Numerical implementation of three-dimensional vectorial complex ray model and application to rainbow scattering of spheroidal drops.

The rainbow patterns of oblate spheroidal drops have been observed in experiments nearly forty years ago [Nature312, 529 (1984)10.1038/312529a0]. However, the prediction for those complex patterns has been a challenge for conventional light scattering models. The vectorial complex ray model (VCRM) allows to account for the direction, the polarization, the phase, the amplitude and the wavefront curvature of waves and provides a powerful tool for the study of the light/electromagnetic wave interaction with a homogeneous object of any shape with smooth surface. In [Opt. Lett.46, 4585 (2021)10.1364/OL.434149], the authors have reported an important breakthrough of VCRM for the three-dimensional scattering (VCRM3D) and the simulated rainbow patterns of oblate drops. The present paper is devoted to the detailed description of the numerical implementation allowing the simulation of the 3D scattering field by a nonspherical particle. Its ability to predict both the fine and coarse intensity structures of the rainbows and the near-backward scattering patterns of spheroids is demonstrated. This work opens perspectives for exploring the 3D scattering characteristics of large objects with any smooth shape and developing relevant optical techniques for particle characterization.

Grating lobe-free silicon optical phased array with periodically bending modulation of dense antennas.

A grating lobe-free silicon optical phased array with large field of view is demonstrated. Antennas with periodically bending modulation are spaced at half wavelength or less. The experimental results show that the crosstalk between adjacent waveguides is negligible at 1550 nm wavelength. Additionally, to reduce the optical reflection caused by the sudden change of refractive index at the output antenna of the phased array, tapered antennas are added to the output end face so that more light will be coupled into the free space. The fabricated optical phased array shows a field of view of 120° without any grating lobes.

High-precision two-dimensional beam steering with a 64-element optical fiber phased array.

Large-scale optical fiber phased arrays (OFPAs) are capable of realizing high-power lasers and high-speed beam steering, which are widely used in long-distance detection and communication. However, dephasing occurring from optical fiber jitter and power amplifier noise can reduce beam quality and steering precision in applications. We demonstrate a two-dimensional 64-element OFPA system that employs a stochastic parallel gradient descent algorithm to synchronize the phases and thus achieve high-quality multi-beam output. Using multi-beam steering, the total scan time for covering a certain field of view can be shorter compared to single-beam steering. Moreover, an avalanche photodiode array is used to enhance the precision of the voltage for beam steering. Experimental results show that the peak sidelobe ratio of the main beam achieves 23.7 dB, and the speed of the beam steering between two discretionary angles is 128 kHz.

Generalized rainbow patterns of oblate drops simulated by a ray model in three dimensions.

The scattering patterns near the primary rainbow of oblate drops are simulated by extending the vectorial complex ray model (VCRM) [Opt. Lett.36, 370 (2011)OPLEDP0146-959210.1364/OL.36.000370] to three-dimensional (3D) calculations. With the curvature of a wavefront as an intrinsic property of a ray, this advanced ray model permits, in principle, to predict the amplitudes and phases of all emergent rays with a rigorous algebraic formalism. This Letter reports a breakthrough of VCRM for 3D scattering with a line-by-line triangulation interpolation algorithm allowing to calculate the total complex amplitude of a scattered field. This makes possible to simulate not only the skeleton (geometrical rainbow angles, hyperbolic-umbilic caustics), but also the coarse (Airy bows, lattice) and fine (ripple fringes) structures of the generalized rainbow patterns (GRPs) of oblate drops. The simulated results are found qualitatively and quantitatively in good agreement with experimental scattering patterns for drops of different aspect ratios. The physical interpretation of the GRPs is also given. This work opens up prominent perspectives for simulating and understanding the 3D scattering of large particles of any shape with a smooth surface by VCRM.

Chip scale GaAs optical phased arrays for high speed beam steering.

High speed photoelectronic optical phased arrays are demonstrated by vertically arranged GaAs-AlGaAs slab waveguides. The optical phased arrays are composed of 15-channel independently tuned waveguide with end-fire emission. We achieve a very fast beam steering step response of 0.34 µs, beam divergence of 4.7°, and beam steering ranges of around 30°with side lobe level better than 8 dB. The presented optical phased arrays provide a superior approach for high speed beam steering on a nano-photoelectronic integrated chip.

High frame-rate computational ghost imaging system using an optical fiber phased array and a low-pixel APD array.

To obtain a high imaging frame rate, a computational ghost imaging system scheme is proposed based on optical fiber phased array (OFPA). Through high-speed electro-optic modulators, the randomly modulated OFPA can provide much faster speckle projection, which can be precomputed according to the geometry of the fiber array and the known phases for modulation. Receiving the signal light with a low-pixel APD array can effectively decrease the requirement on sampling quantity and computation complexity owing to the reduced data dimensionality while avoiding the image aliasing due to the spatial periodicity of the speckles. The results of analysis and simulation show that the frame rate of the proposed imaging system can be significantly improved compared with traditional systems.

Scattering of a Gaussian beam by an elliptical cylinder using the vectorial complex ray model.

The scattered waves of a shaped beam by an infinite cylinder in the far field are, stricto sensu, neither cylindrical nor spherical, so the asymptotic form of special functions involved in the theories based on the rigorous solution of Maxwell equations cannot be used to evaluate scattered intensities, even in the most simple case of Gaussian beam scattering by an infinite circular cylinder. Thus, although theories exist for the scattering of a shaped beam by infinite cylinders with circular and elliptical sections, the numerical calculations are limited to the near field. The vectorial complex ray model (VCRM) developed by Ren et al. describes waves by rays with a new property: the curvature of the wavefront. It is suitable to deal with the scattering of an arbitrarily shaped beam by a particle with a smooth surface of any form. In this paper, we apply this method to the scattering of an infinite elliptical cylinder illuminated by a Gaussian beam at normal incidence with an arbitrary position and orientation relative to the symmetric axis of the elliptical section of the cylinder. The method for calculating the curvature of an arbitrary surface is given and applied in the determination of the two curvature radii of the Gaussian beam wavefront at any point. Scattered intensities for different parameters of the beam and the particle as well as observation distance are presented to reveal the scattering properties and new phenomena observed in the beam scattering by an infinite elliptical cylinder.

Optical absorption analysis and optimization of gold nanoshells.

Gold nanoshells, consisting of a nanoscale dielectric core coated with an ultrathin gold shell, have wide biomedical applications due to their strong optical absorption properties. Gold nanoshells with high absorption efficiencies can help to improve these applications. We investigate the effects of the core material, surrounding medium, core radius, and shell thickness on the absorption spectra of gold nanoshells by using the light-scattering theory of a coated sphere. Our results show that the position and intensity of the absorption peak can be tuned over a wide range by manipulating the above-mentioned parameters. We also obtain the optimal absorption efficiencies and structures of hollow gold nanoshells and gold-coated SiO(2) nanoshells embedded in water at wavelengths of 800, 820, and 1064 nm. The results show that hollow gold nanoshells possess the maximum absorption efficiency (5.42) at a wavelength of 800 nm; the corresponding shell thickness and core radius are 4.8 and 38.9 nm, respectively. They can be used as the ideal photothermal conversation particles for biomedical applications.

Scattering from an elliptical cylinder by using the vectorial complex ray model.

The vectorial complex ray model (VCRM) is applied to the light scattering of an elliptical cylinder illuminated by a plane wave. In the VCRM, all waves are described by vectorial complex rays, and the scattering intensities are computed by the superposition of the complex amplitudes of the vectorial rays. The significant merit of this approach is that the wave properties are integrated in the ray model such that the divergence/convergence of the wave each time it encounters a dioptric surface is deduced by the wavefront curvature equation, and the phase shifts due to the focal lines are determined directly by the curvature of the wavefront. The approach is particularly suitable for a large cylinder with an elliptical cross section.

Debye series analysis of radiation pressure force exerted on a multilayered sphere.

On the basis of generalized Lorenz-Mie theory, the Debye series expansion (DSE) for radiation pressure forces (RPF) exerted on a multilayered sphere induced by focused beams is introduced. The DSE can isolate the contribution of each scattering process to RPF, and give a physical explanation of RPF. Typically, the RPF induced by a Gaussian beam is studied. The DSE is employed to the simulation of RPF corresponding to different scattering processes (diffraction, reflection, refraction, etc.) in detail, and gives the physical mechanism of RPF. The effects of various parameters, such as scattering mode p, beam position, and radius of core for coated spheres, to RPF is researched.

Generalized Debye series expansion of electromagnetic plane wave scattering by an infinite multilayered cylinder at oblique incidence.

The Debye series expansion expresses the Mie scattering coefficients into a series of Fresnel coefficients and gives physical interpretation of different scattering modes, but when an infinite multilayered cylinder is obliquely illuminated by electromagnetic plane waves, the scattering process becomes very complicated because of cross polarization. Based on the relation of boundary conditions between global scattering process and local scattering processes, the generalized Debye series expansion of plane wave scattering by an infinite multilayered cylinder at oblique incidence is derived in this paper. The formula and the code are verified by the comparison of the results with that of Lorenz-Mie theory in special cases and those presented in the literatures.

Geometrical-optics approximation of forward scattering by gradient-index spheres.

By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.

Debye series for Gaussian beam scattering by a multilayered sphere.

The Debye series has been a key tool for the understanding of light scattering features, and it is also a convenient method for understanding and improving the design of optical instruments aimed at optical particle sizing. Gouesbet has derived the Debye series formulation for generalized Lorenz-Mie theory (GLMT). However, the scattering object is a homogeneous sphere, and no numerical result is provided. The Debye series formula for plane-wave scattering by multilayered spheres has been derived before. We have devoted our work to the Debye series of Gaussian beam scattering by multilayered spheres. The integral localized approximation is employed in the calculation of beam-shape coefficients (BSCs) and allows the study of the scattering characteristics of particles illuminated by the strongly focused beams. The formula and code are verified by the comparison with the results produced by GLMT and also by the comparison with the result for the case of plane-wave incidence. The formula is also employed in the simulation of the first rainbow by illuminating the particle with one or several narrow beams.

Debye series of normally incident plane-wave scattering by an infinite multilayered cylinder.

We derive the formula of the Debye-series decomposition for normally incident plane-wave scattering by an infinite multilayered cylinder. A comparison of the scattering diagrams calculated by the Debye series and Mie theory for a graded-index polymer optical fiber is given and the agreement is found to be satisfied. This approach permits us to simulate the rainbow intensity distribution of any single order and the interference of several orders, which is of good use to the study of the scattering characteristics of an inhomogeneous cylinder and to the measurement of the refractive index profile of an inhomogeneous cylinder.

Debye series for light scattering by a multilayered sphere.

We have derived the formula for the Debye-series decomposition for light scattering by a multilayered sphere. This formulism permits the mechanism of light scattering to be studied. An efficient algorithm is introduced that permits stable calculation for a large sphere with many layers. The formation of triple first-order rainbows by a three-layered sphere and single-order rainbows and the interference of different-order rainbows by a sphere with a gradient refractive index, are then studied by use of the Debye model and Mie calculation. The possibility of taking only one single mode or several modes for each layer is shown to be useful in the study of the scattering characteristics of a multilayered sphere and in the measurement of the sizes and refractive indices of particles.