Abstract

A complex-envelope (CE) alternating-direction-implicit (ADI) finite-difference time-domain (FDTD) approach to treat light–matter interaction self-consistently with electromagnetic field evolution for efficient simulations of active photonic devices is presented for the first time (to our best knowledge). The active medium (AM) is modeled using an efficient multilevel system of carrier rate equations to yield the correct carrier distributions, suitable for modeling semiconductor/solid-state media accurately. To include the AM in the CE-ADI-FDTD method, a first-order differential system involving CE fields in the AM is first set up. The system matrix that includes AM parameters is then split into two time-dependent submatrices that are then used in an efficient ADI splitting formula. The proposed CE-ADI-FDTD approach with AM takes 22% of the time as the approach of the corresponding explicit FDTD, as validated by semiconductor microdisk laser simulations.

© 2012 Optical Society of America

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References

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2011 (2)

2008 (3)

K.-Y. Jung and F. L. Teixeira, Phys. Rev. B 77, 125108 (2008).
[CrossRef]

K. Bohringer and O. Hess, Progr. Quantum Electron. 32, 247 (2008).
[CrossRef]

E. L. Tan, IEEE Trans. Antennas Propagat. 56, 170(2008).
[CrossRef]

2007 (3)

K.-Y. Jung, F. L. Teixeira, and R. Lee, IEEE Antennas Wireless Propagat. Lett. 6, 643 (2007).
[CrossRef]

D. Pinto and S. S. A. Obayya, J. Lightwave Technol. 25, 440 (2007).
[CrossRef]

S.-H. Sun and C. T. M. Choi, IEEE Microw. Wireless Compon. Lett. 17, 253 (2007).
[CrossRef]

2006 (1)

2005 (1)

C. Ma and Z. Chen, IEEE Trans. Antennas Propagat. 53, 971 (2005).
[CrossRef]

2002 (1)

H. Rao, R. Scarmozzino, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 477 (2002).
[CrossRef]

1998 (1)

A. S. Nagra and R. A. York, IEEE Trans. Antennas Propagat. 46, 334 (1998).
[CrossRef]

Bohringer, K.

K. Bohringer and O. Hess, Progr. Quantum Electron. 32, 247 (2008).
[CrossRef]

Chen, Z.

C. Ma and Z. Chen, IEEE Trans. Antennas Propagat. 53, 971 (2005).
[CrossRef]

Chen, Z. N.

Choi, C. T. M.

S.-H. Sun and C. T. M. Choi, IEEE Microw. Wireless Compon. Lett. 17, 253 (2007).
[CrossRef]

Coldren, L. A.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

Corzine, S. W.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

Hess, O.

K. Bohringer and O. Hess, Progr. Quantum Electron. 32, 247 (2008).
[CrossRef]

Ho, S. T.

Ho, S.-T.

Huang, Y.

Jung, K.-Y.

K.-Y. Jung and F. L. Teixeira, Phys. Rev. B 77, 125108 (2008).
[CrossRef]

K.-Y. Jung, F. L. Teixeira, and R. Lee, IEEE Antennas Wireless Propagat. Lett. 6, 643 (2007).
[CrossRef]

Lee, R.

K.-Y. Jung, F. L. Teixeira, and R. Lee, IEEE Antennas Wireless Propagat. Lett. 6, 643 (2007).
[CrossRef]

Ma, C.

C. Ma and Z. Chen, IEEE Trans. Antennas Propagat. 53, 971 (2005).
[CrossRef]

Nagra, A. S.

A. S. Nagra and R. A. York, IEEE Trans. Antennas Propagat. 46, 334 (1998).
[CrossRef]

Obayya, S. S. A.

Osgood, R. M.

H. Rao, R. Scarmozzino, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 477 (2002).
[CrossRef]

Pinto, D.

Rao, H.

H. Rao, R. Scarmozzino, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 477 (2002).
[CrossRef]

Scarmozzino, R.

H. Rao, R. Scarmozzino, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 477 (2002).
[CrossRef]

Singh, G.

Sun, S.-H.

S.-H. Sun and C. T. M. Choi, IEEE Microw. Wireless Compon. Lett. 17, 253 (2007).
[CrossRef]

Tan, E. L.

G. Singh, E. L. Tan, and Z. N. Chen, Opt. Lett. 36, 1494 (2011).
[CrossRef]

E. L. Tan, IEEE Trans. Antennas Propagat. 56, 170(2008).
[CrossRef]

Teixeira, F. L.

K.-Y. Jung and F. L. Teixeira, Phys. Rev. B 77, 125108 (2008).
[CrossRef]

K.-Y. Jung, F. L. Teixeira, and R. Lee, IEEE Antennas Wireless Propagat. Lett. 6, 643 (2007).
[CrossRef]

Wang, Q.

York, R. A.

A. S. Nagra and R. A. York, IEEE Trans. Antennas Propagat. 46, 334 (1998).
[CrossRef]

IEEE Antennas Wireless Propagat. Lett. (1)

K.-Y. Jung, F. L. Teixeira, and R. Lee, IEEE Antennas Wireless Propagat. Lett. 6, 643 (2007).
[CrossRef]

IEEE Microw. Wireless Compon. Lett. (1)

S.-H. Sun and C. T. M. Choi, IEEE Microw. Wireless Compon. Lett. 17, 253 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. Rao, R. Scarmozzino, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 477 (2002).
[CrossRef]

IEEE Trans. Antennas Propagat. (3)

C. Ma and Z. Chen, IEEE Trans. Antennas Propagat. 53, 971 (2005).
[CrossRef]

A. S. Nagra and R. A. York, IEEE Trans. Antennas Propagat. 46, 334 (1998).
[CrossRef]

E. L. Tan, IEEE Trans. Antennas Propagat. 56, 170(2008).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

K.-Y. Jung and F. L. Teixeira, Phys. Rev. B 77, 125108 (2008).
[CrossRef]

Progr. Quantum Electron. (1)

K. Bohringer and O. Hess, Progr. Quantum Electron. 32, 247 (2008).
[CrossRef]

Other (1)

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

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Figures (2)

Fig. 1.
Fig. 1.

Plot of (a) gain spectra and (b) lasing wavelength error (with respect to FDTD) versus CPU time. In (b), marker numbers indicate CFLN operating number.

Fig. 2.
Fig. 2.

Snapshots of field Ey using FDTD and CE-ADI.

Equations (14)

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

Eyt=1ϵHxz1ϵHzx1ϵmPymt.
2Pymt2+γmPymt+ωm2Pym=αmEy,
Ncmt=ΔNmΔN(m,m1)C+ΔN(m+1,m)C+Wp.
Eyxt+σxϵ0Eyx=1ϵHzx1ϵ(mPyxmt+σxϵ0Pyxm),
Eyzt+σzϵ0Eyz=1ϵHxz1ϵ(mPyzmt+σzϵ0Pyzm).
Pyξmt=Qyξm
Qyξmt+γmQyξm+ωm2Pyξm=αmEyξ,
Ut=MU,
U˜t=(jωcI+M)U˜,
A1=[jωcϵ02σx2ϵ0001ϵx0jωc20000jωc201μ0x1μ0x0jωcϵ02σx2ϵ0],A2=[σxϵϵ01ϵ00000000000000],A3=[0000αmn200000000αmn200],A4=[jωc21200ωm22jωcγm20000jωc21200ωm22jωcγm2].
v˜n=Da1(IΔt4(Bn1Bn))U˜nDa1Dbv˜n12,
Da1(12IΔt4An)U˜n+12=v˜n.
v˜n+12=Db1U˜n+12Db1Dav˜n,
Db1(12IΔt4Bn)U˜n+1=v˜n+12.

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