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Showing papers on "Mach–Zehnder interferometer published in 2014"


Journal ArticleDOI
TL;DR: In this article, an all-fiber sensor for simultaneous measurement of refractive index and temperature in solutions is proposed and demonstrated, which contains a core-offered Mach-Zehnder interferometer and a fiber Bragg grating (FBG).
Abstract: An all-fiber sensor for simultaneous measurement of refractive index and temperature in solutions is proposed and demonstrated. The sensing head contains a core-offset Mach–Zehnder interferometer (MZI) and a fiber Bragg grating (FBG). The interference fringe of the MZI and the Bragg wavelength of the FBG would shift with the variation of the ambient refractive index (RI) and/or temperature. The experimental results show that the RI sensitivity and the temperature sensitivity for the sensor are 13.7592 nm/RI and 0.0462 nm/°C, respectively. Its low fabrication cost, simple configuration and high sensitivity will have attractive potential applications in chemical and biological sensing.

136 citations


Journal ArticleDOI
TL;DR: An all-optical approach for controlling the phase of a flow of cavity-polaritons, making use of their strong interactions with localized excitons is proposed, by implementing a compact exciton–polariton interferometer, which output intensity and polarization can be optically controlled.
Abstract: Quantum fluids based on light is a highly developing research field, since they provide a nonlinear platform for developing optical functionalities and quantum simulators. An important issue in this context is the ability to coherently control the properties of the fluid. Here we propose an all-optical approach for controlling the phase of a flow of cavity-polaritons, making use of their strong interactions with localized excitons. Here we illustrate the potential of this method by implementing a compact exciton–polariton interferometer, which output intensity and polarization can be optically controlled. This interferometer is cascadable with already reported polariton devices and is promising for future polaritonic quantum optic experiments. Complex phase patterns could be also engineered using this optical method, providing a key tool to build photonic artificial gauge fields.

125 citations


Journal ArticleDOI
TL;DR: A novel fiber in-line Mach-Zehnder interferometer with a large fringe visibility of up to 17 dB, which was fabricated by misaligned splicing a short section of thin core fiber between two sections of standard single-mode fiber could be used to realize simultaneous measurement of tensile strain and temperature.
Abstract: We demonstrated a novel fiber in-line Mach-Zehnder interferometer (MZI) with a large fringe visibility of up to 17 dB, which was fabricated by misaligned splicing a short section of thin core fiber between two sections of standard single-mode fiber. Such a MZI could be used to realize simultaneous measurement of tensile strain and temperature. Tensile strain was measured with an ultrahigh sensitivity of −0.023 dB/μɛ via the intensity modulation of interference fringes, and temperature was measured with a high sensitivity of 51 pm/°C via the wavelength modulation of interference fringe. That is, the MZI-based sensor overcomes the cross-sensitivity problem between tensile strain and temperature by means of different demodulation methods. Moreover, this proposed sensor exhibits the advantages of low-cost, extremely simple structure, compact size (only about 10 mm), and good repeatability.

120 citations


Journal ArticleDOI
TL;DR: In this article, an all-optical NH3 gas sensor based on graphene/microfiber hybrid waveguide (GMHW) is presented, where the wavelength shift induced by the NH3 absorption is spectrally demodulated by using a microfiber-based Mach-Zehnder interferometer (MZI).
Abstract: In this paper, we report an all-optical NH3 gas sensor based on graphene/microfiber hybrid waveguide (GMHW). The study on the sensing mechanism shows that as the adsorption of NH3 modifies the conductivity of graphene and thus the effective refractive index of the GMHW, and the transmitting light along the GMHW is very sensitive to NH3 gas concentration. The wavelength shift induced by the NH3 absorption is spectrally demodulated by using a microfiber-based Mach–Zehnder interferometer (MZI). A high sensitivity of ∼6 pm/ppm is obtained for the NH3 adsorption measurement. The resolution of such a sensor is ∼0.3 ppm, mainly limited by the resolution of the optical spectrum analyzer used. The work of this paper may open a window for the development of novel GMHW-based gas sensors with high sensitivity, small footprint, easy fabrication and low cost.

110 citations


Journal ArticleDOI
01 Oct 2014-Optik
TL;DR: The working principle of Mach–Zehnder interferometer is described and its efficient application to perform digital logic operations such as AND, XOR and XNOR logic gates is described.

102 citations


Journal ArticleDOI
Youfu Geng1, Xuejin Li1, Xiaoling Tan1, Yuanlong Deng1, Xueming Hong1 
TL;DR: In this paper, the authors proposed a compact and ultrasensitive all-fiber temperature sensor based on an in-line fully liquid-filled photonic crystal fiber (PCF) Mach-Zehnder interferometer (MZI).
Abstract: We propose a compact and ultrasensitive all-fiber temperature sensor based on an in-line fully liquid-filled photonic crystal fiber (PCF) Mach-Zehnder interferometer (MZI). It consists of a small piece of index-guiding PCF fully infiltrated by fluid and two standard single-mode fibers offset spliced with PCF. Two core modes LP01 and LP11 are conveniently used as optical arms to form the in-line MZI-type interferometer. Experimental and theoretical investigations of its response to temperature confirm that high temperature sensitivity up to -1.83 nm/°C could be realized with such a compact interferometeric PCF temperature sensor.

97 citations


Journal ArticleDOI
TL;DR: A multimode microfiber (MMMF)-based dual Mach-Zehnder interferometer (MZI) is proposed and demonstrated for simultaneous measurement of refractive index (RI) and temperature, demonstrating the ability to attain highly accurate multiparameter measurements.
Abstract: A multimode microfiber (MMMF)-based dual Mach-Zehnder interferometer (MZI) is proposed and demonstrated for simultaneous measurement of refractive index (RI) and temperature. By inserting a section of MMMFsupporting a few modes in the sensing arm of the MZI setup, an inline interference between the fundamental mode and the high-order mode of MMMF, as well as the interference between the high-order mode of MMMF and the reference arm, i.e., the dual MZI, is realized. Due to different interference mechanisms, the former interferometer achieves RI sensitivity of 2576.584 nm/RIU and temperature sensitivity of 0.193 nm/°C, while the latter one achieves RI sensitivity of 1001.864 nm/RIU and temperature sensitivity of 0.239 nm/°C, demonstrating the ability to attain highly accurate multiparameter measurements.

93 citations


Journal ArticleDOI
TL;DR: In this article, the phase sensitivity of an SU(1,1) interferometer with a coherent state in one input port and a squeezed-vacuum state in the other input port using the method of homodyne detection was theoretically studied.
Abstract: We theoretically study the phase sensitivity of an SU(1,1) interferometer with a coherent state in one input port and a squeezed-vacuum state in the other input port using the method of homodyne detection. In this interferometer, beam splitting and recombination are generated by the parametric amplifiers instead of the beam splitters. Compared with the traditional Mach–Zehnder interferometer, the phase sensitivity of this interferometer can be improved due to the amplification process of the parametric amplifiers. Combined with the squeezed state input, the sensitivity can be improved further due to the noise reduction. The phase sensitivity of our scheme can approach the Heisenberg limit and the associated optimal condition is analyzed. The scheme can be implemented with current experimental technology.

92 citations


Journal ArticleDOI
TL;DR: With further optimization in design and fabrication technology, Si3N4/SiO2 waveguides have a potential to serve as a platform for passive photonic integrated circuits for OCT.
Abstract: Optical coherence tomography (OCT) is a noninvasive, three-dimensional imaging modality with several medical and industrial applications. Integrated photonics has the potential to enable mass production of OCT devices to significantly reduce size and cost, which can increase its use in established fields as well as enable new applications. Using silicon nitride (Si3N4) and silicon dioxide (SiO2) waveguides, we fabricated an integrated interferometer for spectrometer-based OCT. The integrated photonic circuit consists of four splitters and a 190 mm long reference arm with a foot-print of only 10 × 33 mm2. It is used as the core of a spectral domain OCT system consisting of a superluminescent diode centered at 1320 nm with 100 nm bandwidth, a spectrometer with 1024 channels, and an x-y scanner. The sensitivity of the system was measured at 0.25 mm depth to be 65 dB with 0.1 mW on the sample. Using the system, we imaged human skin in vivo. With further optimization in design and fabrication technology, Si3N4/SiO2 waveguides have a potential to serve as a platform for passive photonic integrated circuits for OCT.

88 citations


Journal ArticleDOI
TL;DR: In this paper, the optical switching phenomena has been studied and its efficient application to construct the fulladder/subtractor (A/S) has been projected and the mathematical description of proposed device and thereafter compilation using MATLAB.

86 citations


Journal ArticleDOI
TL;DR: Broad-band Mach-Zehnder interferometry is analytically described and experimentally demonstrated as an analytical tool capable of high accuracy refractive index measurements over a wide spectral range and enhanced sensitivity, optical systems can be designed that employ portable spectrum analyzers with nm range resolution without compromising the sensor analytical capability.
Abstract: Broad-band Mach-Zehnder interferometry is analytically described and experimentally demonstrated as an analytical tool capable of high accuracy refractive index measurements over a wide spectral range. Suitable photonic engineering of the interferometer sensing and reference waveguides result in sinusoidal TE and TM spectra with substantially different eigen-frequencies. This allows for the instantaneous deconvolution of multiplexed polarizations and enables large spectral shifts and noise reduction through filtering in the Fourier Transform domain. Due to enhanced sensitivity, optical systems can be designed that employ portable spectrum analyzers with nm range resolution without compromising the sensor analytical capability. Practical detection limits in the 10−6-10−7 RIU range are achievable, including temperature effects. Finally, a proof of concept device is realized on a silicon microphotonic chip that monolithically integrates broad-band light sources and single mode silicon nitride waveguides. Refractive index detection limits rivaling that of ring resonators with externally coupled laser sources are demonstrated. Sensitivities of 20 μm/RIU and spectral shifts in the tens of a pm are obtained.

Journal ArticleDOI
Xianxin Jiang1, Chen Yangqing1, Fang Yu1, Longhua Tang1, Mingyu Li1, Jian-Jun He1 
TL;DR: An ultrahigh sensitivity silicon photonic biosensor based on cascaded Mach-Zehnder interferometer and ring resonator with the Vernier effect using wavelength interrogation is demonstrated, promising for medical diagnostic applications.
Abstract: We demonstrate an ultrahigh sensitivity silicon photonic biosensor based on cascaded Mach-Zehnder interferometer (MZI) and ring resonator with the Vernier effect using wavelength interrogation. Experimental results show that the sensitivities reached 2870 nm/RIU and 21,500 nm/RIU for MZI sensor and MZI-ring sensor, respectively. A biosensing application was demonstrated by monitoring the interaction between goat and antigoat immunoglobulin G (IgG) pairs. The measured results show that 1 ng/ml IgG resulted in 0.035 nm and 0.5 nm wavelength shift for MZI sensor and MZI-ring sensor, respectively. This high performance sensor is promising for medical diagnostic applications.

Journal ArticleDOI
TL;DR: In this paper, high-speed silicon depletion-mode Mach-Zehnder modulators with flat electro-optic modulation responses and broad bandwidths have been experimentally demonstrated.
Abstract: High-speed silicon depletion-mode Mach-Zehnder modulators are demonstrated and characterized in this paper. Based on the structural dimensions and material parameters, transmission-line parameters and frequency response performances of the modulators are calculated and predicted by a proposed distributed circuit model. Parasitic coupled-slotline mode excited by the modulator is analyzed and suppressed by gold-wire bridges. Using a spectrum analysis method, the effect of this modification on the modulated optical signal is simulated. Over a broad frequency range from 10 MHz to 40 GHz, silicon depletion-mode Mach-Zehnder modulators with flat electro-optic modulation responses and broad bandwidths have been experimentally demonstrated.

Journal ArticleDOI
TL;DR: A complete Mach-Zehnder interferometer monolithically integrated on silicon is presented and employed as a refractive index and bio-chemical sensor and the potential of the proposed device for real-time in situ monitoring applications is established.
Abstract: A complete Mach-Zehnder interferometer monolithically integrated on silicon is presented and employed as a refractive index and bio-chemical sensor. The device consists of broad-band light sources optically coupled to photodetectors through monomodal waveguides forming arrays of Mach-Zehnder interferometers, all components being monolithically integrated on silicon through mainstream silicon technology. The interferometer is photonically engineered in a way that the phase difference of light travelling through the sensing and reference arms is approximately wavelength independent. Consequently, upon effective medium changes, it becomes feasible even with a broad-band source to induce sinusoidal-type of detector photocurrents similar to the classical monochromatic counterparts. The device is completed with its fluidic and interconnect components so that on chip interferometric measurements can be performed. Examples of refractive index and protein sensing are presented to establish the potential of the proposed device for real-time in situ monitoring applications. This is the only silicon device that has achieved complete on-chip interferometry.

Journal ArticleDOI
TL;DR: A twin-core fiber (TCF)-based Mach-Zehnder interferometer (MZI) to develop an ultrasensitive refractive index (RI) sensor that exhibits an ultrahigh RI sensitivity and a low temperature cross-sensitivity.
Abstract: We proposed and experimentally demonstrated a twin-core fiber (TCF)-based Mach–Zehnder interferometer (MZI) to develop an ultrasensitive refractive index (RI) sensor. This fiber MZI was constructed by splicing a short section of TCF between two sections of single mode fibers. A microchannel was drilled through one core of the TCF by means of femtosecond laser micromachining to create one arm of the proposed interferometer, and the other core worked as the second arm. Such a fiber interferometer exhibits an ultrahigh RI sensitivity of −10981 nm/RIU and a low temperature cross-sensitivity of 3.96×10−6 RIU/°C. Moreover, the ultra-compact device size and all-fiber configuration make it very suitable for highly sensitive RI sensing at precise location.

Journal ArticleDOI
TL;DR: In this article, a novel humidity sensor based on an in-fiber Mach-Zehnder interferometer (MZI) is proposed and demonstrated, which has a linear response to humidity with enhanced sensitivity of −0119-dB/%RH in the range of 35-90%RH.

Journal ArticleDOI
28 Aug 2014-Sensors
TL;DR: This work discusses the advancements in interferometric SPR methods to measure the phase shifts due to refractive index changes, and solutions are suggested to enhance the performance parameters that will aid in future biological and chemical sensors.
Abstract: Surface plasmon resonance (SPR) is a novel optical sensing technique with a unique ability to monitor molecular binding in real-time for biological and chemical sensor applications. Interferometry is an excellent tool for accurate measurement of SPR changes, the measurement and comparison is made for the sensitivity, dynamic range and resolution of the different analytes using interferometry techniques. SPR interferometry can also employ phase detection in addition to the amplitude of the reflected light wave, and the phase changes more rapidly compared with other approaches, i.e., intensity, angle and wavelength. Therefore, the SPR phase interferometer offers the advantages of spatial phase resolution and high sensitivity. This work discusses the advancements in interferometric SPR methods to measure the phase shifts due to refractive index changes. The main application areas of SPR sensors are demonstrated, i.e., the Fabry-Perot interferometer, Michelson interferometer and Mach-Zehnder interferometer, with different configurations. The three interferometers are discussed in detail, and solutions are suggested to enhance the performance parameters that will aid in future biological and chemical sensors.

Journal ArticleDOI
TL;DR: A low-power 2×2 silicon electro-optic switch consisting of a double-ring assisted Mach-Zehnder interferometer (DR-MZI) that can perform switching in a 60 GHz spectral window with a crosstalk less than -20 dB and the rise and fall times of the switch are 405 and 414 ps.
Abstract: We propose and experimentally demonstrate a low-power 2×2 silicon electro-optic (EO) switch consisting of a double-ring assisted Mach-Zehnder interferometer (DR-MZI). Active tuning elements based on p-i-n diodes and silicon resistive micro-heaters are embedded in the microrings for high-speed EO switching and low-loss thermo-optic (TO) tuning, respectively. The transmission spectrum shows the device can perform switching in a 60 GHz spectral window with a crosstalk less than -20 dB. After phase error correction with 2.31 mW TO power, the EO switch power from cross to bar states is only 0.69 mW. The rise and fall times of the switch are 405 and 414 ps, respectively. The switch operation of the device is verified by high-throughput optical signal transmission up to 25 Gbps.

Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate a silicon Mach-Zehnder interferometer (MZI) based magneto-optical isolator having an 8 nm bandwidth for more than 20 dB isolation.
Abstract: We demonstrate a silicon Mach–Zehnder interferometer (MZI) based magneto-optical isolator having an 8 nm bandwidth for more than 20 dB isolation. The operational bandwidth of the isolator is determined by the wavelength dependence of a reciprocal phase difference provided by the asymmetric path length of the MZI. Although a shorter path length requires precise control of the waveguide dimensions, we achieve wider-bandwidth operation.

Journal ArticleDOI
TL;DR: In this paper, an ultracompact and high sensitive refractive index (RI) sensor based on Mach-Zehnder interferometer (MZI) structure was presented.

Journal ArticleDOI
TL;DR: The proposed optical clocked D flip-flop is implemented using the OptiBPM software for the proper verification of the discussed schemes and its implementation using the MATLAB simulation result.

Journal ArticleDOI
TL;DR: In this article, a strain sensor based on fiber ring cavity laser with a photonic crystal fiber (PCF) in-line Mach-Zehnder interferometer (MZI) struc- ture is used as an optical band-pass filter and acts as the strain sensing compo- nent.
Abstract: We experimentally demonstrated a strain sensor based on fiber ring cavity laser with a photonic crystal fiber (PCF) in-line Mach-Zehnder interferometer (MZI) struc- ture, which is used as an optical band-pass filter and acts as the strain sensing compo- nent. The fiber ring cavity laser plays the role of enhancing the visibility of the resonant spectrum and narrowing the corresponding 3-dB bandwidth, thus improving the compre- hensive sensing performance. The induced axial strain on the structure is measured by monitoring the central wavelengths of the laser output. A high strain sensing sensitivity of 2.1 pm=�" is successfully achieved in the linear strain range of 0-2100 �" . A parame- ter Q value describing the overall sensing performance is introduced by including the strain sensing sensitivity, sensing sensitivity relative to 3-dB bandwidth of the resonant spectrum and the corresponding visibility. Comparing with the reported strain measure- ments based on a PCF in-line MZI structure, the experimental results based on fiber ring cavity laser sensor present more than nine times larger Q value.

Journal ArticleDOI
TL;DR: In this paper, an all-fiber comb filter using a tapered-erbium-doped fiber in a Mach-Zehnder interferometer structure is presented, where the free spectral range, extinction ratio, bandwidth, and interference pattern of the comb filter can be shaped by controlling the taper waist length and the length of up and down taper transition regions.
Abstract: An all-fiber comb filter using a tapered-erbium-doped fiber in a Mach-Zehnder interferometer structure is presented. The free spectral range, extinction ratio, bandwidth, and interference pattern of the comb filter can be shaped by controlling the taper waist length and the length of up and down taper transition regions. By varying the taper waist length from 5 to 25 mm, the free spectral range changes from 14.7 to 1.0 nm, and the linewidth varies from 3.3 to 0.3 nm, respectively. We demonstrate a tunable dual-wavelength laser by using the tapered-erbium-doped fiber as a gain medium as well as a wavelength-selective element. The laser can be tuned at a resolution of 0.2 nm with a side-mode suppression ratio of up to 46.88 dB and a linewidth of 0.09 nm.

Journal ArticleDOI
TL;DR: Good phase controllability and high production yield in Si-nanowire-based multistage delayed Mach-Zehnder interferometer-type optical multiplexers/demultiplexers fabricated by an ArF-immersion lithography process on a 300 mm silicon-on-insulator (SOI) wafer are reported.
Abstract: We report good phase controllability and high production yield in Si-nanowire-based multistage delayed Mach–Zehnder interferometer-type optical multiplexers/demultiplexers (MUX/DeMUX) fabricated by an ArF-immersion lithography process on a 300 mm silicon-on-insulator (SOI) wafer. Three kinds of devices fabricated in this work exhibit clear 1×4 Ch wavelength filtering operations for various optical frequency spacing. These results are promising for their applications in high-density wavelength division multiplexing-based optical interconnects.

Journal ArticleDOI
Changyu Shen1, Youqing Wang1, Jinlei Chu1, Yanfang Lu1, Yi Li1, Xinyong Dong1 
TL;DR: The obtained sensitivity of -0.385 dB/μm is about 150 times high than that of the current similar existing axial micro-displacement sensor.
Abstract: A Mach-Zehnder interferometer (MZI) based fiber axial micro-displacement sensor was proposed. The MZI was constructed by a bowknot-type taper (BTT) combining with a fiber core-offset between two single mode fibers (SMFs). The axial micro-displacement of the core offset is correlated with the MZI transmission spectrum and varied with the interferometer arm length. For the arm length L of 12, 18, 24 and 30 mm, the proposed sensors showed high sensitivity of -0.362 dB/μm, -0.385 dB/μm, -0.332 dB/μm and -0.235dB/μm, and temperature errors of -0.056 dB/°C, -0.036 dB/°C, -0.044 dB/°C, -0.048 dB/°C, respectively. The theoretical simulations of the energy distributions were also given. The obtained sensitivity of -0.385 dB/μm is about 150 times high than that of the current similar existing axial micro-displacement sensor.

Journal ArticleDOI
TL;DR: In this article, a Mach Zehnder fiber interferometer is demonstrated for sensing of the heavy metal cation, Ni2+ using a responsive polyvinyl alcohol (PVA) based hydrogel.
Abstract: A Mach Zehnder fiber interferometer is demonstrated for sensing of the heavy metal cation, Ni2+ using a responsive poly(vinyl alcohol) (PVA) based hydrogel. The presence of Ni2+ increases degree of cross linkages within the hydrogel and increases its refractive index, leading to phase shift in the interferogram. Ni2+ concentration is monitored by the shifting of interference dips with a sensitivity of 0.214 nm/μM and limit of detection of 1 nM. Design of the PVA hydrogel to optimize sensitivity is discussed and the capability of the gel to immobilize various receptors enables a flexible platform for sensing applications.

Journal ArticleDOI
TL;DR: In this paper, the authors presented the design of the world's first Sagnac speed meter (SSM) interferometer, which is currently being constructed at the University of Glasgow.
Abstract: The second generation of large scale interferometric gravitational wave (GW) detectors will be limited by quantum noise over a wide frequency range in their detection band. Further sensitivity improvements for future upgrades or new detectors beyond the second generation motivate the development of measurement schemes to mitigate the impact of quantum noise in these instruments. Two strands of development are being pursued to reach this goal, focusing both on modifications of the well-established Michelson detector configuration and development of different detector topologies. In this paper, we present the design of the worldʼs first Sagnac speed meter (SSM) interferometer, which is currently being constructed at the University of Glasgow. With this proof-of-principle experiment we aim to demonstrate the theoretically predicted lower quantum noise in a Sagnac interferometer compared to an equivalent Michelson interferometer, to qualify SSM for further research towards an implementation in a future generation large scale GW detector, such as the planned Einstein telescope observatory.

Journal ArticleDOI
TL;DR: This work proposes spectrally resolved incoherent holography using a multifunctional Mach-Zehnder interferometer that can introduce both a radial shear and a variable time delay between the interfering optical fields and permits the measurement of both spatial and temporal coherence functions.
Abstract: Spatial and spectral information holds the key for characterizing incoherently illuminated or self-luminous objects, as well as for imaging fluorescence. We propose spectrally resolved incoherent holography using a multifunctional Mach–Zehnder interferometer that can introduce both a radial shear and a variable time delay between the interfering optical fields and permits the measurement of both spatial and temporal coherence functions, from which a 3D spatial and spectral image of the object is reconstructed. We propose and demonstrate the accurate 3D imaging of the object spectra by in situ calibration.

Journal ArticleDOI
TL;DR: Mach–Zehnder optical modulators with phase shifter length of around 100 μm are fabricated by a standard process compatible with complementary metal-oxide semiconductors, and dispersion-engineered slow light allows more than five-fold enhancement, maintaining a wide working spectrum as well as large temperature tolerance.

Journal ArticleDOI
TL;DR: A method is proposed, which encodes original object image into the encrypted image and then embeds it into host image in the authors' modified Mach-Zehnder interferometer architecture, which can simultaneously realize image encryption and image hiding at a high speed in pure optical system.
Abstract: A method for optical image hiding and for optical image encryption and hiding in the Fresnel domain via completely optical means is proposed, which encodes original object image into the encrypted image and then embeds it into host image in our modified Mach-Zehnder interferometer architecture. The modified Mach-Zehnder interferometer not only provides phase shifts to record complex amplitude of final encrypted object image on CCD plane but also introduces host image into reference path of the interferometer to hide it. The final encrypted object image is registered as interference patterns, which resemble a Fresnel diffraction pattern of the host image, and thus the secure information is imperceptible to unauthorized receivers. The method can simultaneously realize image encryption and image hiding at a high speed in pure optical system. The validity of the method and its robustness against some common attacks are investigated by numerical simulations and experiments.