 figures

Superbunching pseudothermal light has important applications in studying the second- and higher-order interference of light in quantum optics. Unlike the photon statistics of thermal or pseudothermal light is well understood, the photon statistics of superbunching pseudothermal light has not been studied yet. In this paper, we will employ single-photon detectors to measure the photon statistics of superbunching pseudothermal light and calculate the degree of second-order coherence. It is found that the larger the value of the degree of second-order coherence of superbunching pseudothermal light is, the more the measured photon distribution deviates from the one of thermal or pseudothermal light in the tail part. The results are helpful to understand the physics of two-photon superbunching with classical light. It is suggested that superbunching pseudothermal light can be employed to generate non-Rayleigh temporal speckles., Comment: 9 pages, 5 figures. Comments are welcome

Ghost imaging (GI) has been paid attention gradually because of its lens-less imaging capability, turbulence-free imaging and high detection sensitivity. However, low image quality and slow imaging speed restrict the application process of GI. In this paper, we propose a improved GI method based on Denoising Convolutional Neural Networks (DnCNN). Inspired by the corresponding between input (noisy image) and output (residual image) in DnCNN, we construct the mapping between speckles sequence and the corresponding noise distribution in GI through training. Then, the same speckles sequence is employed to illuminate unknown targets, and a de-noising target image will be obtained. The proposed method can be regarded as a general method for GI. Under two sampling rates, extensive experiments are carried out to compare with traditional GI method (basic correlation and compressed sensing) and DnCNN method on three data sets. Moreover, we set up a physical GI experiment system to verify the proposed method. The results show that the proposed method achieves promising performance.

By modulating the intensity of laser light before the rotating groundglass, the well-known pseudothermal light source can be modified into superbunching pseudothermal light source, in which the degree of second-order coherence of the scattered light is larger than 2. With the modulated intensities following binary distribution, we experimentally observed the degree of second- and third-order coherence equaling 20.45 and 227.07, which is much larger than the value of thermal or pseudothermal light, 2 and 6, respectively. Numerical simulation predicts that the degree of second-order coherence can be further improved by tuning the parameters of binary distribution. It is also predicted that the quality of temporal ghost imaging can be improved with this superbunching pseudothermal light. This simple and efficient superbunching pseudothermal light source provides an interesting alternative to study the second- and higher-order interference of light in these scenarios where thermal or pseudothermal light source were employed., Comment: 9 pages, 6 figures

As a promising lensless imaging method for distance objects, intensity interferometry imaging (III) had been suffering from the unreliable phase retrieval process, hindering the development of III for decades. Recently, the introduction of the ptychographic detection in III overcame this challenge, and a method called ptychographic III (PIII) was proposed. We here experimentally demonstrate that PIII can image a dynamic distance object. A reasonable image for the moving object can be retrieved with only two speckle patterns for each probe, and only 10 to 20 iterations are needed. Meanwhile, PIII exhibits robust to the inaccurate information of the probe. Furthermore, PIII successfully recovers the image through a fog obfuscating the imaging light path, under which a conventional camera relying on lenses fails to provide a recognizable image.

In general, the typical approach to discriminate antibunching, bunching or superbunching categories make use of calculating the second-order coherence function ${g^{(2)}}(\tau )$ of light. Although the classical light sources correspond to the specific degree of second-order coherence ${g^{(2)}}(0)$, it does not alone constitute a distinguishable metric to characterize and determine light sources. Here we propose a new mechanism to directly classify and generate antibunching, bunching or superbunching categories of light, as well as the classical light sources such as thermal and coherent light, by Gamma fitting according to only one characteristic parameter $\alpha$ or $\beta$. Experimental verification of beams from four-wave mixing process is in agreement with the presented mechanism, and the in fluence of temperature $T$ and laser detuning $\Delta$ on the measured results are investigated. The proposal demonstrates the potential of classifying and identifying light with different nature, and the most importantly, provides a convenient and simple method to generate light sources meeting various application requirements according to the presented rules. Most notably, the bunching and superbunching are distinguishable in super-Poissonian statistics using our mechanism., Comment: 6 pages, 8 figures

It is challenging for observing superbunching effect with true chaotic light, here we propose and demonstrate a method to achieve superbunching effect of the degree of second-order coherence is 2.42 with broadband stationary chaotic light based on a cascaded Michelson interferometer (CMI), exceeding the theoretical upper limit of 2 for the two-photon bunching effect of chaotic light. The superbunching correlation peak is measured with an ultrafast two-photon absorption detector which the full width at half maximum reaches about 95 fs. Two-photon superbunching theory in a CMI is developed to interpret the effect and is in agreement with experimental results. The theory also predicts that the degree of second-order coherence can be much greater than $2$ if chaotic light propagates $N$ times in a CMI. Finally, a new type of weak signals detection setup which employs broadband chaotic light circulating in a CMI is proposed. Theoretically, it can increase the detection sensitivity of weak signals 79 times after the chaotic light circulating 100 times in the CMI., Comment: 8 pages, 5 figures