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Journal of Optics

Mathematical modelling of a crystal spatial light mixer

Yansong Du, Zheng Yang, Shangzhi Xie, Xu Bo

Published Dec 19, 2019• 0 citations
Publisher

Abstract

Abstract We establish a mathematical model of a crystal spatial light mixer based on the principle of crystal birefringence and splitting. The spatial light mixer consists of two crystals, three quarter-wave plates, four half-wave plates, two planar mirrors and two polarization beam splitting prisms (PBS). After the signal light and the local oscillator light pass through the spatial optical mixer, four channels of coherent light with 90° relative phase differences are output. According to the established mathematical model of spatial optical mixers, the fabrication error of components, the monochromaticity of the light source, the angle between the PBS and the light beam are simulated and analyzed. Error simulation results show that the phase noise is 4.14° when the crystal processing error is 10 nm and the refractive index error is 0.172 when the angle between the beam and the PBS is 0.0183°. The maximum phase noise that can be generated is 2.278°. The phase error of a new spatial optical mixer evolved from the mathematical model satisfies the allowable range of the Costas phase-locked loop error. It can be used in a space coherent laser communication system to improve its detection sensitivity.

DOI
10.1088/2040-8986/ab6424

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Abstract We establish a mathematical model of a crystal spatial light mixer based on the principle of crystal birefringence and splitting. The spatial light mixer consists of two crystals, three quarter-wave plates, four half-wave plates, two planar mirrors and two polarization beam splitting prisms (PBS). After the signal light and the local oscillator light pass through the spatial optical mixer, four channels of coherent light with 90° relative phase differences are output. According to the established mathematical model of spatial optical mixers, the fabrication error of components, the monochromaticity of the light source, the angle between the PBS and the light beam are simulated and analyzed. Error simulation results show that the phase noise is 4.14° when the crystal processing error is 10 nm and the refractive index error is 0.172 when the angle between the beam and the PBS is 0.0183°. The maximum phase noise that can be generated is 2.278°. The phase error of a new spatial optical mixer evolved from the mathematical model satisfies the allowable range of the Costas phase-locked loop error. It can be used in a space coherent laser communication system to improve its detection sensitivity.
Based on the birefraction of crystals and phase retardation of wave plate, a 2 × 4 90-deg crystal spatial optical hybrid is designed. It is comprised of three birefringent optical plates, λ / 4 wave plate and two λ / 2 wave plates. By splitting and recombining the signal beam and local oscillator beam, four mixed beams with phase shift of 90 deg are obtained. The mathematical model of the mixer is established by Jones matrices. The results show that the hybrid has low insertion loss, and by rotating the wave plate, the phase difference and split ratio between in-phase and quadrature-phase can be changed. It proved that the crystal hybrid design method we proposed has good performance; the phase compensation and splitting ratio adjustment scheme is simple, effective, and feasible; and it can be applied to free-space coherent optical communication system well.
Two-wave mixing in photorefractive crystals has been shown to combine coherently a modulated optical signal beam with a strong pump optical field.’ For a phase-modulated signal beam, the induced index of refraction phase grating inside the crystal yields a coupling of the optical fields of the pump and signal so that subsequent intensity detection results in apparent intensity modulation of the transmitted signal or pump beams. This provides an easy way to detect phase differences between two optical beams. Some of the advantages the above scheme offers over commonly used coherent optical phase detection schemes are: no loss of 3 dB in the signal beam intensity at the 50/50 beam splitter (used to combine signal and local oscillator fields); automatic alignment of the index of refraction grating with the two incident optical wavefronts; insensitivity to slow random changes in the phases of both beams. Experimental results are given, and a new definition for the resulting mixing gain for the phase-modulated beam is introduced, through which optimal conditions for input beam intensity ratios can be found. Applications to coherent homodyne detection are discussed.
Abstract A basic experiment on 2-bit quantum calculations related to the Deutsch–Jozsa algorithm on a linear optical quantum computer using a liquid crystal (LC) device as a linear optical element was investigated. By controlling the phase of each of the two split laser beams and checking the number of photons at the output, it is possible to determine if the input bits are “not equal” or “not uniform.” The phase of the laser light was controlled using an LC device and a half-wave plate, and changes in the interference state of the output light and the number of photons were observed. The voltage application to the LC device is set at the input bit. As a result, the interference state changed according to the input bit, and changes in the number of photons were observed.
A new scheme of generating the controllable triple-well optical trap is proposed, in which a liquid-crystal spatial light modulator (SLM) is used to fabricate the phase-type blazed grating and be illuminated with coherent monochromatic light. Three optical wells, each of which has the same intensity distribution, can be formed with relative position of the distribution of an equilateral triangle. The relative positions of the optical wells can be changed by simply and conveniently adjusting the phase distribution of the SLM to realize the evolution and reverse evolution from triple or dual wells to single well. The phase grating is designed by simulation according to the technical parameters of the SLM, and illuminated by the laser with ordinary power. The intensity distributions and intensity changes in the adjustment process for the triple wells are calculated. Results show that the controllable triple-well optical trap with very high peak value of intensity and intensity gradient can be obtained. It has many important applications in the experimental study of atomic and molecular optics.
When a weak optical signal is injected in a photorefractive crystal illuminated with a strong pump beam, it experiences gain via a two-wave mixing process.(1) A problem common to these amplifiers is the presence of noise sources that corrupt the quality of the emerging amplified optical signal. We propose and experimentally demonstrate the first technique, to our knowledge, capable of very significantly reducing the optical noise while maintaining high gain coefficients. Consider two-wave mixing in a slowly rotating crystal. First, we estimate the influence of a crystal rotation (angular velocity Ω around the point O) on the noise intensity in the output plane (Fig. 1a). A noise source located around point A radiates a complex wavefront whose component along the direction of the injected signal is represented by a plane wave of intensity IN (A is a crystal imperfection or interface). It is essential to note that the noise sources are bounded to the crystal and will consequently move with it. This is the basis for the process of discrimination between the noise gratings and the injected signal grating. In the Ox coordinate bounded to the rotating crystal, the interference pattern responsible for the formation of a noise grating around the point A is given by: IN(x,t) = I0 [1 + mN cos KN(t)x], where KN(t) ~ 2π(θ + Ωt)/λ is the time-dependent grating wave vector (we have assumed that the angles inside the crystal are small), I0 is the total incident intensity (I0 ~ IP0), θ is the angle between the beams inside the crystal, λ = λ0/n is the optical wavelength in the crystal with refractive index n, and mN is the fringe modulation.
A modified Michelson interferometer in which one of the mirrors is driven by a piezoelectric crystal connected to a Gaussian random-noise generator has been used to phase modulate a light beam from a Spectra Physics 119 model laser. The recombination of the modulated and the unmodulated beam reflected by a stationary prism generates a randomly varying interference pattern whose intensity distribution has been analyzed by means of a standard photon-counting technique. The experimental data agree with the theoretical semiclassical predictions in the range of linearity of the piezoelectric crystal. Deviations from the theory have been detected and correlated with the hysteresis of the crystal for large root-mean-square voltages applied to it.