Numerical analysis of planar optical waveguides using matrix approach
TL;DR: In this article, a simple matrix method for obtaining propagation characteristics, including losses for various modes of an arbitrarily graded planar waveguide structure which may have media of complex refractive indices, is presented.
Abstract: We present here a simple matrix method for obtaining propagation characteristics, including losses for various modes of an arbitrarily graded planar waveguide structure which may have media of complex refractive indices. We show the applicability of the method for obtaining leakage losses and absorption losses, as well as for calculating beat length in directional couplers. The method involves straightforward 2 × 2 matrix multiplications, and does not require the solutions of any transcendental or differential equations.
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TL;DR: In this article, a distributed coupling between a dielectric waveguide and the surface plasmon mode in a metal-coated waveguide was proposed for the first time.
Abstract: Guided-wave optical biosensors have great potential for use in the field of environmental monitoring. In particular, planar waveguide technologies offer the possibility of producing compact, monolithic, multisensor devices which may be connected to instrumentation using optical fibres, allowing remote operation. Optical evanescent field sensing techniques presently under investigation include grating couplers, waveguide interferometers and surface plasmon resonance (SPR) sensors. In the latter case, the surface plasmon is generally excited using a "bulk" optical component such as a prism, and equipment using this technique is now commercially available. One potential advantage of the SPR technique is that the metal film which supports the surface plasmon may also be used as an electrode for electrochemical control of sensing reactions. However, recent reports have indicated that the "bulk" SPR devices may not ultimately be as sensitive as fully guided-wave approaches such as the Mach-Zehnder interferometer. An alternative to the "bulk" SPR devices which has recently emerged is the use of distributed coupling between a dielectric waveguide and the surface plasmon mode in a metal-coated waveguide. This has the advantage of combining greater design flexibility and the potential for monolithic integration with the well-established technique of SPR. However, at present no adequate model for the performance of these devices exists. ...
290 citations
IBM1
TL;DR: In this paper, a transfer matrix technique was proposed for optical harmonic generation from a multilayer sample consisting of an arbitrary number of parallel slabs of arbitrary thicknesses, where the nonlinear depletion of the pump beam can be neglected.
Abstract: Optical harmonic generation from a multilayer sample consisting of an arbitrary number of parallel slabs of arbitrary thicknesses can be treated exactly (in the limit where the nonlinear depletion of the pump beam can be neglected) by using a transfer matrix technique. This approach is described, and the results are given in a computationally convenient form. The technique is illustrated by application to a typical case.
209 citations
TL;DR: In this article, a simple, accurate, and fast algorithm for solving the one-dimensional time-independent Schrodinger equation is presented, based on the transfer matrix method, which makes it possible to calculate all bound and quasi-bound energy levels and the corresponding wave functions for an arbitrarily shaped potential profile.
Abstract: A simple, accurate, and fast algorithm for solving the one-dimensional time-independent Schrodinger equation is presented. The algorithm is based on the transfer matrix method. This makes it possible to calculate all bound and quasi-bound energy levels and the corresponding wave functions for an arbitrarily shaped potential profile. The results of calculations are compared with those obtained by other authors for various types of problems. A central part of this study deals with solving the Schrodinger equation in quantum-well structures. The results show that the transfer matrix method is as accurate as other methods, but it is easier to implement and, hence, is superior for calculations on small computer, such as a PC. >
205 citations
TL;DR: In this paper, an efficient numerical method for accurately determining the real and/or complex propagation constants of guided modes and leaky waves in general multilayer waveguides is presented.
Abstract: An efficient numerical method for accurately determining the real and/or complex propagation constants of guided modes and leaky waves in general multilayer waveguides is presented. The method is applicable to any lossless and/or lossy (dielectric, semiconductor, metallic) waveguide structure. The method is based on the argument principle theorem and is capable of extracting all of the zeros of any analytic function in the complex plane. It is applied to solving the multilayer waveguide dispersion equation derived from the well known thin-film transfer matrix theory. Excellent agreement is found with seven previously published results and with results from two limiting cases where the propagating constants can be obtained analytically. >
185 citations
TL;DR: In this paper, two numerical methods, the reflection pole method (RPM) and the wavevector density method (WDM), are introduced for determining the propagation constants of guided and leaky modes in planar multilayer waveguides.
Abstract: Two numerical methods, the reflection pole method (RPM) and the wavevector density method (WDM), are introduced for determining the propagation constants of guided and leaky modes in lossless and lossy planar multilayer waveguides. These methods are based on the extraction of propagation constants from Lorentzian-type peaks of the reflection coefficient (RPM) or on the density of wavevectors of the structure (WDM). Furthermore, in the case of the RPM the propagation constants can be determined with the help of the phase variation of the denominator of the reflection coefficient in conjunction with an optimization procedure. Both methods are tested on numerically "challenging" multilayer waveguides such as a two-metal-layer waveguide, a multilayer lossy waveguide, and an ARROW waveguide. The results produced by both methods are in good agreement with other numerical techniques but are obtained without the need for solving a dispersion equation in the complex plane. In addition, an approximate but easily implementable method is proposed which verifies whether a cluster of radiation modes can be accurately represented by a single leaky mode.
162 citations
Cites background or methods from "Numerical analysis of planar optica..."
...It is expected that for waveguide modes with a large imaginary part, the Lorentzian function representation of a single waveguide mode fails (see, e.g., [ 6 ], [26])....
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...One candidate method is the extremely popular local-excitationefficiency method [ 6 ], which detects guided and leaky modes in lossy and lossless waveguides....
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...For structures involving nonidentical guiding regions the method of [ 6 ] must be applied times....
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...Both methods described in [ 6 ], [8] are included within these generalized classes....
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...In addition RPM does not need the addition of a fictitious high index layer as does the method in [ 6 ] which alters the character and the propagation constants of the waveguide modes....
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References
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01 Jan 1959
TL;DR: In this paper, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,815 citations
[...]
01 Oct 1999
TL;DR: In this article, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,503 citations
2,467 citations
1,892 citations
TL;DR: In this paper, a 2 × 2 matrix method is applied to planar multilayer optical waveguides to satisfy substrate-to-cover field transfer equations that reduce to the equation 0 for bound modes and leaky waves.
Abstract: A standard 2 × 2 matrix method-used in thin-film optics is applied to planar multilayer optical waveguides. All modes are required to satisfy substrate-to-cover field-transfer equations that reduce to the equation γcm11 + γcγsm12 + m21 + γsm22 = 0 for bound modes and leaky waves. Expressions are derived for the field profiles and the power in each medium. A first-order perturbation theory is developed and applied to absorbing multilayer guides and to the reflection of plane waves from the prism-loaded lossy multilayer guide. The latter leads to experimental arrangements for measuring losses in which the gap thickness and propagation constant are accessible parameters.
419 citations