Coherent Beam Combination of Three Fiber Amplifiers with Multi-dithering Technique

Coherent beam combination of three W-level fiber amplifiers with multi-dithering technique is demonstrated. The multi-dithering technique is used for phase control in two channels. In the experiment, two channels are modulated by sine wave with 70 kHz and 100 kHz respectively, and two regular commercial DSP lock-in amplifiers and an industrial computer are used for electric signal processing in the feedback loop. The fringe contrast is advanced from 12% to 81%, and 78% coherent combination efficiency is obtained when the feedback loop is closed.     

A Time Domain Algorithm on the Reconstruction of Rough Surfaces

We consider the inverse scattering problem of a perfectly conducting one-dimensional rough surface in the case that the incident field is unnecessary to be time harmonic. Based on our previous investigation of the frequency domain algorithm, a new time domain algorithm is proposed, in which we approximate the incident pulse by a finite sum of time harmonic fields and then apply the frequency domain algorithm for time harmonic waves. Numerical experiments indicate that the time domain algorithm shows great accuracy of reconstruction of the surface profile and yields significant improvement than the frequency domain algorithm.     

Self-mixing interference effects in orthogonally polarized dual-frequency Nd:YAG lasers at different feedback levels

The self-mixing interference effects are investigated in birefringence dual-frequency Nd:YAG lasers at different optical feedback levels. For weak feedback level, both of the intensities of the two modes are sinusoidally modulated by external cavity length with a feedback period of half laser wavelength. While these two modes can only coexist in a part of feedback period at moderate feedback level, i.e., one mode reaches its maximum intensity, the other one extinguishes. At high feedback level, complete polarization switching (one mode oscillating, the other one extinguishing) between two polarized modes is observed, and every switching corresponds to quarter-wavelength variation of external cavity length. Furthermore, two feedback schemes, i.e., isotropic optical feedback (IOF) and polarized optical feedback (POF) are taken into account. The theoretical analysis based on a model of two-mode-coupled laser is presented, which is in good agreement with experimental results. Our results can advance the research of self-mixing interferometer of orthogonally polarized dual-frequency lasers.     

Sensitive birefringence measurement in a high-finesse resonator using diode laser optical self-locking

We demonstrate a new method to measure weak birefringence of dielectric mirrors with excellent spatial resolution and sensitivity (<10^-7 radians). We exploit a well-known optical feedback scheme for line-width narrowing and frequency locking of a diode laser to a high-finesse cavity. Feedback comes from the intracavity field which builds up at resonance, selected by its change in polarization with respect to the incident field. This change, due to the residual birefringence of the cavity mirror coatings, was already exploited for birefringence measurements using an active laser-locking scheme. Here we measure the optical feedback rate as a function of rotation angle of one of the cavity mirrors (around the cavity axis). A stable feedback signal is obtained since the laser, as soon as it locks to a cavity resonance, effectively behaves as a monochromatic source. By fitting the data with a theoretical expression, we determine quantitatively the local birefringence vectors of both mirrors, which are around 10^-6 radians. Our scheme is simple, works with cavities of very high finesse (F∼10⁵), and is promising for measuring birefringence in gases induced by external fields. Received: 18 July 2001 / Final version: 14 March 2002 / Published online: 8 May 2002     

Matrix-Based Polarization Analysis and Application of Semiconductor Optical Amplifiers

Employing the Mueller matrix method with polar decomposition, we analyse the polarization rotation (PR) effects in semiconductor optical amplifiers (SOAs) and demonstrate that the PR angle is linear to the birefringence dependent gain while the average PR coefficient is about 0.625 for the employed SOA. It is further evident that the current and optical intensity dependent PRs rotate reversely around the same axis. Thus we propose an optical-electric synchronous control scheme to obtain orthogonal polarization states with power-equalization, and implement it by a polarization-sensitive SOA. The polarization duration time is about 10 ns which is applicable to high-speed polarization state generation.     

Influence of Feedback Levels on Polarized Optical Feedback Characteristics in Zeeman-Birefringence Dual Frequency Lasers

The influence of feedback levels on the intensity and polarization properties of polarized optical feedback in a Zeeman-birefringence dual frequency laser is systematically investigated. By changing the feedback power ratio, different feedback levels are obtained. Three distinct regimes of polarized optical feedback effects are found and defined as regimes Ⅰ, Ⅱ and Ⅲ The feedback level boundaries among the regimes are acquired experimentally. The theoretical analysis is presented to be in good agreement with the experimental results.     

FDTD Investigation on Electromagnetic Scattering from Two-Layered Rough Surfaces under UPML Absorbing Condition

Electromagnetic scattering from one-dimensional two-layered rough surfaces is investigated by using finite-difference time-domain algorithm （FDTD）. The uniaxial perfectly matched layer （UPML） medium is adopted for truncation of FDTD lattices, in which the finite-difference equations can be used for the total computation domain by properly choosing the uniaxial parameters. The rough surfaces are characterized with Gaussian statistics for the height and the autocorrelation function. The angular distribution of bistatic scattering coefficient from single-layered perfect electric conducting and dielectric rough surface is calculated and it is in good agreement with the numerical result with the conventional method of moments. The influence of the relative permittivity, the incident angle, and the correlative length of two-layered rough surfaces on the bistatic scattering coefficient with different polarizations are presented and discussed in detail.     

Rough surface scattering simulations using graphics cards

In this article we present results of rough surface scattering calculations using a graphical processing unit implementation of the Finite Difference in Time Domain algorithm. Numerical results are compared to real measurements and computational performance is compared to computer processor implementation of the same algorithm. As a basis for computations, atomic force microscope measurements of surface morphology are used. It is shown that the graphical processing unit capabilities can be used to speedup presented computationally demanding algorithms without loss of precision.     

Fast calculation technique for scattering in T-matrix method

In scattering calculations using the T-matrix method, the calculation of the T-matrix involves multiplication and inversion of matrices. These two types of matrix operations are time-consuming, especially for the matrices with large size. Petrov et al. [D. Petrov, Y. Shkuratov, G. Videen, Opt. Lett. 32 (2007) 1168] proposed an optimized matrix inversion technique, which suggests the inversion of two matrices, each of which contains half the number of rows. This technique reduces time-consumption significantly. On the basis of this approach, we propose another fast calculation technique for scattering in the T-matrix method, which obtains the scattered fields through carrying out only the operations between matrices and the incident field coefficient. Numerical results show that this technique can decrease time-consumption by more than half that of the optimized matrix inversion technique by Petrov et al.     

Experimental observations of the spectrum of light diffracted at a slit as a secondary source

In this paper, we investigated both theoretically and experimentally the normalized spectrum of partially coherent light radiated from a secondary source which is produced by an imaging system. The experimental results show that, if the imaging lens is achromatic, the normalized spectrum of the light radiated from a secondary source shifts either towards the red side or towards the blue side, compared to the spectrum of the source, and the spectral shifts change for different position of the observation points. It is found that the experimental results are consistent with the theoretical ones. A chromatic lens, acting as the imaging lens, is used to investigate the effect of the chromatic aberration on the normalized spectrum of the light field. The results show that the influence of the chromatic aberration on the normalized spectrum is considerable and cannot be neglected in high-precision spectral measurement experiments.     

Polarization-selective grating mirrors used in the generation of radial polarization

Two novel methods to control the polarization of laser radiation are presented. The discrimination between different polarization distributions isperformed with a corrugation grating in the top high-index layer of a multilayer mirror, which couples the undesired polarization into a lossy waveguidemode of the multilayer. The generation of radially polarized radiation in a laser resonator is presented as a practical verification of the principle.This revised version was published online in May 2005. The Article Category was removed.This revised version was published online in August 2005 with a corrected cover date.     

Phase control algorithms for focusing light through turbid media

Light propagation in materials with microscopic inhomogeneities is affected by scattering. In scattering materials, such as powders, disordered metamaterials or biological tissue, multiple scattering on sub-wavelength particles makes light diffuse. Recently, we showed that it is possible to construct a wavefront that focuses through a solid, strongly scattering object. The focusing wavefront uniquely matches a certain configuration of the particles in the medium. To focus light through a turbid liquid or living tissue, it is necessary to dynamically adjust the wavefront as the particles in the medium move. Here we present three algorithms for constructing a wavefront that focuses through a scattering medium. We analyze the dynamic behavior of these algorithms and compare their sensitivity to measurement noise. The algorithms are compared both experimentally and using numerical simulations. The results are in good agreement with an intuitive model, which may be used to develop dynamic diffusion compensators with applications in, for example, light delivery in human tissue.     

Anomalous reflection and excitation of surface waves in metamaterials

We consider reflection of electromagnetic waves from layered structures with various dielectric and magnetic properties, including metamaterials. Assuming periodic variations in the permittivity, we find that the reflection is in general anomalous. In particular, we note that the specular reflection vanishes and that the incident energy is totally reflected in the backward direction, when the conditions for resonant excitation of leaking surface waves are fulfilled.     

Large Positive and Negative Lateral Displacements from Total Internal Reflection Configuration with a Weakly Absorbing Dielectric Film

It is theoretically shown that the simultaneously large positive and negative lateral displacements will appear when the resonant condition is satisfied for a TE-polarized light beam reflected from the total internal reflection configuration with a weakly absorbing dielectric film. Appearance of the enhanced negative lateral displacement is relative to the incidence angle, absorption of the thin film and its thickness. If we select an appropriate weakly absorbing dielectric film and its thickness, the simultaneously enhanced positive and negative lateral displacements will appear at different resonant angles. These phenomena may lead to convenient measurements and interesting applications in optical devices.     

Spatial coherence properties of azimuthally polarized laser modes

Understanding of coherence properties of optical fields is of basic importance both in classical optics and in quantum physics. Coherence properties of electromagnetic laser modes are only now beginning to be explored and have not yet been tested experimentally, except in the simplest cases. In this paper, we first study theoretically the coherence properties of azimuthally polarized laser modes and we clarify the distinction between coherence and correlations in stochastic electromagnetic fields, a distinction which has up to now not been fully understood and has, in fact, been a subject of controversy. Our analysis clearly illustrates the distinction between these two concepts. After elucidating theoretically the coherence properties of radially polarized laser modes, we describe an experimental study of their properties, made by the use of a recently introduced reversed-wavefront Young’s interferometer. A good agreement between theory and experiment has been found.     

Negative refraction of ultra-short electromagnetic pulses

We study pulse propagation across a boundary that separates an ordinary medium from a medium with simultaneously negative dielectric permittivity and magnetic permeability. Solving Maxwell’s equations with two spatial coordinates (one longitudinal, one transverse) and time we find negative refraction as the wave packet undergoes significant and unusual shape distortions. The pulse acquires and maintains a chirp as it traverses the interface, as expected, but with a sign that is opposite to the chirp attained upon traversal into a positive-index material. Both a direct calculation of the spatial derivative of the instantaneous, local phase of the pulse and a Fourier analysis of the signal reveal the same inescapable fact: that inside a negative-index material, a transmitted, forward-moving wave packet is indeed a superposition of purely negative wave vectors. The central findings of this paper are a confirmation that causality is not violated in the short-pulse regime, and that energy and group velocities never exceed the speed of light in vacuum.     

Photonic band gap properties of GaP opals with a new topology

In this paper, we propose that the “anomalous” optical response exhibited by GaP and InP infiltrated opals is due to the peculiar morphology shown by these materials when grown within the pores. In order to account for their optical response, we propose a new structural model consisting of a network of high dielectric spheres located in the pores of the bare opal, interconnected by cylinders of the same material. A fair agreement between the theoretical predictions using this model and the experimental measurements has been found. We also show that the inverse structure presents very interesting optical properties.     

Rigorous electromagnetic analysis of dual-closed-surface microlens arrays

In this paper, we investigated the focal performance of the dual-closed-surface microlens arrays (DCSMAs) based on rigorous electromagnetic theory and boundary element method (BEM) in the case of TE polarization. The DCSMAs are designed with different substrate thickness and different distance between microlenses. DCSMAs designed according to different wavelengths are surveyed. The DCSMAs with different incident angles are also studied. Several focusing performance measures, such as the focal spot size, the focal position on the preset focal plane, the diffraction efficiency and the normalized transmitted power, are presented. Numerical results indicate the DCSMAs with different parameters can implement focusing beams and the focal performance of DCSMAs is easily influenced by the substrate thickness and the incident wavelength. Furthermore, the optimal thickness for the maximal diffraction efficiency of the DCSMAs is given. It is expected that the DCSMAs may be used as a parallel processing device in micro-optics systems.     

Coherent Beam Combining of Three Watt-Level Fiber Amplifiers Using a DSP-Based Stochastic Parallel Gradient Descent Algorithm

We present an experimental study on coherent beam combining of three watt-level fiber amplifiers using a stochas- tic parallel gradient descent （SPGD） algorithm. Phase controlling is performed by running the SPGD algorithm on a digital-signal-processor （DSP） chip with a voltage updating rate of 16500 times per second. Energy encircled in the target pinhole is 2.62 times more than that in an open loop. The combining efficiency is as high as 87%.     

Reply to “Comment on ‘The Imbert-Fedorov shift of paraxial light beams’”

This is a reply to the Comment by Bliokh on our paper that appeared in Opt. Commun. 281 (2008) 3427. After a brief introduction of the representation theory of vector electromagnetic beams advanced in a recent paper, I point out that the Imbert-Fedorov effect is the evidence of the change of the beam parameter Θ and the polarization ellipticity σ caused by the reflection or transmission process in the linear approximation. Then I explain that it is because the linear approximation of the incident beam that we used in our paper had been assumed in previous works that we reproduced their results.