Abstract

We demonstrate a new and efficient technique for modeling and simulation of spatially incoherent sources using the Wiener chaos expansion method. By implementing this new model, we show that a practical-size photonic structure with a spatially incoherent input source can be analyzed more than 2 orders of magnitude faster compared with the conventional models without sacrificing the accuracy.

© 2007 Optical Society of America

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References

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  1. A. G. Yodh and B. Chance, Phys. Today 48(3), 34 (1995).
    [CrossRef]
  2. Z. Xu, Z. Wang, M. E. Sullivan, and D. J. Brady, Opt. Express 11, 2126 (2003).
    [CrossRef] [PubMed]
  3. C. Hsieh, O. Momtahan, A. Karbaschi, and A. Adibi, Opt. Lett. 30, 836 (2005).
    [CrossRef] [PubMed]
  4. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).
  5. B. Momeni, E. Shah Hosseini, M. Askari, S. Mohammadi, and M. Soltani, Proc. SPIE 6480, 648012 (2007).
    [CrossRef]
  6. B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, A. Adibi, and M. Rakhshandehroo, Opt. Express 14, 2413 (2006).
    [CrossRef] [PubMed]
  7. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  8. T. Y. Hou, W. Luo, B. Rozovskii, and H. Zhou, J. Comput. Phys. 216, 687 (2006).
    [CrossRef]

2007 (1)

B. Momeni, E. Shah Hosseini, M. Askari, S. Mohammadi, and M. Soltani, Proc. SPIE 6480, 648012 (2007).
[CrossRef]

2006 (2)

2005 (1)

2003 (1)

2000 (1)

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

1995 (2)

A. G. Yodh and B. Chance, Phys. Today 48(3), 34 (1995).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Adibi, A.

Askari, M.

B. Momeni, E. Shah Hosseini, M. Askari, S. Mohammadi, and M. Soltani, Proc. SPIE 6480, 648012 (2007).
[CrossRef]

B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, A. Adibi, and M. Rakhshandehroo, Opt. Express 14, 2413 (2006).
[CrossRef] [PubMed]

Brady, D. J.

Chance, B.

A. G. Yodh and B. Chance, Phys. Today 48(3), 34 (1995).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

Hou, T. Y.

T. Y. Hou, W. Luo, B. Rozovskii, and H. Zhou, J. Comput. Phys. 216, 687 (2006).
[CrossRef]

Hsieh, C.

Huang, J.

Karbaschi, A.

Luo, W.

T. Y. Hou, W. Luo, B. Rozovskii, and H. Zhou, J. Comput. Phys. 216, 687 (2006).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Mohammadi, S.

B. Momeni, E. Shah Hosseini, M. Askari, S. Mohammadi, and M. Soltani, Proc. SPIE 6480, 648012 (2007).
[CrossRef]

B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, A. Adibi, and M. Rakhshandehroo, Opt. Express 14, 2413 (2006).
[CrossRef] [PubMed]

Momeni, B.

B. Momeni, E. Shah Hosseini, M. Askari, S. Mohammadi, and M. Soltani, Proc. SPIE 6480, 648012 (2007).
[CrossRef]

B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, A. Adibi, and M. Rakhshandehroo, Opt. Express 14, 2413 (2006).
[CrossRef] [PubMed]

Momtahan, O.

Rakhshandehroo, M.

Rozovskii, B.

T. Y. Hou, W. Luo, B. Rozovskii, and H. Zhou, J. Comput. Phys. 216, 687 (2006).
[CrossRef]

Shah Hosseini, E.

B. Momeni, E. Shah Hosseini, M. Askari, S. Mohammadi, and M. Soltani, Proc. SPIE 6480, 648012 (2007).
[CrossRef]

Soltani, M.

B. Momeni, E. Shah Hosseini, M. Askari, S. Mohammadi, and M. Soltani, Proc. SPIE 6480, 648012 (2007).
[CrossRef]

B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, A. Adibi, and M. Rakhshandehroo, Opt. Express 14, 2413 (2006).
[CrossRef] [PubMed]

Sullivan, M. E.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

Wang, Z.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Xu, Z.

Yodh, A. G.

A. G. Yodh and B. Chance, Phys. Today 48(3), 34 (1995).
[CrossRef]

Zhou, H.

T. Y. Hou, W. Luo, B. Rozovskii, and H. Zhou, J. Comput. Phys. 216, 687 (2006).
[CrossRef]

J. Comput. Phys. (1)

T. Y. Hou, W. Luo, B. Rozovskii, and H. Zhou, J. Comput. Phys. 216, 687 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Today (1)

A. G. Yodh and B. Chance, Phys. Today 48(3), 34 (1995).
[CrossRef]

Proc. SPIE (1)

B. Momeni, E. Shah Hosseini, M. Askari, S. Mohammadi, and M. Soltani, Proc. SPIE 6480, 648012 (2007).
[CrossRef]

Other (2)

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

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Figures (3)

Fig. 1
Fig. 1

Schematic of a 2D square lattice PC structure of air holes in silicon with hole radius r and lattice constant a. The input (or source) and output lines are shown by A and B, respectively.

Fig. 2
Fig. 2

Electric field power spectrum as a function of normalized frequency at a typical point on the output line B in Fig. 1. The simulation result of WCE model was obtained with only M = 15 expansion coefficients.

Fig. 3
Fig. 3

Percentage relative error of the WCE model with respect to the brute-force model as a function of the number of expansion coefficients ( M ) .

Equations (10)

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2 E z ( x , y , t ) μ ϵ ( x , y ) 2 E z ( x , y , t ) t 2 = μ J z ( x , y , t ) t ,
J z ( y , t ) = d W ( y ) V ( t ) ,
d W ( y ) = i ξ i m i ( y ) ,
ξ i = 0 y m i ( s ) d W ( s ) , i = 1 , 2 , .
2 E z i ( x , y , t ) μ ϵ ( x , y ) 2 E z i ( x , y , t ) t 2 = μ m i ( y ) d V ( t ) d t ,
i = 1 , 2 , ,
V ( t ) = sin [ ω ( t t 0 ) ] exp [ ( t t 0 T ) 2 ] ,
m 1 ( y ) = 1 y f ,
m i ( y ) = 2 y f cos [ ( i 1 ) π y y f ] , i = 2 , 3 , ,
E z 2 ( x , y , t ) e = i E z i ( x , y , t ) 2 .

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