Towards growing challenges of information security and authentication, various optical techniques based on holography, diffraction, interference, metasurfaces, etc., deliver promising solutions with low energy consumption and parallel high-speed information processing. Here, we report on a new dimension–second-order coherence found in the well-known Hanbury Brown and Twiss (HBT) effect–for performing optical authentication and secret sharing. We develop a method to generate a pair of correlated phase-only masks, each of which is distributed to a shareholder and can produce a specific pattern as authentication under coherent illumination, while two secret images are encrypted in the mutual information of two masks. By combining two masks in two configurations, two secret images can be extracted through spatially cascaded display under coherent illumination and intensity correlation under incoherent illumination, respectively. Conspicuously, two extremes of coherence–spatially coherent or incoherent–will enable the encoding and decoding of two different images with the same phase masks, indicating that the first-order and second-order coherence can be two independent channels for optical cryptography just like other degrees of freedom of light (e.g., polarization). Moreover, we demonstrate a polarization-multiplexing scheme to achieve polarization-selective HBT-type optically secret-sharing with increased capacity, and this type of polarization-phase masks can be readily replaced with metasurfaces.
Towards growing challenges of information security and authentication, various optical techniques based on holography, diffraction, interference, metasurfaces, etc., deliver promising solutions with low energy consumption and parallel high-speed information processing. Here, we report on a new dimension–second-order coherence found in the well-known Hanbury Brown and Twiss (HBT) effect–for performing optical authentication and secret sharing. We develop a method to generate a pair of correlated phase-only masks, each of which is distributed to a shareholder and can produce a specific pattern as authentication under coherent illumination, while two secret images are encrypted in the mutual information of two masks. By combining two masks in two configurations, two secret images can be extracted through spatially cascaded display under coherent illumination and intensity correlation under incoherent illumination, respectively. Conspicuously, two extremes of coherence–spatially coherent or incoherent–will enable the encoding and decoding of two different images with the same phase masks, indicating that the first-order and second-order coherence can be two independent channels for optical cryptography just like other degrees of freedom of light (e.g., polarization). Moreover, we demonstrate a polarization-multiplexing scheme to achieve polarization-selective HBT-type optically secret-sharing with increased capacity, and this type of polarization-phase masks can be readily replaced with metasurfaces.
Secret sharing is a promising technology for information encryption by splitting the secret information into different shares. However, the traditional scheme suffers from information leakage in decryption process since the amount of available information channels is limited. Herein, we propose and demonstrate an optical secret sharing framework based on the multi-dimensional multiplexing liquid crystal (LC) holograms. The LC holograms are used as spatially separated shares to carry secret images. The polarization of the incident light and the distance between different shares are served as secret keys, which can significantly improve the information security and capacity. Besides, the decryption condition is also restricted by the applied external voltage due to the variant diffraction efficiency, which further increases the information security. In implementation, an artificial neural network (ANN) model is developed to carefully design the phase distribution of each LC hologram. With the advantage of high security, high capacity and simple configuration, our optical secret sharing framework has great potentials in optical encryption and dynamic holographic display.
The researches on higher-order coherence and quantum statistics of light field are the important researching issues in quantum optics. In 1956, Hanbury-Brown and Twiss (HBT) (Hanbury-Brown R, Twiss R Q 1956 Nature 177 27) revolutionized optical coherence and demonstrated a new form of photon correlation. The landmark experiment has far-reaching influenced and even inspired the quantum theory of optical coherence that Glauber developed to account for the conclusive observation by HBT. Ever since then, the HBT effect has motivated extensive studies of higher-order coherence and quantum statistics in quantum optics, as well as in quantum information science and cryptography. Based on the HBT scheme, the degree of coherence and photon number distribution of light field can be derived from correlation measurement and photon counting technique. With the rapid development of the photoelectric detection technology, single-photon detection, which is the most sensitive and very widespread method of optical measurement, is used to characterize the natures of light sources and indicate their differences. More recently, HBT scheme combined with single-photon detection was used to study spatial interference, ghost imaging, azimuthal interference effect, deterministic manipulation and detection of single-photon source, etc. Due to broadband RF spectrum, noiselike feature, hypersensitivity to the initial conditions and long-term unpredictability, chaotic laser meets the essential requirements for information security and cryptography, and has been developed in many applications such as chaos-based secure communications and physical random number generation, as well as public-channel secure key distribution. But the research mainly focused on macroscopic dynamics of the chaotic laser. Moreover, the precision of measurement has reached a quantum level at present. Quantum statistcs of light field can also uncover profoundly the physical nature of the light. Thus, it is important to exploit the higher-order degree of coherence and photon statistics of chaotic field, which contribute to characterizing the field and distinguishing it from others. In this paper, photon number distribution and second-order degree of coherence of a chaotic laser are analyzed and measured based on HBT scheme. The chaotic laser is composed of a distributed feedback laser diode with optical feedback in fiber external cavity configuration. The bandwidth of the chaotic laser that we obtain experimentally is 6.7 GHz. The photon number distribution of chaotic laser is fitted by Gaussian random distribution, Possionian distribution and Bose-Einstein distribution. With the increase of the mean photon number, the photon number distribution changes from Bose-Einstein distribution into Poissonian distribution and always accords with Gaussian random distribution well. The second-order coherence g(2)(0) drops gradually from 2 to 1. By changing the bias current (I = 1.0Ith-2.0Ith) and feedback strength (010%), we compare and illustrate different chaotic dynamics and g(2)(0). From low frequency fluctuation to coherence collapse, the chaotic laser shows bunching effect and fully chaotic field can be obtained at the broadest bandwidth. Furthermore, the physical explanation for sub-chaotic or weakening of bunching effect is provided. It is concluded that this method can well reveal photon statistics of chaotic laser and will open up an avenue to the research of chaos with quantum optics, which merges two important fields of modern physics and is extremely helpful for the high-speed remote chaotic communication.
Multi-channel information encryption technology has been implemented by metasurfaces owing to their superior capability in manipulating phase, amplitude, wavelength and polarization of incident light. However, any non-full-channel decoding may lead to the leakage of secret information. To further improve the security of information, in this paper, we propose a channel shared information encoding scheme by integrating visual secret sharing scheme with metasurface-based phase-encoding technique. The secret information can be reconstructed only by decoding all the wavelength channels of the metasurface, whiles meaningless images would be extracted in other channel decoding processes, without revealing any original information. The simulated results show the feasibility and adjustability of our encryption system, which can be potentially applied in future optical information security systems.
As a typical technology for optical encryption, phase retrieval algorithms have been widely used in optical information encryption and authentication systems. This paper presents three applications of two-dimensional (2D) phase retrieval for optical encryption and authentication: first, a hierarchical image encryption system, by which multiple images can be hidden into cascaded multiple phase masks; second, a multilevel image authentication system, which combines (t, n) threshold secret sharing (both t and n are positive integers, and t ≤ n ) and phase retrieval, and provides both high-level and low-level authentication; and finally, a hierarchical multilevel authentication system that combines the secret sharing scheme based on basic vector operations and the phase retrieval, by which more certification images can be encoded into multiple cascaded phase masks of different hierarchical levels. These three phase retrieval algorithms can effectively illustrate phase-retrieval-based optical information security. The principles and features of each phase-retrieval-based optical security method are analyzed and discussed. It is hoped that this review will illustrate the current development of phase retrieval algorithms for optical information security and will also shed light on the future development of phase retrieval algorithms for optical information security.
Hanbury Brown and Twiss (HBT) effect has broad applications in optics and other branches of physics, and traditionally this effect is considered in pure spatial or temporal domain. Here we investigate the spatiotemporal HBT effect, extending this phenomenon from spatial or temporal to spatiotemporal domain. By assuming the Gaussian statistics of partially coherent spatiotemporal pulsed sources, we find the generalized analytical results for spatiotemporal HBT effect in the compact form, with the help of the matrix-optics method, which can consider the HBT effect in spatial and temporal domain simultaneously. Furthermore, for Gaussian Schell-model pulsed beams (GSMPBs) used as a spatiotemporal correlated source, we have obtained the generalized expression to calculate spatiotemporal HBT effect, which is useful for up to three-dimensional cases in any second-order linear dispersive medium. By taking a simple two-dimensional case and using air as an example of a linear dispersive medium, we numerically illustrate the properties of the spatiotemporal HBT effect by adjusting the spatial and temporal parameters of the GSMPB source, and reveal the influence of both the spatial and temporal parameters on the spatiotemporal HBT effect. This work paves the path towards the detailed study of HBT effect for a source containing spatiotemporal information with Gaussian statistics.
In the history of optical science, we were satisfied with the measurement of mean intensity of light, namely the measurement of first-order coherence of light, for optical studies and observations, until the middle of 20th century when two astrophysicists Hanbury Brown and Twiss (HBT) introduced their “intensity interferometer”. “Correlation” emphasizes its statistical nature, while “coherence” emphasizes its interference nature. The chapter extends the concept of second-order coherence to Nth-order coherence (N > 2) and analyzes a few simple measurements on the third-order temporal and spatial coherence of thermal field. It also calculates the second-order temporal coherence function and the second-order spatial coherence function of thermal field by assuming idealized photodetectors and correlation measurement electronics.