Wide-angle BPM

I. Ilic, R. Scarmozzino, and Jr. Osgood, R.M. Investigation of the pade approximant-based wide-angle beam propagation method for accurate modeling of waveguiding circuits. Journal of Lightwave Technology, 14(12):2813-22, 1996.
An analytical and numerical study of the accuracy of the beam propagation method that includes approximate treatments of wide-angle propagation based on Pade rational functions is presented. The investigation identifies the error terms associated with a sequence of higher order operators and the range of validity of different approximant operators is studied through examination of two-dimensional (2-D) waveguide structures. An analytical model for the general error in Pade-based wide-angle schemes is developed and compared with numerical simulations of simple waveguiding devices for which the exact solution is known. Guidelines for determining the range of error pertinent to the Pade operator are established
BPM simulations of MMI devices
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Bidirectional BPM

[1] Hongling Rao, R. Scarmozzino, and Jr. Osgood, R.M. A bidirectional beam propagation method for multiple dielectric interfaces. IEEE Photonics Technology Letters, 11(7):830-2, 1999.
A novel approach to the bidirectional beam propagation method, which can treat multiple dielectric interfaces, is developed and implemented using iterative methods. Comparisons with two previously published results demonstrate its accuracy, as well as its efficiency in computation time and memory. Finally, its capability in simulating and designing complex structures is also demonstrated via a three-channel add-drop multiplexer
[2] Hongling Rao, M.J. Steel, R. Scarmozzino, and Jr. Osgood, R.M. Complex propagators for evanescent waves in bidirectional beam propagation method. Journal of Lightwave Technology, 18(8):1155-60, 2000.
Existing algorithms for bidirectional optical beam propagation proposed to simulate reflective integrated photonic devices do not propagate evanescent fields correctly. Thus inaccuracy and instability problems can arise when fields have significant evanescent character. We propose complex representations of the propagation operator by choosing either a complex reference wave number or a complex representation of Pade approximation to address this issue. Therefore correct evolution of both propagating waves and evanescent waves can be simultaneously realized, significantly reducing the inaccuracy and instability problems. Both test problems and practical problems are presented for demonstration
Distributed Feedback Grating (DFB)
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Add-Drop Multiplexer
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VCSEL design

Hongling Rao, M.J. Steel, R. Scarmozzino, and Jr. Osgood, R.M. VCSEL Design Using the Bidirectional Beam Propagation Method, submitted to Journal of Quantum Electronics, December 2000.
We present an optical modeling approach for calculating vertical cavity surface emitting lasers (VCSEL) modes based on the bidirectional beam propagation method (BiBPM). Compared with existing approaches, it is flexible, efficient and convenient. To demonstrate and validate the approach, we examine several design problems for oxide-confined VCSEL devices. Specifically, we model the blue-shift phenomenon in small oxidized VCSELs and compared our calculation with previous results. We also examined the dependence of the threshold gain on different oxide aperture-shape designs and on the thickness and placement of an aperture layer.
Modes in a typical oxide-confined VCSEL
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Wavelength blueshift of an oxide-confined VCSEL
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Magnetic Effects in Photonic Bandgap Structures

[1] M.J. Steel, M. Levy, and Jr. Osgood, R.M. High transmission enhanced faraday rotation in one-dimensional photonic crystals with defects. IEEE Photonics Technology Letters, 12(9):1171-3, 2000.
Photonic crystals containing defects produce enhanced Faraday rotation but existing designs have low intensity output. We show that designs with two-defects possess sufficient freedom to attain high transmission over a large range of rotation angles in very short lengths. We optimize such systems for 45 degrees rotation in optical isolators
[2] M.J. Steel, M. Levy, and Jr. Osgood, R.M. Photonic bandgaps with defects and the enhancement of faraday rotation. Journal of Lightwave Technology, 18(9):1297-308, 2000.
We investigate enhancement of magnetooptical rotation in periodic magnetic garnet thin-film stacks with defects using a combination of coupled-mode theory and matrix calculations. We prove that a combination of high rotation per unit length and high output is unattainable for a symmetric grating with a single central defect. We demonstrate that the addition of a second defect introduces sufficient degrees of freedom to allow high transmission for a much larger range of rotation angles than was previously possible. We present a number of designs with emphasis an achieving 45 degrees rotation in very short propagation lengths
[3] M.J. Steel, M. Levy, and Jr. Osgood, R.M. Large magnetooptical kerr rotation with high reflectivity from photonic bandgap structures with defects. Journal of Lightwave Technology, 18(9):1289-96, 2000.
We perform a theoretical study of enhancement of magnetooptical rotation on reflection of light from a periodic system with a defect. Using calculations based on a coupled mode approach and the transfer matrix method we demonstrate that an asymmetric placing of a single defect allows arbitrary Kerr rotations with better than 99% reflectivity from very short devices

Photonic Crystal Fibers

M.J. Steel and Jr. Osgood, R.M. Elliptical-hole photonic crystal fibers. Optics Letters, 26(4):229-31, 2001.
We study the dispersive properties of photonic crystal fibers (PCF’s) with elliptical air holes. The unusual guidance of PCF leads to novel behavior of the birefringence, group-velocity walk-off, and dispersion parameters, including the possibility of zero walk-off with high birefringence in the single-mode regime. A number of these effects are closely tied to the underlying radiation states of the air-hole lattice
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Thin Film Modulators

I.-L. Gheorma, P. Savi, and Jr. Osgood, R.M. Thin layer design of x-cut linbo/sub 3/ modulators. IEEE Photonics Technology Letters, 12(12):1618-20, 2000.
Microwave-optical velocity matching and 50 Omega impedance matching are difficult to achieve with LiNbO/sub 3/ traveling wave modulators. We perform a detailed study (simulations) of the microwave and optical performance characteristics for modulators using thin layer (few micrometers), X-cut LiNbO/sub 3/ and find significant improvements in velocity and impedance matching together with a lower V/sub pi /L

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