Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides--II: Blazing effects

Grating-coupled radiation in lasers and waveguides is analyzed for trapezoidal-shaped grating teeth which includes all triangular shapes. A perturbation technique is used which involves calculating the modes in a geometry with an inhomogeneous refractive index profile in the grating region. Curves are presented for radiated power from traveling waves as a function of blazing angle, grating tooth height, refractive index, and grating period. It is shown that the ratio of power radiated into the outer media depends greatly on tooth shape and size. By judiciously selecting parameters this ratio can exceed 50:1.     

Analysis of second-order gratings

The results of an analysis of second-order gratings used as distributed Bragg reflectors in surface-emitting lasers are presented. The gratings provide reflection, output coupling, and power transmission to other gain segments for purposes of injection locking. The analysis determines these quantities for arbitrary-shaped grating teeth and includes the presence of a substrate reflector to reduce the radiated power in that direction. The reflector is shown to be effective, but only if it can be precisely positioned. Examples illustrating variations in dimensions, tooth shapes and heights, waveguide loss, and detuning are included. Second-order, square gratings, whose conventional coupling coefficient is identically zero, exhibit substantial reflectivity which is primarily produced by the radiation reaction. The analysis also forms the basis for calculating the far-field grating coupled radiation patterns     

Analysis of a dual grating-type surface emitting laser

The grating-coupled surface emitter (GSE) consists of a gain section between two grating sections, which are not necessarily identical. The gratings act as both distributed Bragg reflectors and output couplers. An analysis that applies to arbitrary grating shapes and has provisions to include the presence of a substrate reflector to reduce the radiated power into that medium is carried out. Thresholds, differential efficiencies, and far-field patterns are compared for the low-threshold longitudinal modes of the system. Examples illustrating variations in tooth shapes and heights, waveguide loss, the presence of a substrate reflector, and detuning from the Bragg condition are included     

Analysis of the blazing effect in second-order gratings

The validity of the blazing effect for improving the output-coupling efficiency of second-order gratings for use in grating-coupled surface-emitting lasers is examined. The Floquet-Bloch expansion method is used for the analysis of finite-length gratings with asymmetric tooth shapes operated in resonance condition. It is shown that for saw-tooth gratings the blazing effect is almost lost around the second-order Bragg wavelength because the reflected guide mode generated in the distributed Bragg reflector radiates preferentially into the substrate. By using a parallelogram grating with equal tooth and groove lengths, however, a high efficiency of radiation into the air is attainable even at the Bragg wavelength while the reflectivity is reduced     

Analysis of directional grating-coupled radiation in waveguide structures

Radiation scattered from diffraction gratings on the surface of waveguides is analyzed using the volume current method. This technique allows the interpretation of the grating elements as scattering centers of the underlying waveguide mode, and radiating sources for the diffracted fields. The framework allows separation of the effects of the grating array global periodicity and the effects of the specific shape of the individual grating elements. A straightforward analogy between the effects of the grating element shape and the behavior of phased-antenna array systems allows a clear and intuitive understanding of the effects of blazed gratings on the directionality of grating-coupled radiation. The analysis is applied to some specific geometries.     

Deep Gratings with a χ(2)Nonlinearity: Analysis and Solutions

Using a systematic approach based on a Bloch function expansion and the method of multiple scales, we present a rigorous derivation of the coupled-mode equations for light propagation through deep quadratically nonlinear gratings. The coupled-mode equations for deep gratings differ from those derived previously for shallow gratings in that the coefficients have different values and additional nonlinear terms appear. In the shallow grating limit these equations reduce to the standard coupled-mode equations. Our results show that deep grating effects can be significant in GaAs–AlAs thin film stacks, while in glass optical fibers these effects are too small to play a role. Using a standard shooting technique, bright soliton solutions to the new equations are obtained.     

Electromagnetic emission from two-dimensional plasmons in a semiconductor-dielectric structure with metal grating: Rigorous theory

The spectrum of electromagnetic (EM) radiation from two-dimensional(2D) plasmons in a semiconductor-dielectric structure with metal grating has been calculated in a strict electromagnetic approach. It is shown that radiation frequency and linewidth vary over a broad range of magnitude as a function of the grating parameters. The radiative decay linewidth is found to be two orders of magnitude larger than expected from the perturbation theory. Comparison of the results with previously published experimental data on 2D plasmons in GaAs heterostructures makes us conclude that the main contribution to the experimental decay linewidth arises from dielectric losses in the layers of the structure.     

Analysis of nonlinear grating couplers by singular perturbationtechnique

The properties of the nonlinear output and input grating couplers are analyzed by using the singular perturbation technique with the multiple space scales. We first introduce the perturbation parameter concerned with the nonlinear parameter and the grating depth. After the wave functions are expanded, the perturbation solutions to satisfy the equivalent boundary conditions are derived. From the solvability condition to have nontrivial solutions on each perturbation order, the nonlinear equations to describe the power leakage of the guided wave due to the second-order coupling to the first-order waves are obtained. The dependence of the radiated field and the input efficiency on the power are discussed numerically     

Nonorthogonal coupled-mode theory of grating-assisted codirectionalcouplers

Grating-assisted codirectional couplers are analyzed by a nonorthogonal coupled-mode theory. The coupled-mode equations are solved exactly, and the effects of all the space harmonics generated by the periodic gratings are included in the analysis. More rigorous relations among the grating period, the grating height, and the coupling length are established. The power exchange between the guides is investigated as a function of the propagation distance and the wavelength. A comparison with previous approximate solutions is made and discussed     

Surface emitting characteristics of silicon waveguides

This paper concerns the surface emitting characteristics of silicon waveguides in the millimeter-wave frequency band. The waveguides used in the experiment are rectangular slabs of high resistivity silicon (30,000 ohm-cm). A series of periodic perturbations on the waveguide surface provide a radiating antenna. A rectangular grating with a period of Λ=1.8 mm, a height of 0.35 mm, and a duty cycle of 0.46 was sawn into the top surface of a silicon waveguide with a width of 3 mm and a height of 1.41 mm. Experiments were performed to measure the attenuation, dispersion and the radiation characteristics of the waveguides. The test setup was used to monitor the frequency, radiation angle, and the radiated power. Measurements are made over a band of frequencies around the second Bragg frequency. The detector was scanned from 88–95 GHz and changes were observed in the attenuation constant, dispersion relation and the far field radiation pattern. From these results we were able to verify the grating theory.     

Frequency-scanned gratings consisting of photo-etched arrays

Frequency-scanned gratings consisting of periodic arrays of thin conducting elements are investigated. The principle used is to let the first higher-order diffracted wave propagate and serve as the frequency-scanned beam. The grating structures are designed for optimum blazing to the desired diffracted wave (i.e., for optimal power conversion from the incident wave to the diffracted wave) by the use of an iterative optimization process. Both reflection and transmission gratings are considered; the elements investigated are single dipoles and crossed dipoles. The theoretical analysis is based on Floquet's theorem and the method of moments. Several numerical examples are presented showing that this type of grating structure has a high blazing efficiency and is suitable for frequency scanning. The theoretical results are verified by comparison with experimental results     

Millimeter wave beams diffracted from reflecting gratings

According to the angular-spectrum method, a radiation beam of an antenna horn in the Fresnal region is decomposed into the plane waves with the fast Fourier transform algorithm and the waves diffracted from a reflection grating are superposed as a diffracted beam. Compared with the reflected beam from the same size mirror, the radiation half width of the diffracted beam from a grating is narrower and its lateral shape is shift. These performances have been experimentally verified at Ka-band by: (1). The relative diffraction efficiencies in the first order with two triangular gratings which is put along propagating direction of a beam produced by a conical lens-horn. (2). H-plane lateral width with power—3dB lapsed of the focus beam from a grating and a mirror in a grating spectrometer for millimeter waves (25–100 GHz).     

Polymer waveguide notch filter using two stacked thermooptic long-period gratings

A polymer waveguide notch filter using two stacked thermooptic long-period gratings is proposed. It is a long-period waveguide grating whose transmission spectrum can be dynamically controlled. Thermooptic index perturbation, i.e., grating is temporarily induced by two groups of periodic heaters stacked vertically on the filter surface. The periods of the two groups are determined such that two different resonance bands are generated in the spectrum by the respective groups. Thus, the overall spectrum may be actively shaped by controlling the individual power applied to the two groups. Its feasibility is demonstrated experimentally by fabricating it with thermocurable polymers.     

Generation of 1180 Å period gratings with a Xe ion laser

Holographic lithography with the 2315 Å line of a xenon ion laser is used to produce gratings in polymethylmethacrylate. An 1180 Å period grating is made and examined with a scanning electron microscope (SEM). This grating period is appropriate for use as a first-order grating with a GaAs distributed feedback laser     

Analysis of detuned second-order grating output couplers with an integrated superlattice reflector

Analysis is presented of second-order gratings at wavelengths detuned from the reflection bandwidth. These gratings have applications, for example, as surface-emitting output couplers in monolithic integrated master oscillator power amplifier (M-MOPA) configurations. The grating output couplers have reflectivities below 10/sup -4/ at an emission wavelength of 874 nm when the Bragg condition of the second-order grating occurs at 904 nm. When used in conjunction with a superlattice reflector integrated into the substrate, the surface emission can exceed 85% of the radiation incident on a 250 mu m long grating. Consequently, these gratings can act as nearly ideal output couplers in a M-MOPA without introducing undesirable feedback to the amplifier or master oscillator.<>     

Gain clamping in semiconductor optical amplifiers with second-order index-coupled DFB grating

A systematic investigation of gain-clamped semiconductor optical amplifiers (GC-SOAs) based on the second-order index-coupled DFB gratings is carried out by way of simulation. In particular, we focus on the main effects of the radiation loss caused by the first-order diffraction of the gratings on the amplifier performance. The magnitude of the total complex coupling coefficient is the main factor to determine the level of gain clamping. We demonstrate that a high-performance GC-SOA can be realized by using purely loss-coupled second-order DFB gratings with more relaxed tolerance on grating strength and period. It is shown that, in the presence of weak reflection-related coupling, the parasitic radiation loss associated with the second-order grating always helps to expand the linear amplification region and to reduce the longitudinal spatial hole burning along the cavity. Further, we demonstrate through comparison that the GC-SOAs have higher saturation power and much shorter carrier lifetime than the conventional SOAs. An improved design by longitudinal variation of the grating duty cycle is proposed such that the noise performance of the amplifier can be enhanced without much sacrifice on the linear amplification regime.     

Inverse black body radiation

The total power spectrum radiated by a black body with a given area-temperature distribution is given by Planck's law. The inverse black body radiation problem is thus the problem of determining the area-temperature distribution of a black body, given its (measured) total radiated power spectrum. The concept of a normalized absolute "coldness" as the (proportional to the) reciprocal of the absolute temperature is introduced, yielding an integral equation for the inverse black body radiation problem. This integral equation is solved analytically with the aid of the (inverse) Laplace transform and a very simple iterative process (the method of successive approximations) that converges in two iterations. Numerico-experimental results for the reconstruction of a Gaussian area-coldness distribution are presented.     

Radiation loss coefficients of asymmetric dielectric waveguides with shallow sinusoidal corrugations

Kiselev [10] has solved the boundary equations for an asymmetric slab waveguide with a shallow sinusoidal corrugation, and derived explicit, closed expressions for the TE radiation loss coefficients of various waveguide geometries. For many practical applications in integrated optics, the Rayleigh assumption justifying the boundary-matching procedure and the approximations of linear perturbation analysis employed in this derivation are both satisfied. We have extended this procedure to TM modes and found that the expressions for both TE and TM modes in all of the geometries so treated agree identically with those derived by coupled-mode theory. The dependence of the TM radiation loss coefficient in each waveguide geometry on the grating period, radiation angle, refractive index profile, and mode polarization is illustrated graphically, and compared with its TE counterpart.     

二元矩形位相光栅用于高斯光束的空间整形

本文研究了透射式二元矩形位相光栅实现高斯光束空间整形的基本原理,并作了理论推导;提出了光栅加工的技术指标,对实验工作作了具体描述,并分析了实验结果。透射式二元矩形位相光栅的主要技术指标为:栅槽宽度:1.5mm;栅槽深度:0.55μm;光栅有效尺寸:15mm;透射率:大于90%;波长覆盖:0.55μm～0.65μm;破坏阈值:平均功率10W。整形参数:功率效率:大于75%;能量效率:大于90%;衍射距离要求:大于10m;整形后光束强度的径向非均匀起伏:小于9.3%。     

折射率非线性调制的双重光纤光栅特性

利用耦合模理论 ,系统分析了双重光纤光栅在折射率深度调制或非线性调制情况下的光谱特性。结果发现 ,在折射率非线性调制情况下 ,双重光纤光栅具有规则的多波长反射特性 ,同时 ,其反射光谱中的二次谐波也变得非常强 ,因此 ,它是一种实现多通道波分复用器、分插复用器及多波长激光器等的潜在技术。