Abstract

An efficient frequency-domain method, the phase variation monitoring (PVM) method, is proposed to determine the electromagnetic eigenmodes in two-dimensional photonic crystal waveguides. The proposed method is based on monitoring the reflection and transmission coefficients of incident plane waves. It is successfully applied to an illustrative line-defect photonic crystal waveguide and proved to be capable of calculating the in-plane leakage through the finite-size photonic crystal surrounding the line-defect. Calculation of the leakage loss is not only important for proper understanding of wave propagation within the defect but also for its significant role in applications of photonic structures.

© 2012 Optical Society of America

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2009

2008

2005

S. Shi, C. Chen, and D. W. Prather, Appl. Phys. Lett. 86, 043104 (2005).
[CrossRef]

2002

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, and T. Yoshie, IEEE Trans. Nanotechnol. 1, 4 (2002).
[CrossRef]

1999

1996

1995

X. Li and R. T. Deck, Appl. Phys. Lett. 66, 130 (1995).
[CrossRef]

1992

R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, IEEE J. Quantum Electron. 28, 1520 (1992).
[CrossRef]

1987

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Anemogiannis, E.

Benisty, H.

J. M. Lourtioz, H. Benisty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer-Verlag, 2008).

Berger, V.

J. M. Lourtioz, H. Benisty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer-Verlag, 2008).

Chen, C.

S. Shi, C. Chen, and D. W. Prather, Appl. Phys. Lett. 86, 043104 (2005).
[CrossRef]

Deck, R. T.

X. Li and R. T. Deck, Appl. Phys. Lett. 66, 130 (1995).
[CrossRef]

Forbes, G. W.

R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, IEEE J. Quantum Electron. 28, 1520 (1992).
[CrossRef]

Gaylord, T. K.

Gerard, J. M.

J. M. Lourtioz, H. Benisty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer-Verlag, 2008).

Glytsis, E. N.

Hagness, S. C.

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

Houde-Walter, S. N.

R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, IEEE J. Quantum Electron. 28, 1520 (1992).
[CrossRef]

Jahromi, A. K.

Khavasi, A.

Li, L.

Li, X.

X. Li and R. T. Deck, Appl. Phys. Lett. 66, 130 (1995).
[CrossRef]

Loncar, M.

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, and T. Yoshie, IEEE Trans. Nanotechnol. 1, 4 (2002).
[CrossRef]

Lourtioz, J. M.

J. M. Lourtioz, H. Benisty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer-Verlag, 2008).

Maystre, D.

J. M. Lourtioz, H. Benisty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer-Verlag, 2008).

Mehrany, K.

Nevière, M.

M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (CRC, 2003).

Painter, O.

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, and T. Yoshie, IEEE Trans. Nanotechnol. 1, 4 (2002).
[CrossRef]

Popov, E.

M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (CRC, 2003).

Prather, D. W.

S. Shi, C. Chen, and D. W. Prather, Appl. Phys. Lett. 86, 043104 (2005).
[CrossRef]

Sarrafi, P.

Scherer, A.

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, and T. Yoshie, IEEE Trans. Nanotechnol. 1, 4 (2002).
[CrossRef]

Shi, S.

S. Shi, C. Chen, and D. W. Prather, Appl. Phys. Lett. 86, 043104 (2005).
[CrossRef]

Smith, R. E.

R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, IEEE J. Quantum Electron. 28, 1520 (1992).
[CrossRef]

Taflove, A.

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

Tchelnokov, A.

J. M. Lourtioz, H. Benisty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer-Verlag, 2008).

Vuckovic, J.

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, and T. Yoshie, IEEE Trans. Nanotechnol. 1, 4 (2002).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Yoshie, T.

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, and T. Yoshie, IEEE Trans. Nanotechnol. 1, 4 (2002).
[CrossRef]

Appl. Phys. Lett.

S. Shi, C. Chen, and D. W. Prather, Appl. Phys. Lett. 86, 043104 (2005).
[CrossRef]

X. Li and R. T. Deck, Appl. Phys. Lett. 66, 130 (1995).
[CrossRef]

IEEE J. Quantum Electron.

R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, IEEE J. Quantum Electron. 28, 1520 (1992).
[CrossRef]

IEEE Trans. Nanotechnol.

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, and T. Yoshie, IEEE Trans. Nanotechnol. 1, 4 (2002).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Phys. Rev. Lett.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Other

J. M. Lourtioz, H. Benisty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer-Verlag, 2008).

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

M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (CRC, 2003).

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Figures (3)

Fig. 1.
Fig. 1.

Sample of a periodic photonic structure. The direction of confinement is x, and the propagation occurs along the z direction, which is the direction of periodicity.

Fig. 2.
Fig. 2.

Phase constant dispersion diagram for an E-polarized photonic structure; dots, PVM method; squares, finite-difference time domain (FDTD) method; solid-line, Galerkin’s method with Hermite–Gauss expansion [12].

Fig. 3.
Fig. 3.

Attenuation constant dispersion diagram for an E-polarized photonic structure; circles, squares, and diamonds, results of the PVM method for 2, 3, and 4 arrays of rods; solid, dashed, and dash-dot lines, corresponding results of FDTD.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

ψ1=i=Aiexp(jk1,i.r)+i=Ai+exp(jk1,i+.r)
ψ3=i=Bi+exp(jk3,i+.r)+i=Biexp(jk3,i.r)
[A+;A]=M[B+;B].
(R1I)=(M11M12M21M22)(OT1).
T1=(M22×I)/det(M22),
R1=(M12×M22×I)/det(M22).
det(M22)=0.
Tm1(ω0,β)=F(β)A(β)n=0Nz(βγn)/m=0Np(βγm),
θF(β)α01/{1+[(ββ0)/α0]2},

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