Coherent Beam Array Research Articles

Study on Supermode Control of External Cavity VCSEL Array with Parallel-Coupled Model

A vertical-cavity surface-emitting laser (VCSEL) is easily made into a two-dimensional array to improve its output power. However, if the near-field complex amplitude output cannot be stabilized in the lowest supermode generated by the fundamental transverse mode, the spot cannot converge on the center normal of the far-field array geometry, and the energy will be diverged. The external cavity is prepared for the VCSEL array, and the output of the array can be stabilized in the lowest order supermode generated by the fundamental transverse mode by supermode control through diffraction coupling. In this study, the parallel-coupled model for the 2-dimensional VCSEL array based on Fresnel diffraction integration was established and used to numerically calculate and analyze the influence on the supermodes’ thresholds of different array distributions, array elements’ transverse modes and duty ratios versus the length of the external cavity. The simulation results show that the square array provides a wider range of external cavity control length (0.2d2/λ and approximately 0.9 to 1.0d2/λ). The lowest supermode of the fundamental transverse mode can be outputted. For the regular hexagonal array with the length of the external cavity of 0.15d2/λ and 0.6d2/λ. The results have important reference significance for the design of an external cavity VCSEL array, which can control the supermode and obtain VCSEL coherent array beams with high power and near diffraction limits.

Propagation properties of partially coherent array beams with a non-uniform polarization

We study a new class of partially coherent array beams with a non-uniform polarization, named radially polarized Gaussian Schell-model array (RPGSMA) beams and analyze the reliability conditions for the array beams based on the unified theory of coherence and polarization, Moreover, the statistical properties of such beam propagating in free space are investigated in detail. It is found that, the propagation properties of the RPGSMA beams are closely related to initial beam parameters. With an appropriate choice of the beam parameters, the average intensity will evolve into optical lattice patterns, and the degree of coherence (DOC) from the lattice distribution on the original plane evolves into a Gaussian profile in the far field, and the degree of polarization (DOP) appears a periodical grid-like distribution on propagation. These results may be beneficial to particle trapping and free-space optical communications.

Changes in orbital angular momentum distribution of a twisted partially coherent array beam in anisotropic turbulence.

Based on the generalized Huygens Fresnel integral, we derive the analytical formula of the cross-spectral density of a twisted partially coherent array beam propagating in non-Kolmogorov anisotropic turbulence, and investigate the changes in orbital angular momentum (OAM). The results show that the anisotropy of the turbulence causes different effects in horizontal and vertical directions. The spectral density distribution of twisted partially coherent array beam in turbulence presents self-splitting and rotation, which combines the interesting effects of the twist phase and coherent structure. Although OAM is conserved, the spatial distribution of OAM flux density can be changed by changing the propagation distance, power and anisotropy of turbulence, and the modulation of the twist phase affects not only the magnitude of OAM but also its distribution. Our work is helpful for exploring new forms of OAM sources, and promote the application of free-space optical communications and optical field modulation.

The Combined Effect of Jet and Atmospheric Turbulence on the Propagation of Airborne Partially Coherent Array Beams

AbstractThe exhaust from engines close to the fuselage can cause extreme turbulence and have a significant impact on the performance of airborne laser systems. In this paper, the combined effect of the jet engine and atmospheric turbulence on propagation of a Gaussian Schell‐model (GSM) array beam over long distances is studied in detail. Based on the two‐step propagation method, the analytical expressions of the cross‐spectral density (CSD) function, mean‐squared beam width and spectral degree of spatial coherence (DOC) of GSM array beams are derived. It is shown that the jet engine turbulence has a significant effect on the beam broadening even at a very short distance. As the propagation distance in the jet engine turbulence increases, the beam width is less effected by the spatial coherence. Meanwhile, the resistance of lower spatially coherent beam to the turbulence increases as the distance of the jet engine turbulence or the strength of the atmospheric turbulence increases. It is demonstrated that the effect of jet engine turbulence on the beam spreading can be equivalent to moderate or even severe atmospheric turbulence. Moreover, the DOC is a function with oscillatory phenomenon when the propagation distance is short or the strength of turbulence is low.

Orbital angular momentum mode detection of the combined vortex beam generated by coherent combining technology.

Coherent beam combining (CBC) technology has distinct advantages in generating high power vortex beam. In this paper, a circularly arranged coherent beam array (CBA) with discrete vortex phases is constructed to generate vortex beams. We demonstrated that the combined vortex beam (CVB) generated by the CBA is a multiplexing vortices optical field, which sidelobe is the coaxial interference pattern of these spiral harmonic components. Using the designed Dammam vortex grating (DVG), the orbital angular momentum (OAM) spectrum of the CVB is detected. Moreover, taking the target OAM mode purity of the CVB as the evaluation function of active phase control system, we realized the closed-loop phase control of the CBA and obtained the phase-locked output of the CVB.

SSPIM: a beam shaping toolbox for structured selective plane illumination microscopy

Selective plane illumination microscopy (SPIM) represents a preferred method in dynamic tissue imaging, because it combines high spatiotemporal resolution with low phototoxicity. The OpenSPIM system was developed to provide an accessible and flexible microscope set-up for non-specialist users. Here, we report Structured SPIM (SSPIM), which offers an open-source, user-friendly and compact toolbox for beam shaping to be applied within the OpenSPIM platform. SSPIM is able to generate digital patterns for a wide range of illumination beams including static and spherical Gaussian beams, Bessel beams and Airy beams by controlling the pattern of a Spatial Light Modulator (SLM). In addition, SSPIM can produce patterns for structured illumination including incoherent and coherent array beams and tiling for all types of the supported beams. We describe the workflow of the toolbox and demonstrate its application by comparing experimental data with simulation results for a wide range of illumination beams. Finally, the capability of SSPIM is investigated by 3D imaging of Drosophila embryos using scanned Gaussian, Bessel and array beams. SSPIM provides an accessible toolbox to generate and optimize the desired beam patterns and helps adapting the OpenSPIM system towards a wider range of biological samples.

非Kolmogorov大气湍流对径向部分相干阵列光束瑞利区间和湍流距离的影响

非Kolmogorov大气湍流对径向部分相干阵列光束瑞利区间和湍流距离的影响

无线光通信系统中部分相干阵列光束的传输特性研究

无线光通信系统中部分相干阵列光束的传输特性研究

Beam wander of partially coherent array beams through non-Kolmogorov turbulence.

Based on the theory of second moments and non-Kolmogorov spectrum, the beam wander theory is extend to non-Kolmogorov turbulence, the general analytical expression of beam wander in non-Kolmogorov turbulence is derived. Beam wander depends on the non-Kolmogorov turbulence parameters and the initial second moments of the laser beam at the input plane. Taking the Gaussian Schell model array beams as an example, the effects of the generalized exponent parameter, inner scale, and outer scale of non-Kolmogorov turbulence and the beam separation distance, beam number, and coherence degree on the beam wander are studied in detail. It has been shown that the beam wander varies non-monotonically with increasing generalized exponent parameter of the turbulence. Furthermore, it increases as the inner scale decreases or outer scale increases, and decreases as the beam separation distance and beam number increase and the coherence of the beam becomes weaker. Our results also indicate that the beam wander could be reduced by adjusting the beam parameters appropriately.

Spatial correlation properties of coherent array beams modulated by space-time random phase

The coherent array beams modulated by space-time random phase will produce a time-variant speckle field, i.e. partially coherent light field. The spatial correlation properties of the light field are investigated in detail. The analytical expressions of far-field intensity expectation, covariance and spatial correlation function are derived firstly. From the formulae, the effects of array geometry, the elements number, and the cycle number of phase modulation on the spatial correlation properties, including transverse coherence length, correlation coefficient are discussed. Numerical simulations are provided as auxiliary means to illustrate the analysis results.

Turbulence distance for laser beams propagating through non-Kolmogorov turbulence

Based on the second-order moments and the non-Kolmogorov turbulence spectrum, the general analytical expression for the turbulence distance of laser beams propagating through non-Kolmogorov turbulence is derived, which depends on the non-Kolmogorov turbulence parameters including the generalized exponent parameter α, inner scale l(0), and outer scale L(0) and the initial second-order moments of the beams at the plane of z=0. Taking the partially coherent Hermite-Gaussian linear array (PCHGLA) beam as an illustrative example, the effects of non-Kolmogorov turbulence and array parameters on the turbulence distance are discussed in detail. The results show that the turbulence distance z(Mx)(α) of PCHGLA beams through non-Kolmogorov turbulence first decreases to a dip and then increases with increasing α, and the value of z(Mx)(α) increases with increasing beam number and beam order and decreasing coherence parameter, meaning less influence of non-Kolmogorov turbulence on partially coherent array beams than that of fully coherent array beams and a single partially coherent beam. However, the value of z(Mx)(α) for PCHGLA beams first increases nonmonotonically with the increasing of the relative beam separation x0' for x0'≤1 and increases monotonically as x0' increases for x0'>1. Moreover, the variation behavior of the turbulence distance with the generalized exponent parameter, inner scale, and outer scale of the turbulence and the beam number is similar, but different with the relative beam separation for coherent and incoherent combination cases.

Theoretical study on the spectral shifts of partially coherent array beams passing through ABCD optical systems

According to the extended Huygens–Fresnel integral, the expressions for the on-axis spectrum of partially coherent Gaussian Schell-model (GSM) rectangular array beams passing through ABCD optical systems have been derived. The generalized Fresnel number of the system, the spatial coherent parameter of array beamlets and the array beam parameters including the number of beamlets and the separation distance between beamlets have been taken as the characteristic parameters to compare the spectral shifts of GSM array beams for the two types of the superposition, i.e. the correlated superposition and the uncorrelated superposition. In particular, the effect of characteristic parameters on the on-axis relative spectral shifts has been discussed in detail. The results show that the spectral intensity of GSM array beams for the two types of the superposition passing through ABCD systems depends on the source spectral density S 0(ω), the spatial coherent parameter of array beamlets β, the generalized Fresnel number of the system F and the array beam parameters. Furthermore, for the uncorrelated superposition, the spectrum of GSM array beams only exhibit the blue-shift, whereas for the correlated superposition, GSM array beams exhibit the spectral switch and the number of spectral switches increases with the increase of array beam parameters in the near field due to the interference between beamlets. In particular, the effect of the array beam parameters on the on-axis relative spectral shift is more obvious.

Propagation characteristics of coherent array beams from carbon dioxide waveguide lasers

The characteristics of coherent array beams generated by waveguide carbon dioxide laser structures have been investigated, with particular emphasis on their propagation and transformation properties. Methods of array beam generation are presented, and measurements of array beam quality are given through the use of the M/sup 2/ parameter. Efficient transformation of an array beam from the antisymmetric to symmetric pattern is achieved through the use of a binary phase plate, and spatial filtering is shown to improve the beam quality at the expense of only a moderate loss of total beam power. Coherence effects in the near-field propagation of array beams are also explored.