Hollow dielectric waveguide for distributed feedback lasers

Hollow dielectric waveguides with gas-filled core and a dielectric tube seem promising as laser structures. The tube fulfills the dual role of a guidance structure for the electromagnetic radiation as well as that of a container for the plasma of the gas laser. Feedback for laser oscillation is achieved by providing coupling between forward- and backward-traveling modes by means of periodic ripples of the inner surface of the hollow dielectric tube. This paper is devoted to the derivation of the coupling coefficients between two guided modes that are coupled by ripples in the tube wall. The calculation is based on the model of a slab waveguide. Expressions for the leaky-mode losses and the scattering losses inevitably introduced by the coupling mechanism are also presented.     

硅基波导光栅耦合器与波导传输损耗的研究

对硅(Si)基波导光栅耦合器的设计与耦合性能进 行了研究。采用本征模展开法对光栅耦合器进行设计与 优化,通过实验测量了光栅的耦合性能,并对均匀光栅、自聚焦光栅和反射光栅等3种光栅 耦合器的耦合 性能进行了比较,耦合效率分别达到了达到47.86、56. 36和48.98%,自聚焦光栅可以有效改善光纤到 光纤的传输效果,耦合效率提高了8.5%。通过实验测量了基于耦合光 栅技术的Si基条形波导和槽型波导的 传输损耗,结果显示,条形波导和槽型波导的传输损耗分别为2.34d B/cm和6.31dB/mm。     

TE modes of graded-index slab waveguides

An analysis of the TE modes of a slab waveguide with graded refractive-index distribution is presented. The refractive index is approximated by a piecewise-linear distribution for which exact solutions of the guided-wave problem can be obtained. For multimode guides, useful approximate solutions can be worked out with the help of the Wentzel-Kramers-Brillouin (WKB) approximation. A formula is given for the total number of guided TE modes supported by the waveguide. The coupling efficiency of a prism coupler is investigated by studying the radiation losses of the guided modes escaping from the waveguide through the coupling prism. It is found that the radiation losses of the modes of the graded-index waveguide are more nearly constant than those of the asymmetric slab waveguide.     

Improved coupled-mode formulation based on composite modes forparallel grating-assisted co-directional couplers

An improved coupled-mode formulation based on the ideal modes of the coupled waveguides (ideal composite modes) is presented. In comparison with the formulation based on the ideal modes of the individual waveguides (ideal waveguide modes), the formulation in terms of composite modes is more rigorous and yields a more accurate grating period and coupling lengths. In addition, the radiation loss due to input and output junctions can in the composite-mode formulation. A new to the coupled-mode equations is derived in which all the spatial harmonics generated by the periodic grating are taken into account. The power exchange between the waveguides is examined by considering the input and the output conditions. The phase-matching conditions and the coupling lengths are calculated and compared with the analysis in terms of the waveguide modes. The grating period predicted by the waveguide-mode formulation agrees very well with that by the composite-mode formulation; however, dramatically different coupling lengths are predicted by the two formulations     

Out-of-plane losses of line-defect photonic crystal waveguides

A numerical model is presented for computing the out-of-plane losses of a general class of two-dimensional photonic crystals superimposed. onto a slab confinement structure. The usefulness of this model is demonstrated by calculating the propagation loss of a single-row-defect waveguide composed of hexagonal air holes etched into two different slab structures. The results are interpreted in terms of a simple coupled-mode-theory picture in which loss is due to resonant coupling between the fundamental and certain radiative slab modes. These calculations show that low-loss photonic crystal waveguides should be possible by carefully designing the slab waveguide     

Pseudoreversibility condition for minimizing radiation loss at discontinuities of coupled waveguides

A design condition is derived for lossless discontinuities of coupled waveguides by finding solutions, which satisfy time reversibility of guided modes. The derived condition is used as a bound for minimizing radiation loss. Even when there is strong coupling between guided modes, the radiation loss can be minimal. A comparison between different grating designs in a 2 /spl times/ 2 backward coupler demonstrates that two coherently coupled gratings can significantly reduce radiation loss, as compared to a single grating.     

Directional couplers made of nonidentical asymmetric slabs. Part I: Synchronous couplers

We discuss TE and TM mode directional couplers made of nonidentical asymmetric slab waveguides. Approximate expressions are provided for the coupling coefficients of synchronous (no grating) couplers and their accuracy is checked by comparison with exact solutions that are based on solving the guided mode problem of the total structure consisting of the two slabs considered to be a single waveguide.     

Energy loss in a planar waveguide caused by a high refracting andabsorbing overlay

An explanation of the mode behavior in dielectric waveguides with an absorbing, high-refractive-index cladding is given. By considering the total waveguiding system as two separate waveguides, it is possible to attribute the behavior of the complex refractive index of the guided modes to the mixing of the modes of both waveguides. For systems with absorption, so-called quasi-leaky waves are observed in the total system for finite thicknesses of the overlay. For absorptionless systems these leaky waves are found only for infinite thicknesses of the overlay. The occurrence and behavior of these quasi-leaky waves versus the increasing overlay thickness are interpreted. A method for calculating the coupling efficiency of modes at the junction unclad waveguide-clad waveguide, taking into consideration waveguides with absorption, is presented. An experimental method for measuring the absorption coefficient for the guided modes in the cladded waveguide and the coupling losses at the unclad-clad waveguide junction was developed. The measured values are in a good agreement with the theoretical calculations     

Improved coupled mode analysis of corrugated waveguides and lasers

Corrugated waveguides and lasers in resonant and non-resonant situations are analyzed by an improved coupled mode theory based on a set of the coupled mode equations for guided modes and radiation continuum. The distributed feedback (DFB) coefficient and the radiation loss coefficient are given in closed forms. The formulation can be applicable to arbitrarily shaped gratings and multilayer waveguide structures. The accuracy of the theory is examined by comparing it with Tamir's exact calculation for a nonresonant situation and also with Streifer's one for a DFB structure. Reasonable accuracy is obtained by the proper choice of the unperturbed waveguide parameter. The dependence of the two coefficients on the grating depth, the grating period, the guide layer thickness, and the refractive index difference between core and cladding layers is obtained for all Bragg orders up to the fourth, and for four typical grating shapes, namely, for rectangular, sinusoidal, symmetric triangular, and sawtooth gratings. Both the threshold gain of DFB lasers utilizing higher order Bragg reflection and the output coupling efficiency of grating beam couplers are also calculated for these parameters. A new multilayer structure for controlling the radiation loss is proposed and analyzed. This structure is suitable for the suppression of the radiation loss in DBR reflectors as well as for the improvement of the output coupling efficiency in grating beam couplers.     

Properties of the slab modes in photonic crystal optical waveguides

We show that by placing a slab of semiconductor material between two photonic bandgap (PBG) mirrors, waveguide modes at frequencies out of the PBG can be obtained. These modes are similar to the modes of a conventional dielectric slab waveguide. Using these modes, we can obtain very good coupling between a PBG waveguide and a dielectric slab waveguide with similar slab properties. We discuss the properties of these slab modes and outline the guideline for the optimization of the PBG waveguides based on these properties     

On the Theory of Corrugated Optical Disk Waveguides

The corrugated disk dielectric waveguide is investigated by considering a linear combination of orthogonal wavefunctions of the uncorrugated device. It is shown that, just as in the case of corrugated planar slab waveguides, codirectional as well as contradirectional coupling of guided modes is possible. Some potential applications of the device are discussed and device parameters are investigated for specific waveguide materials.     

Theory of optical-waveguide distributed feedback lasers: A Green's functions approach

The total scattered electric field of a periodic dielectric optical waveguide is derived in terms of the Green's functions of the unperturbed structure. A condition for self-excitation that takes into account the coupling between radiation and guided modes is obtained in a very general manner and, therefore, is valid for arbitrary periods of the grating structure. Results show that the effect of the coupling between the oscillating guided field and radiation modes is to change the dependence of the threshold gain on the amplitude of the periodic perturbation: increasing the depth of the grating beyond an optimum value causes an increase in threshold due to larger coupling to radiation modes.     

Wavelength-selective coupling between vertically integratedthin-film waveguides via supermode by a pair of grating couplers

Grating coupling between vertically integrated waveguides via supermode was discussed and demonstrated. Two thin-film waveguides with grating couplers were stacked on a substrate. A guided wave in one waveguide is converted by a grating coupler to a supermode propagating contradirectionally, and then converted by another grating coupler to a guided wave in the other waveguide. The coupling shows high wavelength selectivity, and the wavelength-division add/drop multiplexing function can be combined. A demonstrator was designed and fabricated. Theoretically predicted coupling efficiency was almost 100% with wavelength selectivity of 2 nm, while the experimentally obtained value was 40% in the efficiency and 1 nm in the selectivity     

AlGaAs-based two-dimensional photonic crystal slab with defectwaveguides for planar lightwave circuit applications

An AlGaAs-based near-infrared 2-D photonic crystal (PC) with an air-bridge structure featuring defect waveguides has been developed. For the sample without defect waveguides, measurements of the optical transmission characteristics in the wavelength range from 850 nm to 1100 nm showed a deep attenuation due to a bandgap with 30-35 dB attenuation and transmittance of nearly 100% for the guided modes. Optical propagation properties of defect waveguides were obtained by two methods: measurements of transmission spectra and plan-view observations of the optical beam trace along the waveguide with an infrared-vidicon camera. 3-D finite-difference time-domain simulations for the band structure and transmission spectra in the air-bridge slab with and without defect waveguides have revealed the appearance of four defect propagation modes specific to the defect waveguide, between two slab modes for the defect-free photonic crystal slab. These defect modes were experimentally identified in the measured transmission spectra     

Diffraction from an abruptly terminated dielectric slab waveguide in the presence of a cylindrical scatterer

The efficiency of using an adaptor lens in front of an abruptly terminated symmetric slab optical waveguide is examined analytically in this paper. The adaptor lens is assumed to be of cylindrical shape with a constant refractive index. The coupling of the modes propagating inside the slab guide into radiation waves in the presence of the lens is treated by integral equation methods. In the first step an integral equation is derived for the Green's functionG(r/r')of an abruptly terminated slab waveguide. The integral equation is solved approximately by an iterative procedure giving accurate results when the difference of the refractive indices between the slab waveguide and substrate-cover regions is small. The Green's function is then used to formulate another integral equation for the unknown field inside the adaptor lens. The latter integral equation for the cylindrical lens cross section area is solved by adopting a cylindrical partial wave expansion for the unknown interior field. After determining this field, the reflection-coupling coefficients for the guided modes propagating in the opposite direction of the incident wave, are computed by using the Green's functionG(r/r'). Radiation patterns are also derived in the far field region for an incident slab guided mode. Numerical results are computed and presented for several guide dimensions, lens radii, and refractive indices.     

Modal conversion in a gradient-index channel waveguide due to boundary perturbations

The effect of boundary perturbations on channel waveguides has been calculated following the effective-index method. As required by this approach, the index perturbations are assumed separable-a form describing defects expected using planar waveguide fabrication techniques. For sinusoidal perturbations, coupling occurs to, at most, one other guided mode and to a small band of radiation modes. As in the planar case, losses at step-index boundaries are greater than those at graded-index boundaries.     

Light propagation characteristics of straight single-line-defectwaveguides in photonic crystal slabs fabricated into asilicon-on-insulator substrate

Straight single-line defect optical waveguides in photonic crystal slabs are designed by the finite difference time-domain method and fabricated into a silicon-on-insulator (SOI) wafer. By employing an airbridge structure, clear light propagation for both polarizations is observed without any leakage along the waveguide. This experimental result is well explained by photonic bands of pure guided modes. Minimum propagation loss is estimated to be 11 dB/mm. This value is lower than that reported so far for three-line-defect waveguides with an SOI slab structure and almost comparable to that for an index confinement waveguide with a rectangular Si core. This propagation loss is dominated by the scattering loss by some irregularities. However, photonic crystal waveguides have the possibility of an essential lower scattering loss than in the index confinement waveguide because of the inhibition of radiation modes by the photonic bandgap     

Rigorous analysis of coupling between laser and passive waveguidein multilayer slab waveguide

An approach that combines the finite-element and boundary-element methods (FEM/BEM) is extended to the analysis of arbitrarily shaped discontinuities in a multilayer slab waveguide. Here all the eigenmodes, namely, guided modes, substrate radiation modes, and substrate-cover radiation modes, are taken into account and are constructed by an extended matrix method. Computed results are given for the rigorous analysis of the coupling between a five-or six-layer laser and a four-layer passive waveguide in a monolithically integrated circuit. Some of the results are for multimode incidence. Since the coupling is one of the most important discontinuity problems in practice, this result confirms the usefulness of the approach     

Concept of multiorder multimode resonant optical filters

The idea of implementing optical filters by coupling evanescent waves from several diffracted orders into multiple leaky waveguide modes is studied theoretically. Using a dielectric thin-film structure consisting of a coupling grating placed between adjacent waveguides, guided-mode resonance filters exhibiting multiple reflection peaks within a specified wavelength range can be obtained. These peaks originate in the resonant waveguide modes that are excited by the diffracted waves dispersed by the grating. It is shown that this device can be used to realize multiwavelength as well as wide-band spectral filters.     

Coupling of Modes in Uniform, Composite Waveguides

The principle of coupling of modes is used to compute the phase constant in a uniform waveguide Iilled with two ditferent dielectric materials. The natural modes of two hypothetical waveguides filled with the different dielectrics are computed. The propagation of the combined system is computed by considering the coupling between the two sets of modes. Comparison is made between the approximate theory and an exact theory.