Eigenmode analysis of symmetric parallel waveguide couplers

An analysis of a laterally symmetric parallel waveguide structure has been carried out by using symmetric and antisymmetric eigenmodes in the coupled mode equations. As opposed to modes of each individual guide, eigenmodes are orthogonal and therefore comply with coupled mode formalism. Of particular interest has been the popular configurationZ-cut LiNbO3with Wave propagation along the crystalY-axis. The theory shows that output versus voltage characteristics are nonperiodic in voltage, and furthermore, they are asymmetric if the eigenmodes are not equally excited. The uniform electrode coupler can easily be explained in terms of eigenmode coupling and interference.     

Analysis of diode laser properties

An analytic model of diode lasers applicable to both the lasing and the nonlasing states is described. For these homogeneously broadened devices, spectral envelope widths for TE00and TM00modes are related to power in each modal family and are shown to depend critically on spontaneous emission coupling into the transverse modes. Thus, lasers with real-refractive index waveguiding (and associated weak spontaneous emission coupling) operate single longitudinal mode above threshold, whereas gain-guided devices run multimode. After connecting gain and spontaneous emission, a charge conservation equation, containing optical power in the form of a stimulated emission term, pumping current, spontaneous emission, and spectral width, is derived. These equations are then demonstrated to suffice for determination of the completeLversusIcharacteristic. For lasers in which both charge and mode confinement exist, such as the buried heterostructure (BH) and channelled-substrate narrow stripe (CNS) types, it is shown that both TM00power and spectral envelope width approach limiting values at threshold, whereas TE00mode power grows in conjunction with TE00spectral envelope narrowing.     

Harmonic analysis approach to the "TunneLadder": A modified Karp circuit for millimeter-wave TWTA's

A field approach to the summed harmonic analysis of the "TunneLadder" structure--a modified forward-wave Karp circuit-is developed by Combining TM01and TE11modes. Results suggest the suitability of this structure as a high impedance, about 1-percent bandwidth circuit, millimeter-wave forward-wave-type amplifier that is voltage tunable over about a 5-percent frequency range and has excellent power handling ability. Theory gives good agreement with experimental results obtained by Karp in ω-β dispersion and predicts qualitatively the appearances of the antisymmetric mode discussed and of the so called "Hightron" mode that was discussed earlier in [7] and [8], in addition to the desired symmetric mode.     

Coupling between closely spaced back-to-back paraboloidal antennas

Using the geometrical theory of diffraction (GTD), a method of calculating the power coupling between closely spaced back-to-back paraboloidal antennas is presented. The method is illustrated by considering the coupling between two identical front-fed symmetric paraboloids, each of which is fed by a TE11mode circular waveguide.     

Plasmonic States From Visible Light to Microwaves

Plasmonics is a phenomenon often considered in the visible light and near infrared, whereas typical metal waveguide modes are studied in the microwave regime. We demonstrate how plasmonic modes become conventional waveguide modes as the frequency varies from visible light to microwaves. In particular, given the metal permittivity at microwaves, the plasmonic dispersion becomes the conventional waveguide dispersion. Moreover, the surface plasmon dispersion at a single metal/insulator boundary can be extracted over a metal/insulator/metal (MIM) heterostructure if the metal-to-metal spacing is taken infinite. In doing so, the coupling effect of plasmonic modes is clearly revealed. As the symmetric coupled plasmon mode is known to correspond to the TEM $({hbox{TM}}_{0})$ mode, we found that the antisymmetric coupled surface plasmon mode is essentially related to the ${hbox{TM}}_{1}$ mode.      

Output coupling for closely confined Pb1-xSnxTe double-heterostructure lasers

The output coupling of an idealized, symmetric model of a double-heterostructure (DH) laser is analyzed theoretically using parameters suitable to Pb1-xSnxTe. For the TEOmode incident at the laser mirror and for thin optical guiding regions such that only the TEO, TE1, TMO, and TM1modes may propagate, an exact formulation of the coupling problem is obtained including mode coupling at the mirror into the continuum of unguided radiation modes. Using this formulation, the power reflection and transmission coefficients, the fraction of incident power coupled into the radiation modes, the mirror illumination, and the far-field pattern are calculated for typical parameters. Significant mode coupling can occur, limiting the maximum external efficiency of such lasers. This and other potentially undesirable characteristics resulting from close optical confinement, such as large output beam divergence, must be considered in design criteria for DH structures in this alloy system.     

A note on gyrotron traveling-wave amplifiers using rectangular waveguides

The coupling constant ε between a relativistic electron beam and the TE10rectangular waveguide mode is calculated. By reducing the height of the waveguide, this coupling constant may exceed the corresponding value for the operation with the TE11circular polarized mode, under identical conditions of the electron beam. The calculation is followed by a discussion on optimum mode choice in gyro-TWA's.     

Modes of a symmetric slab optical waveguide in birefringent media, part II: Slab with coplanar optical axis

We study the modes of a symmetric thin-film slab waveguide composed of birefringent crystalline material in the film and in the equivalent substrate and superstrate. In addition we assume that the optical axes of the uniaxial materials of film and substrate are parallel to each other and also parallel (coplanar) to the plane of the film. This simple anisotropic waveguide has interesting properties. It supports only hybrid modes but in the limit of propagation along the optical axis and at right angles to it the modes become almost of the TE and TM type. Moreover, some of the modes become leaky waves as they propagate at increasingly larger angles relative to the optical axis of the dielectric material. For guides made of materials whose ordinary refractive index nois larger than the extraordinary index ne, the extraordinary wave modes, which approximate TE modes, become leaky; and forn_{e} > n_{o}, the ordinary wave modes, which approximate TM modes, become leaky. The leakage losses are large near a "critical angle," where leakage begins to appear but may be insignificant at larger angles, measured between the optical axis and the direction of propagation.     

Far-infrared guided wave optics experiments with anisotropic crystal quartz waveguides

The TE and TM modes of anisotropic dielectric waveguides of crystal quartz have been studied in the far infrared using an optically pumped waveguide laser with a hybrid output mirror. Using Si and Ge prism couplers, excitation efficiencies of 56 percent of the theoretically calculated values were obtained for the TE0mode. The measured propagation constants were found to agree closely with theory when the perturbation of the guided modes by the prism couplers was included. The attenuation constant for the TE0mode atlambda_{0} = 496.1mum was found to be as low asalpha_{TE_{0}} = 0.05cm^-1. A metal grating coupler for backward-wave coupling through a prism shaped TPX plastic substrate was also used to couple 89 percent of the guided energy in the TE0mode out of the waveguide in the reverse direction.     

The Ubitron, a high-power traveling-wave tube based on a periodic beam interaction in unloaded waveguide

The Ubitron is a high-power traveling-wave tube which makes use of the interaction between a magnetically undulated periodic electron beam and the TE01mode in unloaded waveguide. The electron-wave interaction exhibits the same type of first-order axial beam bunching characteristic of the conventional slow-wave traveling-wave tube; hence, it can be used in place of conventional O-type interaction in extended interaction klystrons and electron accelerators, as well as traveling-wave tubes. Experimental results are presented for the simplest physical embodiment of the Ubitron, which consists of an undulated pencil beam in a rectangular waveguide. Two of the unique features of this tube are very broad interaction bandwidth which results from the absence of a dispersive slow-wave circuit, and variable interaction phase velocity--hence, variable saturation power level. Among the physical embodiments of the Ubitron are a number of higher-order mode waveguide and beam configurations. These include plane, coaxial, and circular waveguides, all supporting the TE01mode, interacting with magnetically undulated sheet, hollow and cylindrical beams, respectively. The advantage of these configurations, which have not yet been tested experimentally, is that they provide a very large interaction area for beam placement. This property, plus the fact that the peak interacting field is far from the waveguide walls, makes the Ubitron an interesting prospect for high-power millimeter wave amplification.     

Channeled substrate nonplanar laser analysis--Part II: Lasers with tapered active regions

Light versus current (LversusI) characteristics are calculated for double-heterostructure diode lasers whose active regions decrease in thickness laterally from a maximum on axis. This variation produces lateral real refractive index waveguiding which in turn stabilizes the spatial mode such that the modal field becomes anastigmatic and theLversusIplot becomes linear. In addition to determining threshold current and differential quantum efficiency, we compute the TE00mode patterns, active region charge density distribution, and the power levelP*_{1}at which spatial hole burning causes the TE01mode to begin lasing. The maximum power density at the facet for that power levelP*_{1}is also obtained. All these characteristics are presented as functions of the various device parameters including carrier spontaneous recombination time, diffusion length, optical gain, unpumped band-to-band absorption, internal losses, antiguidance index, wavelength, cladding Al content, active region dimensions, current spreading resistance, facet reflectivity, laser length, and stripe width. Utilizing this information, a design is developed for a laser with low threshold current (40-50 mA) and high differential quantum efficiency (50-65 percent) that operates stable single lowest order (TE00) spatial mode to powers well in excess of 50 mW.     

Nonlinear waves in saturable self-focusing thin films bounded bylinear media

Nonlinear guided wave behavior in the symmetric and asymmetric versions of an optical waveguide is studied. The waveguides are made to cut off at low field intensities by a step-index decrement in the dielectric constant of the film relative to those of the bounding media. The influence of this decrement on solutions of the TE₀ mode is calculated. The mode index variation of the asymmetric solution in the symmetric waveguide is shown to depend strongly on the index decrement as well as the saturation level. By making the media bounding the film have sufficiently different dielectric constants, only one solution is shown to be obtainable. This solution is followed both on the locus diagram relating the field intensities on the film boundaries and on dispersion plots     

Coupled-mode analysis of highly asymmetric directional couplerswith periodic perturbation

This paper presents an in-depth analysis of highly asymmetric grating assisted directional couplers. The directional coupler consists of a polymer waveguide with dimensions and refractive indices closely matching a single-mode fiber fabricated atop a Ga_0.6Al_0.4As/GaAs/Ga_0.4Al_0.6 As waveguide. The structure is investigated analytically by means of a new orthogonal coupled-mode theory formulated in terms of the Lorentz reciprocity theorem. For the first time, the analysis includes three distinct loss mechanisms, namely, the leakage of power toward the semiconductor substrate, the power lost to radiation modes (mode mismatching), and the grating radiation loss     

Analysis of stripe multilayer waveguides with effective index andfinite element methods

An algorithm for a fast and accurate analysis of stripe multiple quantum well (MQW) waveguides is presented. The technique is based on the combination of effective index and finite element methods. The stripe MQW structure is replaced by an equivalent planar waveguide, using the effective index method to derive the (refractive index) profile of the planar guide from the original problem. The propagation constants and field intensity profiles of E_mn^X and E_mn^Y modes for the equivalent structure are then calculated with the one-dimensional finite element method. The results obtained with this technique are presented for both symmetric and asymmetric stripe MQW structures with an arbitrary number of wells. Propagation characteristics obtained for a six-well MQW waveguide are in good agreement with those evaluated (for comparison) using full two-dimensional finite element analysis     

Analysis of doped layer step waveguides using dark modes

Results for the analysis of index profiles in steplike waveguide layers formed by proton exchange in LiNbO₃ and epitaxially grown Ge-doped quartz are presented. Modeling of the profile with real modes is difficult unless many modes propagate. However, an analysis which includes the substrate modes recorded in dark mode measurements greatly increases the data and hence the confidence in the model of the index profile. Analysis using a reflectivity function provides the required precision. The data demonstrate that the epitaxial GeO₂ -doped layer has an index variation with depth     

Flatband Slow Light in Asymmetric Line-Defect Photonic Crystal Waveguide Featuring Low Group Velocity and Dispersion

In this paper, an asymmetric photonic crystal (PC) waveguide is proposed for slow light transmission. A row of air holes is removed to form a line-defect waveguide, and the lateral symmetry of the waveguide is broken by shifting the holes in the PC cladding on one side along the waveguide axis. Two structural parameters are carefully adjusted: the amount of shift compared with the array of holes in the cladding on the other side, and the radius of the holes closest to the waveguide core in the shifted PC cladding. In the asymmetric waveguide, it is possible to obtain flat band modes with low group velocity (c/50) and low dispersion (on the order of 10⁴ ps²/km) over a signal bandwidth of 40 GHz. The delay-bandwidth product (DBP) of the proposed slow-light device is analyzed and compared with the DBP of the PC waveguides reported in literatures. We find that our structure yields a significant increase in DBP, and improves the effective bandwidth in which we can obtain slow modes with both low group velocity and vanishing dispersion.     

An approximate expression for the effective refractive index in symmetric DH lasers

Using a variational method and an approximate equation for the confinement factor, a simple expression for the effective refractive index of the TE0modes in a symmetric double heterostructure (DH) laser is obtained. The relative error is smaller than 1.2 percent. Its applications are discussed.     

Losses in optical waveguide formed by silver-sodium ion exchange

Propagation losses of optical waveguides formed by ion exchange from molten salts of silver nitrate are discussed. The refractive index in pyrex glass substrates is shown to obey an exponential profile and the resultant mode functions are also examined for the graded-index surface waveguide in order to understand the mechanism of a scattering loss. The attenuation of the sample waveguides is found to range from 2.0 to 2.5 dB/cm for TE0mode excitation and to be decreasing with increasing both the mode number of the guided beam and the waveguide thickness that is proportional to a square root of diffusion time. These results indicate that the predominant loss origin is silver ion concentration diffused in the glass.     

808 nm大功率无铝有源区非对称波导结构激光器

采用分别限制非对称波导结构,将光场从对称分布变为非对称分布,降低了载流子光吸收损耗,并允许p型区具有更高的掺杂水平,从而使器件电阻降低.对GaAsP/GaInP张应变单量子阱(SQW)非对称波导结构激光器的光场特性进行了理论分析,设计了波导层厚度,并制作了波长为808 nm的无铝有源区大功率半导体激光器.器件综合特性测试结果为:腔长900μm器件的阈值电流密度典型值为400 A/cm2,内损耗低至1.0 cm-1;连续工作条件下,150μm条宽器件输出功率达到6 W,最大斜率效率为1.25 W/A.器件激射波长为807.5 nm,平行和垂直结的发散角分别为3.0°和34.8°.20~70℃范围内特征温度达到133 K.结果表明,分别限制非对称波导结构是降低内损耗,提高大功率半导体激光器特性的有效措施.     

Coupling efficiency of waveguide laser resonators formed by flat mirrors: Analysis and experiment

We present a new and more efficient method of calculating the losses of a waveguide laser resonator consisting of a hollow circular dielectric waveguide and flat mirrors, taking into account the effects of waveguide modes up to order HE13. Both symmetric and asymmetric cavities are considered. We show that low cavity losses, only slightly exceeding the HE11waveguiding losses, are predicted to be possible for much larger mirror distances than had previously been suspected, provided that an optimum total cavity length is chosen. The low losses arise when the HE11and HE12modes emerge from the guide with relative amplitudes and phases such that the returning diffraction patterns interfere to produce a narrow beam with low aperture losses. The theoretical predictions were checked experimentally for CO2lasers having various waveguide dimensions. Good qualitative agreement was found, but the optimum total cavity lengths were typically 3-5 percent longer than predicted. Possible explanations of this discrepancy are discussed. We also predicted and experimentally verified that variations of the cavity length over a few centimeters can exert a coarse wavelength selectivity sufficient to determine the band and branch on which a CO2laser oscillates; conversely, that for a grating tuned laser, the cavity length must be varied by a similar amount as the wavelength is tuned in order to maintain low cavity losses over the entire wavelength range.