The design of triple rib waveguide couplers by the discretespectral index method

The operations of three-guide couplers are usually controlled by the width and refractive index of the guides. However, when rib waveguides are used in three-guide couplers and power dividers, we propose to use the dimensions of the ribs as the governing parameters instead. Formulating a new transcendental equation using the discrete spectral index (DSI) method, triple rib waveguide couplers are accurately analyzed for the first time. The new accurate and fast analysis of triple rib waveguides shows that the propagation constants of the various modes are dominantly controlled by the height of the middle rib. A systematic and simple procedure is consequently introduced to design quasi-transverse electric (TE) polarized triple rib waveguide couplers, which ensures maximum power transfer from one outermost guide to the other outermost guide. For triple rib power dividers, the height of the middle rib is found to control the amount of power that can be transferred from the excited middle rib waveguide to the two outer rib waveguides. Maximum power division is achieved when the three ribs of the waveguide are identical     

Field configurations and propagation constants of modes in hollow rectangular dielectric waveguides

The field configurations and propagation constants of linearly polarized low-loss modes in hollow dielectric waveguides with rectangular cross section are computed analytically under the assumption that the dimensions of the rectangular cross section are much larger than the free-space wavelength. The attenuation constant is then equal to the sum of the corresponding TE- and TM-mode attenuation constants in parallel-plate waveguides.     

Compact electro-optic polarization scramblers for opticallyamplified lightwave systems

Fast polarization scramblers have become important components in optically amplified transoceanic communication systems to eliminate anisotropic gain saturation (polarization hole burning) in the erbium-doped fiber amplifiers by depolarizing the launched optical carrier. This paper reviews the operation and implementation of compact electro-optic polarization scramblers on x-cut and z-cut lithium niobate. These integrated-optic devices employ low-loss single-mode waveguides and allow polarization modulation at variable frequencies ranging from a few 100 Hz to more than 10 GHz. We describe simple linear phase retarders that depolarize light in a fixed, well-maintained polarization state as well as cascaded multi-stage scramblers that are capable of depolarizing arbitrarily polarized light. These scramblers can be operated over a broad optical bandwidth of more than 40 nm with less than 5% residual degree of polarization and are further wavelength-tunable over more than 100 nm     

Birefringence in magneto-optical rib waveguides made by SiO2/TiO2 doped with γ-Fe2O3

Magneto-optic waveguides are the basic elements for nonreciprocal integrated optics; the phase matching between the fundamental TE and TM modes is an essential condition in magneto-optic waveguides. This condition can be satisfied with selected geometries planar or rib waveguides. We simulated the performance of such devices and determined the waveguide dimensions (height, width, and etching depth) that would allow the same propagation constants for both polarizations TE and TM.     

Investigation of polarization dispersion in long lengths of single-mode fiber using multilongitudinal mode lasers

We have used multilongitudinal mode lasers to investigate the polarization properties of long lengths of single-mode fiber cable. We find that the individual longitudinal modes are >99-percent polarized after propagation through 54.6 km of cabled fiber; however, the different longitudinal modes have different states of polarization at the output. This difference is caused by polarization dispersion, and we estimate a propagation delay difference for the two principal states of polarization to be 0.42 ps in the 54.6 km of cabled fiber.     

Unidirectional magnetooptic polarization converters

Inclination of the bias magnetization in a magnetooptic waveguide yields both nonreciprocal phase shifts and polarization conversion. This enables the design of unidirectional polarization converters, i.e., waveguides that switch between orthogonal polarizations for one direction of light propagation, but keep the polarization state for light propagating in the opposite direction. Simulations of double layer raised strip waveguides show that these constraints can be met with properly adjusted geometries. The results lead to the proposal of a polarization independent integrated optical circulator based on two unidirectional polarization converters between a front and a back polarization splitter     

Analysis of polarization independent Mach-Zehnder-type integratedoptical isolator

This paper proposes, for the first time, an integrated optical isolator independent of light polarization. A Mach-Zehnder interferometer (MZI) with two nonreciprocal phase shifters, one for transverse electric (TE) modes and another one for transverse magnetic (TM) modes can be adjusted so that it blocks the fundamental modes of the waveguides constituting the interferometer propagating in one direction and is transparent for the modes propagating in the opposite direction. If the interferometer branch waveguides are in single mode regime, the performance of the device will not depend on the polarization of incoming light. The nonreciprocal phase shifters can be realized on structures with magnetization tangential to the propagation direction. Three geometries of nonreciprocal phase shifters are discussed and tolerances are estimated     

High-power TE11 and TM11 circular polarizers in oversized waveguides at 70 GHz

Elliptical deformation of oversized, smooth-wall circular waveguides can produce choosable elliptical or circular polarization from a linearly polarized TE11 or TM11 mode used as intermediate linearly polarized modes in TEO1 to HE11 mode conversion sequences in electron cyclotron resonance heating (ECRH) of magnetically confined thermonuclear fusion plasmas with high-power gyrotrons. Mode coupling in elliptically distorted overmoded circular waveguides has been studied theoretically and experimentally in order to optimize TE11 (and TM11) polarizers (I.D.=27.79 mm) for the 1 MW/70 GHz long-pulse (3s) ECRH system on the Garching Stellarator W VII-AS. Coupling coefficients for ellipticity coupling of non-degenerate modes are given (coupled-mode differential equations formalism). The polarization converters essentially consist of smooth-wall circular waveguides which are gradually squeezed. A sine-squared function of the length coordinate is used to get an almost elliptical crosssection in the middle and circular cross sections at both ends. Arbitrary elliptical polarization states can be generated introducing an extremely low level (<<1%) of undesired spurious modes. Well defined differential phase characteristics have been achieved.     

Effects of Two-Photon Absorption on Pump-Induced Refractive-Index Change in AlAsSb–InGaAs–AlAs Optical Waveguides

Injection of transverse-magnetic polarized 1.55- mum pump light pulses having an excessively high intensity into heavily-doped AlAsSb-InGaAs-AlAs coupled-double-quantum-well optical waveguides causes a large amount of electrons in the ground state of the subbands in the conduction band to transit to the excited state and results in bandgap shrinkage as well as a large amount of vacant sites in the ground state. Consequently, the simultaneously injected continuous-wave transverse-electric polarized 1.54- mum probe light is absorbed by the valence-band electrons through two-photon absorption (TPA) and transit to the vacant sites in the ground state of the subbands in the conduction band. As a result, the probe power is reduced instantaneously but recovers at a time constant in the order of 10^-10s. A theoretical evaluation of the effect of the above intersubband-pump-assisted TPA of the probe light shows that the pump-induced net refractive-index change in these devices is reduced by 50% when intersubband absorption and ISB-pump-assisted TPA of the probe light are of equal strength. Characterization of the TPA in these devices indicates that these devices have a TPA coefficient of 25 cm/GW.     

Scattering at a Junction of Two Waveguides with Different Surface Impedances

We consider junction of two cylindrical waveguides and derive the scattering matrix when a single mode is incident in one of the two waveguides. We are interested primarily in the case of two corrugated waveguides with different longitudinal impedances, but the analysis applies also to waveguides with nonzero transverse impedances. It is shown that, under certain general conditions the infinite set of equations specifying the junction scattering coefficients can be solved exactly by the residue-calculus method. Very simple expressions are then obtained between the scattering coefficients and the propagation constants gamma/sub n/ and y/sub i/ of the modes in the two waveguides. These expressions, obtained previously only in special cases, are direct consequences of certain simple relations derived here for the coupling coefficients between the modes of the two waveguides. In those cases in which the scattering coefficients cannot be determined exactly, we determine them approximately by a perturbation analysis.     

A simple and accurate model analysis of strip-loaded opticalwaveguides with various index profiles

A simple first-order perturbation approach has been developed to study the propagation characteristics of strip-loaded diffused waveguides with various refractive index profiles. Propagation constants of the guided modes of rib waveguides and strip-loaded waveguides with exponential and Gaussian refractive index profiles are obtained. The results are in good agreement with those reported in the literature that were obtained by variational and numerical techniques. The presented technique provides analytical expressions for the modal field profile that should be useful in the design of various integrated optical devices     

Flexible,Low-loss Waveguide Designs for Efficient Coupling to Quantum Cascade Lasers in the Far-infrared

We coupled linearly polarized and azimuthally polarized Terahertz quantum cascade lasers (QCLs) to the low-loss optical modes of hollow core waveguides having a sequence of different metallic or dielectric inner coatings. The latter waveguides have been specifically designed to force the propagation of a dominant optical mode once the thickness (d) of the inner dielectric coating is properly chosen. Our results demonstrate that both the TE01 and the TE11 modes can be easily converted to a hybrid one when d > 6 μm allowing the propagation of THz QCL beams with transmission losses as low as 1.5 dB/m, bending losses < 1.1 dB and reasonably high coupling efficiencies (87%).     

Propagation and radiation characteristics of the circular electric,circular magnetic and hybrid waveguide modes

The field distributions and propagation constants of the circular electric, circular magnetic and hybrid modes of oversized waveguides are expressed, taking the effects of walls into account. These effects are described by wall functions which depend on surface impedances of the wall, and are determined for different types of guides. The near and far field patterns are derived in the case of real wall functions. It is shown that, for very oversized waveguides, the terms containing wall functions can be ignored in the calculations, and it results that the expressions of fields and propagation constants become independent of the types of waveguides. An application to corrugated waveguides for Electron Cyclotron Resonance Heating experiments shows the variations of the radiation characteristics versus geometric parameters of the corrugations and determines the ranges of interest for these parameters.     

Simple Broadband Circular Polarizer in Oversized Waveguide

In this paper, a possibility is shown to realize a simple waveguide polarizer producing nearly the same circular polarization over a broad frequency range up to an octave. It is based upon the combination of two smoothly squeezed oversized waveguides with different diameters. The principle is similar to an achromatic lens in optics, where two counteracting lenses with differently sloped wavelength dependencies of the refractive index are combined to compensate the dispersion in the desired wavelength range. Consequently, two different wavelengths of light are brought into focus at the same plane. A waveguide for the transmission of microwaves has a similar frequency dependence of the refractive index resulting in a frequency-dependent phase shift between two propagating waves polarized along the symmetry axes of a waveguide with an elliptical cross section. For this reason, an incident wave with a linear polarization between the axes of symmetry can be only converted into a circularly polarized wave over a limited frequency range. However, the diameter and the shape along two counteracting squeezed waveguides can be adjusted in such a way that the frequency dependence of the resultant phase shift is finally canceled out.     

Propagation in Rectangular Waveguides with Arbitrary Internal and External Media

The propagation characteristics of electromagnetic waves in a rectangular waveguide of a homogeneous medium embedded in a different medium have been found approximately. The total field is assumed to consist of four crossing plane waves interconnected at the boundaries by reflection matrices. The method is more accurate than other approximate techniques. New results are presented for tunnel propagation and attenuation of degenerate modes in metallic waveguides.     

Waveguide and resonator perturbation techniques measuring chiralityand nonreciprocity parameters of biisotropic materials

Waveguide and resonator perturbation techniques are considered for determining electromagnetic parameters of general biisotropic, or nonreciprocal chiral, materials. The bisotropic materials are the most general linear isotropic media, whose constitutive relations are governed by four complex material parameters. The material parameters of bisotropic media can be obtained through measuring the change in the propagation constant of waveguide modes or measuring the shift in the resonant frequency for resonators with perturbation techniques. To measure these parameters a method utilizing waveguides or cavity resonators with two degenerate modes is proposed     

Wave Propagation and Attenuation in the General Class of Circular Hollow Waveguides with Uniform Curvature

A general method has been developed to evaluate the propagation constant in oversized circular hollow-core waveguides characterized by a surface impedance and admittance due to a uniform bend. Completely different formulas are obtained for the attenuation constants of the modes in metallic or dielectric hollow waveguides from those obtained by Marcatili and Schmeltzer. Electric-field lines are also presented for several lower order modes in bent waveguides.     

Anisotropic fiber couplers with nonaligned optical axes

Evanescent-type couplers composed of identical anisotropic cores with nonaligned stress axes reveal interesting propagation characteristics, such as power transfer occurring on two different length scales and reduced polarization holding capacity. The four normal modes have different propagation constants and electric field vectors which are skew to each other     

Semivectorial beam-propagation method for analyzing polarized modesof rib waveguides

The authors report a semivectorial beam-propagation method which can determine the form birefringence in rib or channel waveguides. In this approach, a finite-difference equation is solved by using the alternating-implicit method to simulate the propagation of the optical beam. Since boundary conditions are incorporated into the finite-difference equation, polarized modes can be simulated. Numerical results on three well-known rib waveguides are presented with comparisons to published data     

Random coupling theory of single-mode optical fibers

A random coupling theory is developed for analyzing the propagation characteristics of the polarization state of light in single-mode optical fibers (including conventional and polarization maintaining fibers) under random disturbances. The basic idea is that the disturbances that a fiber suffers in practice continuously change with time and space, so time-varying coupling will occur along the fiber between two linearly polarized modes HE₁₁ that may propagate in the fiber. A coupled-mode equation of single-mode fibers under random disturbances is derived and solved rigorously with few assumptions. A random coupled-mode equation is derived considering time and space variation. Analytic solutions are obtained and used for analyzing the effect of random birefringence, polarization dispersion, polarization fluctuation, and evolution of the degree of polarization in single-mode fibers and for characterizing fiber properties