T. G. Nguyen, R. S. Tummidi, T. L. Koch, A. Mitchell, "Lateral leakage of TM-like
mode in thin-ridge silicon-on-insulator bent waveguides and ring resonators," Opt. Exp. 18, 7243-7252 (2010).

A. Säynätjoki, B. Bai, A. Tervonen, J. Turunen, S. Honkanen, "Enhanced vertical confinement in angled-wall
slot waveguides," Opt. Rev. 17, 181-186 (2010).

E. J. Teo, A. A. Bettiol, B. Xiong, M. B. H. Breese, P. T. Shuvan, "An all-silicon, single-mode Bragg cladding
rib waveguide," Opt. Exp. 18, 8816-8823 (2010).

S. Zhao, "High order matched interface
and boundary methods for the Helmholtz equation in media with arbitrarily
curved interfaces," J. Comput. Phys. 229, 3155-3170 (2010).

J. Xiao, X. Sun, "Full-vector analysis of optical dielectric
waveguide bends using improved finite difference method based on E fields
in cylindrical coordinate systems," J. Opt. 12, 055404 (2010).

J. Xiao, H. Ma, N. Bai, X. Liu, X. Sun, "Full-vectorial
mode solver for bending waveguides using multidomain pseudospectral method
in a cylindrical coordinate system," IEEE Photon.
Technol. Lett. 21, 1779-1781 (2009).

S. Zhao, "High order vectorial analysis
of waveguides with curved dielectric interfaces," IEEE
Microw. Wireless Compon. Lett. 19, 266-268 (2009).

J. Xiao, H. Ma, N. Bai, X. Liu, X. Sun, "Full-vectorial
analysis of bending waveguides using finite difference method based on H-fields
in cylindrical coordinate systems," Opt. Commun. 282, 2511-2515 (2009).

J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, M. Lipson, "Low loss etchless silicon photonic waveguides," Opt. Exp. 17, 4752-4757 (2009).

D. M. Shyroki, "Exact equivalent straight waveguide
model for bent and twisted waveguides," IEEE
Trans. Microw. Theory Tech. 56, 414-419 (2008).

A. F. Oskooi, L. Zhang, Y. Avniel, S. G. Johnson, "The failure of perfectly matched layers,
and towards their redemption by adiabatic absorbers," Opt.
Exp. 16, 11
376-11 392 (2008).

J. Xiao, H. Ni, X. Sun, "Full-vector mode solver for bending waveguides based on
the finite-difference frequency domain method in cylindrical coordinate systems," Opt. Lett. 33, 1848-1850 (2008).

R. Jedidi, R. Pierre, "High-order finite-element methods
for the computation of bending loss in opticalwaveguides," J. Lightw. Technol. 25, 2618-2630 (2007).

M. Oxborrow, "Traceable 2-D finite-element
simulation of the whispering-gallery modes of axisymmetric electromagnetic
resonators," IEEE Trans. Microw. Theory Tech. 55, 1209-1218 (2007).

K. Kakihara, N. Kono, K. Saitoh, M. Koshiba, "Full-vectorial finite element method in
a cylindrical coordinate system for loss analysis of photonic wire bends," Opt. Exp. 14, 11 128-11 141 (2006).

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, "Improving accuracy by subpixel
smoothing in the finite-difference time domain," Opt.
Lett. 31, 2972-2974 (2006).

M. Krause, H. Renner, E. Brinkmeyer, "Polarization-dependent curvature
loss in silicon rib waveguides," IEEE J. Sel.
Top. Quantum Electron. 12, II1359-1362 (2006).

M. Krause, H. Renner, A. Harke, J. Müller, E. Brinkmeyer, "Leakage loss in trench-bulge waveguides," J. Lightw. Technol. 23, 1890-1895 (2005).

L. Prkna, M. Hubálek, J. Čtyroký, "Field modeling of circular
microresonators by film mode matching," IEEE
J. Sel. Top. Quantum Electron. 11, 217-223 (2005).

Y. Tsuji, M. Koshiba, "Complex modal analysis of curved
optical waveguides using a full-vectorial finite element method with perfectly
matched layer boundary conditions," Electromagnetics 24, 39-48 (2004).

G. R. Hadley, "High-accuracy finite-difference
equations for dielectric waveguide analysis I: Uniform regions and dielectric
interfaces," J. Lightw. Technol. 20, 1210-1218 (2002).

N.-N. Feng, G.-R. Zhou, C. Xu, W.-P. Huang, "Computation of full-vector modes for bending
waveguide using cylindrical perfectly matched layers," J.
Lightw. Technol. 20, 1976-1980 (2002).

Y.-C. Chiang, Y.-P. Chiou, H.-C. Chang, "Improved full-vectorial finite-difference
mode solver for optical waveguides with step-index profiles," J. Lightw. Technol. 20, 1609-1618 (2002).

P. D. Sewell, T. M. Benson, "Efficient curvature analysis
of buried waveguides," J. Lightw. Technol. 18, 1321-1329 (2000).

J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, X. S. Li, J. W. H. Liu, "A supernodal approach to sparse partial
pivoting," SIAM J. Matrix Anal. Applic. 20, 720-755 (1999).

W. W. Lui, C.-L. Xu, T. Hirono, K. Yokoyama, W.-P. Huang, "Full-vectorial wave propagation in semiconductor
optical bending waveguides and equivalent straight waveguide approximations," J. Lightw. Technol. 16, 910-914 (1998).

W. C. Chew, J. M. Jin, E. Michielssen, "Complex coordinate stretching
as a generalized absorbing boundary condition," Microw.
Opt. Technol. Lett. 15, 363-369 (1997).

F. L. Teixeira, W. C. Chew, "Systematic derivation of anisotropric
PML absorbing media in cylindrical and spherical coordinates," IEEE Microw. Guided Wave Lett. 7, 371-373 (1997).

M. Rivera, "Accurate full vector beam propagation
method for bent channel waveguides," Integr.
Photon. Res. OSA Tech. Dig.6, (1996) paper IMB3.

R. Pregla, "The method of lines for the
analysis of dielectric waveguide bends," J.
Lightw. Technol. 14, 634-639 (1996).

S. Kim, A. Gopinath, "Vector analysis of optical
dielectric waveguide bends using finite-difference method," J. Lightw. Technol. 14, 2085-2092 (1996).

V. P. Tzolov, M. Fontaine, N. Godbout, S. Lacroix, "Nonlinear self-phase-modulation
effects: A vectorial first-order perturbation approach," Opt. Lett. 20, 456-458 (1995).

Z. S. Sacks, D. M. Kingsland, R. Lee, J.-F. Lee, "A perfectly matched anisotropic absorber
for use as an absorbing boundary condition," IEEE
Trans. Antennas Propag. 43, 1460-1463 (1995).

C. Vassallo, "Improvement of finite difference
methods for step-index optical waveguides," Proc.
Inst. Elect. Eng.—J 139, 137-142 (1992).

J.-S. Gu, P.-A. Besse, H. Melchior, "Method of lines for the analysis
of the propagation characteristics of curved optical rib waveguides," IEEE J. Quantum Electron. 27, 531-537 (1991).

J. Saijonmaa, D. Yevick, "Beam-propagation analysis of
loss in bent optical waveguides and fibers," J.
Opt. Soc. Amer. 73, 1785-1791 (1983).

M. Heiblum, J. H. Harris, "Analysis of curved optical
waveguides by conformal transformation," IEEE
J. Quantum Electron. QE-11, 75-83 (1975).

Y. Tsuji, M. Koshiba, "Complex modal analysis of curved
optical waveguides using a full-vectorial finite element method with perfectly
matched layer boundary conditions," Electromagnetics 24, 39-48 (2004).

M. Heiblum, J. H. Harris, "Analysis of curved optical
waveguides by conformal transformation," IEEE
J. Quantum Electron. QE-11, 75-83 (1975).

L. Prkna, M. Hubálek, J. Čtyroký, "Field modeling of circular
microresonators by film mode matching," IEEE
J. Sel. Top. Quantum Electron. 11, 217-223 (2005).

S. Zhao, "High order vectorial analysis
of waveguides with curved dielectric interfaces," IEEE
Microw. Wireless Compon. Lett. 19, 266-268 (2009).

Z. S. Sacks, D. M. Kingsland, R. Lee, J.-F. Lee, "A perfectly matched anisotropic absorber
for use as an absorbing boundary condition," IEEE
Trans. Antennas Propag. 43, 1460-1463 (1995).

D. M. Shyroki, "Exact equivalent straight waveguide
model for bent and twisted waveguides," IEEE
Trans. Microw. Theory Tech. 56, 414-419 (2008).

J.-S. Gu, P.-A. Besse, H. Melchior, "Method of lines for the analysis
of the propagation characteristics of curved optical rib waveguides," IEEE J. Quantum Electron. 27, 531-537 (1991).

M. Krause, H. Renner, E. Brinkmeyer, "Polarization-dependent curvature
loss in silicon rib waveguides," IEEE J. Sel.
Top. Quantum Electron. 12, II1359-1362 (2006).

F. L. Teixeira, W. C. Chew, "Systematic derivation of anisotropric
PML absorbing media in cylindrical and spherical coordinates," IEEE Microw. Guided Wave Lett. 7, 371-373 (1997).

J. Xiao, H. Ma, N. Bai, X. Liu, X. Sun, "Full-vectorial
mode solver for bending waveguides using multidomain pseudospectral method
in a cylindrical coordinate system," IEEE Photon.
Technol. Lett. 21, 1779-1781 (2009).

M. Oxborrow, "Traceable 2-D finite-element
simulation of the whispering-gallery modes of axisymmetric electromagnetic
resonators," IEEE Trans. Microw. Theory Tech. 55, 1209-1218 (2007).

M. Rivera, "Accurate full vector beam propagation
method for bent channel waveguides," Integr.
Photon. Res. OSA Tech. Dig.6, (1996) paper IMB3.

R. Pregla, "The method of lines for the
analysis of dielectric waveguide bends," J.
Lightw. Technol. 14, 634-639 (1996).

N.-N. Feng, G.-R. Zhou, C. Xu, W.-P. Huang, "Computation of full-vector modes for bending
waveguide using cylindrical perfectly matched layers," J.
Lightw. Technol. 20, 1976-1980 (2002).

J. Saijonmaa, D. Yevick, "Beam-propagation analysis of
loss in bent optical waveguides and fibers," J.
Opt. Soc. Amer. 73, 1785-1791 (1983).

S. Zhao, "High order matched interface
and boundary methods for the Helmholtz equation in media with arbitrarily
curved interfaces," J. Comput. Phys. 229, 3155-3170 (2010).

Y.-C. Chiang, Y.-P. Chiou, H.-C. Chang, "Improved full-vectorial finite-difference
mode solver for optical waveguides with step-index profiles," J. Lightw. Technol. 20, 1609-1618 (2002).

M. Krause, H. Renner, A. Harke, J. Müller, E. Brinkmeyer, "Leakage loss in trench-bulge waveguides," J. Lightw. Technol. 23, 1890-1895 (2005).

S. Kim, A. Gopinath, "Vector analysis of optical
dielectric waveguide bends using finite-difference method," J. Lightw. Technol. 14, 2085-2092 (1996).

W. W. Lui, C.-L. Xu, T. Hirono, K. Yokoyama, W.-P. Huang, "Full-vectorial wave propagation in semiconductor
optical bending waveguides and equivalent straight waveguide approximations," J. Lightw. Technol. 16, 910-914 (1998).

P. D. Sewell, T. M. Benson, "Efficient curvature analysis
of buried waveguides," J. Lightw. Technol. 18, 1321-1329 (2000).

G. R. Hadley, "High-accuracy finite-difference
equations for dielectric waveguide analysis I: Uniform regions and dielectric
interfaces," J. Lightw. Technol. 20, 1210-1218 (2002).

R. Jedidi, R. Pierre, "High-order finite-element methods
for the computation of bending loss in opticalwaveguides," J. Lightw. Technol. 25, 2618-2630 (2007).

J. Xiao, X. Sun, "Full-vector analysis of optical dielectric
waveguide bends using improved finite difference method based on E fields
in cylindrical coordinate systems," J. Opt. 12, 055404 (2010).

W. C. Chew, J. M. Jin, E. Michielssen, "Complex coordinate stretching
as a generalized absorbing boundary condition," Microw.
Opt. Technol. Lett. 15, 363-369 (1997).

A. F. Oskooi, L. Zhang, Y. Avniel, S. G. Johnson, "The failure of perfectly matched layers,
and towards their redemption by adiabatic absorbers," Opt.
Exp. 16, 11
376-11 392 (2008).

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, "Improving accuracy by subpixel
smoothing in the finite-difference time domain," Opt.
Lett. 31, 2972-2974 (2006).

J. Xiao, H. Ma, N. Bai, X. Liu, X. Sun, "Full-vectorial
analysis of bending waveguides using finite difference method based on H-fields
in cylindrical coordinate systems," Opt. Commun. 282, 2511-2515 (2009).

K. Kakihara, N. Kono, K. Saitoh, M. Koshiba, "Full-vectorial finite element method in
a cylindrical coordinate system for loss analysis of photonic wire bends," Opt. Exp. 14, 11 128-11 141 (2006).

E. J. Teo, A. A. Bettiol, B. Xiong, M. B. H. Breese, P. T. Shuvan, "An all-silicon, single-mode Bragg cladding
rib waveguide," Opt. Exp. 18, 8816-8823 (2010).

J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, M. Lipson, "Low loss etchless silicon photonic waveguides," Opt. Exp. 17, 4752-4757 (2009).

T. G. Nguyen, R. S. Tummidi, T. L. Koch, A. Mitchell, "Lateral leakage of TM-like
mode in thin-ridge silicon-on-insulator bent waveguides and ring resonators," Opt. Exp. 18, 7243-7252 (2010).

V. P. Tzolov, M. Fontaine, N. Godbout, S. Lacroix, "Nonlinear self-phase-modulation
effects: A vectorial first-order perturbation approach," Opt. Lett. 20, 456-458 (1995).

J. Xiao, H. Ni, X. Sun, "Full-vector mode solver for bending waveguides based on
the finite-difference frequency domain method in cylindrical coordinate systems," Opt. Lett. 33, 1848-1850 (2008).

A. Säynätjoki, B. Bai, A. Tervonen, J. Turunen, S. Honkanen, "Enhanced vertical confinement in angled-wall
slot waveguides," Opt. Rev. 17, 181-186 (2010).

C. Vassallo, "Improvement of finite difference
methods for step-index optical waveguides," Proc.
Inst. Elect. Eng.—J 139, 137-142 (1992).

J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, X. S. Li, J. W. H. Liu, "A supernodal approach to sparse partial
pivoting," SIAM J. Matrix Anal. Applic. 20, 720-755 (1999).

R. B. Lehoucq, D. C. Sorensen, C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems
With Implicitly Restarted Arnoldi Methods (1998) Society for Industrial & Applied Mathematics.

S. D. Gedney, A. Taflove, Computational Electrodynamics:
The Finite-Difference Time-Domain Method (Artech
House, 2000).

O. Horn, J. Amthor, T. Lipka, J. Müller, "Tunable silicon photonic wires fabricated
by contact lithography and thermal oxidation," Proc.
SPIE Photonic Materials, Devices, and Applications III (2009) pp. 73660C.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman
and Hall, 1983).