Abstract

First-principles simulation of active nanophotonic devices is indispensable to optical engineering. However, direct simulation of active devices with traditional time-domain methods have been prohibitively expensive due to the inherently large time-scale difference between optical and modulation frequencies. To overcome this challenge, we present a multi-frequency finite-difference frequency-domain algorithm that efficiently performs first-principles steady-state simulations in active devices. We validate our algorithm by simulating a modulated waveguide device and find that the result of the simulation is in excellent agreement with that of coupled mode theory, while also revealing features that are neglected in typical coupled mode theory treatments. We further demonstrate that this algorithm makes it possible to effectively simulate realistic active optical devices. Our algorithm should facilitate and expedite the design and analysis of active nanophotonic components.

© 2016 Optical Society of America

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References

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  1. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
    [Crossref]
  2. Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, Opt. Express 15, 430 (2007).
    [Crossref]
  3. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubio, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
    [Crossref]
  4. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
    [Crossref]
  5. V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, Nanophotonics 1, 17 (2012).
    [Crossref]
  6. S. Sandhu and S. Fan, Opt. Express 20, 4280 (2012).
    [Crossref]
  7. E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. Watts, Nat. Commun. 5, 4008 (2014).
    [Crossref]
  8. C. A. Barrios, V. R. Almeida, R. Panepucci, and M. Lipson, J. Lightwave Technol. 21, 2332 (2003).
    [Crossref]
  9. M. Ziebell, D. Marris-Morini, G. Rasigade, P. Crozat, J. M. Fedeli, P. Grosse, E. Cassan, and L. Vivien, Opt. Express 19, 14690 (2011).
    [Crossref]
  10. W. M. J. Green, M. J. Rooks, L. Sekaric, and Y. Vlasov, Opt. Express 15, 17106 (2007).
    [Crossref]
  11. K. Kubota, J. Noda, and O. Mikami, IEEE J. Quantum Electron. 16, 754 (1980).
    [Crossref]
  12. R. Alferness, IEEE J. Quantum Electron. 17, 946 (1981).
    [Crossref]
  13. J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, Opt. Express 16, 4177 (2008).
    [Crossref]
  14. G. L. Li, C. K. Sun, S. A. Pappert, W. X. Chen, and P. K. L. Yu, IEEE Trans. Microwave Theory Tech. 47, 1177 (1999).
    [Crossref]
  15. S. Irmscher, R. Lewen, and U. Eriksson, IEEE Photon. Technol. Lett. 14, 923 (2002).
    [Crossref]
  16. Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009).
    [Crossref]
  17. K. Fang, Z. Yu, and S. Fan, Nat. Photonics 6, 782 (2012).
    [Crossref]
  18. K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
    [Crossref]
  19. H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
    [Crossref]
  20. Y. Hadad, D. L. Sounas, and A. Alu, Phys. Rev. B 92, 100304(R) (2015).
    [Crossref]
  21. Y. Hadad, D. L. Sounas, and A. Alu, Proc. Natl. Acad. Sci. USA 113, 3471 (2016).
    [Crossref]
  22. Y. Shi and S. Fan, Appl. Phys. Lett. 108, 021110 (2016).
    [Crossref]
  23. L. Lu, J. D. Joannopoulos, and M. Soljacic, Nat. Photonics 8, 822 (2014).
  24. L. Yuan, Y. Shi, and S. Fan, Opt. Lett. 41, 741 (2016).
    [Crossref]
  25. T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: from optical isolation to 4D quantum Hall physics,” arXiv:1510.03910 (2015).
  26. A. Taflove and S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  27. N. J. Champagne, J. G. Berryman, and H. M. Buettner, J. Comput. Phys. 170, 830 (2001).
    [Crossref]
  28. W. Shin and S. Fan, J. Comput. Phys. 231, 3406 (2012).
    [Crossref]
  29. W. Shin and S. Fan, Opt. Express 21, 22578 (2013).
    [Crossref]
  30. G. Veronis, R. W. Dutton, and S. Fan, Opt. Letters 29, 2288 (2004).
    [Crossref]
  31. K. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
    [Crossref]
  32. K. S. Kundert and A. Sangiovanni-Vincentelli, IEEE Trans. Microwave Theory Tech. 5, 521 (1986).
  33. B. Troyanovsky, Z. Yu, and R. W. Dutton, J Comput. Methods Appl. Mech. Eng. 181, 467 (2000).
    [Crossref]
  34. S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
    [Crossref]
  35. J. Bunch and J. Hopcroft, Math. Comput. 28, 231 (1974).
    [Crossref]
  36. R. Fletcher, Numerical Analysis, Vol. 506 of Lecture Notes in Mathematics (Springer-Verlag, 1976), pp. 73–89.
  37. R. Freund and N. Nachtigal, Numerische Mathematik 60, 315 (1991).
    [Crossref]
  38. J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
    [Crossref]
  39. H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  40. S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
    [Crossref]
  41. M. Y. Chen, S. M. Hsu, and H. C. Chang, Opt. Express 17, 5965 (2009).
    [Crossref]
  42. J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley-IEEE, 2002).
  43. T. A. Davis, ACM Trans. Math. Software 30, 196 (2004).
    [Crossref]

2016 (3)

Y. Hadad, D. L. Sounas, and A. Alu, Proc. Natl. Acad. Sci. USA 113, 3471 (2016).
[Crossref]

Y. Shi and S. Fan, Appl. Phys. Lett. 108, 021110 (2016).
[Crossref]

L. Yuan, Y. Shi, and S. Fan, Opt. Lett. 41, 741 (2016).
[Crossref]

2015 (1)

Y. Hadad, D. L. Sounas, and A. Alu, Phys. Rev. B 92, 100304(R) (2015).
[Crossref]

2014 (3)

L. Lu, J. D. Joannopoulos, and M. Soljacic, Nat. Photonics 8, 822 (2014).

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. Watts, Nat. Commun. 5, 4008 (2014).
[Crossref]

2013 (1)

2012 (6)

W. Shin and S. Fan, J. Comput. Phys. 231, 3406 (2012).
[Crossref]

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, Nanophotonics 1, 17 (2012).
[Crossref]

S. Sandhu and S. Fan, Opt. Express 20, 4280 (2012).
[Crossref]

K. Fang, Z. Yu, and S. Fan, Nat. Photonics 6, 782 (2012).
[Crossref]

K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
[Crossref]

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[Crossref]

2011 (1)

2010 (1)

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
[Crossref]

2009 (2)

2008 (1)

2007 (3)

2005 (1)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[Crossref]

2004 (3)

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubio, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[Crossref]

G. Veronis, R. W. Dutton, and S. Fan, Opt. Letters 29, 2288 (2004).
[Crossref]

T. A. Davis, ACM Trans. Math. Software 30, 196 (2004).
[Crossref]

2003 (1)

2002 (1)

S. Irmscher, R. Lewen, and U. Eriksson, IEEE Photon. Technol. Lett. 14, 923 (2002).
[Crossref]

2001 (1)

N. J. Champagne, J. G. Berryman, and H. M. Buettner, J. Comput. Phys. 170, 830 (2001).
[Crossref]

2000 (1)

B. Troyanovsky, Z. Yu, and R. W. Dutton, J Comput. Methods Appl. Mech. Eng. 181, 467 (2000).
[Crossref]

1999 (1)

G. L. Li, C. K. Sun, S. A. Pappert, W. X. Chen, and P. K. L. Yu, IEEE Trans. Microwave Theory Tech. 47, 1177 (1999).
[Crossref]

1994 (1)

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[Crossref]

1991 (1)

R. Freund and N. Nachtigal, Numerische Mathematik 60, 315 (1991).
[Crossref]

1986 (1)

K. S. Kundert and A. Sangiovanni-Vincentelli, IEEE Trans. Microwave Theory Tech. 5, 521 (1986).

1981 (1)

R. Alferness, IEEE J. Quantum Electron. 17, 946 (1981).
[Crossref]

1980 (1)

K. Kubota, J. Noda, and O. Mikami, IEEE J. Quantum Electron. 16, 754 (1980).
[Crossref]

1974 (1)

J. Bunch and J. Hopcroft, Math. Comput. 28, 231 (1974).
[Crossref]

1966 (1)

K. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[Crossref]

Alferness, R.

R. Alferness, IEEE J. Quantum Electron. 17, 946 (1981).
[Crossref]

Almeida, V. R.

Alu, A.

Y. Hadad, D. L. Sounas, and A. Alu, Proc. Natl. Acad. Sci. USA 113, 3471 (2016).
[Crossref]

Y. Hadad, D. L. Sounas, and A. Alu, Phys. Rev. B 92, 100304(R) (2015).
[Crossref]

Andreani, L. C.

Barrios, C. A.

Berenger, J. P.

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[Crossref]

Berryman, J. G.

N. J. Champagne, J. G. Berryman, and H. M. Buettner, J. Comput. Phys. 170, 830 (2001).
[Crossref]

Biberman, A.

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. Watts, Nat. Commun. 5, 4008 (2014).
[Crossref]

Brosi, J. M.

Buettner, H. M.

N. J. Champagne, J. G. Berryman, and H. M. Buettner, J. Comput. Phys. 170, 830 (2001).
[Crossref]

Bunch, J.

J. Bunch and J. Hopcroft, Math. Comput. 28, 231 (1974).
[Crossref]

Carusotto, I.

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: from optical isolation to 4D quantum Hall physics,” arXiv:1510.03910 (2015).

Cassan, E.

Cerjan, A.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

Champagne, N. J.

N. J. Champagne, J. G. Berryman, and H. M. Buettner, J. Comput. Phys. 170, 830 (2001).
[Crossref]

Chang, H. C.

Chen, M. Y.

Chen, W. X.

G. L. Li, C. K. Sun, S. A. Pappert, W. X. Chen, and P. K. L. Yu, IEEE Trans. Microwave Theory Tech. 47, 1177 (1999).
[Crossref]

Cohen, O.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubio, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[Crossref]

Crozat, P.

Davis, T. A.

T. A. Davis, ACM Trans. Math. Software 30, 196 (2004).
[Crossref]

Dutton, R. W.

G. Veronis, R. W. Dutton, and S. Fan, Opt. Letters 29, 2288 (2004).
[Crossref]

B. Troyanovsky, Z. Yu, and R. W. Dutton, J Comput. Methods Appl. Mech. Eng. 181, 467 (2000).
[Crossref]

Eriksson, U.

S. Irmscher, R. Lewen, and U. Eriksson, IEEE Photon. Technol. Lett. 14, 923 (2002).
[Crossref]

Esterhazy, S.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

Fan, S.

L. Yuan, Y. Shi, and S. Fan, Opt. Lett. 41, 741 (2016).
[Crossref]

Y. Shi and S. Fan, Appl. Phys. Lett. 108, 021110 (2016).
[Crossref]

W. Shin and S. Fan, Opt. Express 21, 22578 (2013).
[Crossref]

W. Shin and S. Fan, J. Comput. Phys. 231, 3406 (2012).
[Crossref]

K. Fang, Z. Yu, and S. Fan, Nat. Photonics 6, 782 (2012).
[Crossref]

K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
[Crossref]

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[Crossref]

S. Sandhu and S. Fan, Opt. Express 20, 4280 (2012).
[Crossref]

Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009).
[Crossref]

G. Veronis, R. W. Dutton, and S. Fan, Opt. Letters 29, 2288 (2004).
[Crossref]

Fang, K.

K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
[Crossref]

K. Fang, Z. Yu, and S. Fan, Nat. Photonics 6, 782 (2012).
[Crossref]

Fedeli, J. M.

Fletcher, R.

R. Fletcher, Numerical Analysis, Vol. 506 of Lecture Notes in Mathematics (Springer-Verlag, 1976), pp. 73–89.

Freude, W.

Freund, R.

R. Freund and N. Nachtigal, Numerische Mathematik 60, 315 (1991).
[Crossref]

Gardes, F. Y.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
[Crossref]

Ge, L.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

Goldman, N.

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: from optical isolation to 4D quantum Hall physics,” arXiv:1510.03910 (2015).

Green, W. M. J.

Grosse, P.

Hadad, Y.

Y. Hadad, D. L. Sounas, and A. Alu, Proc. Natl. Acad. Sci. USA 113, 3471 (2016).
[Crossref]

Y. Hadad, D. L. Sounas, and A. Alu, Phys. Rev. B 92, 100304(R) (2015).
[Crossref]

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Haus, H.

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Hopcroft, J.

J. Bunch and J. Hopcroft, Math. Comput. 28, 231 (1974).
[Crossref]

Hosseini, E. S.

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. Watts, Nat. Commun. 5, 4008 (2014).
[Crossref]

Hsu, S. M.

Irmscher, S.

S. Irmscher, R. Lewen, and U. Eriksson, IEEE Photon. Technol. Lett. 14, 923 (2002).
[Crossref]

Jin, J. M.

J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley-IEEE, 2002).

Joannopoulos, J. D.

L. Lu, J. D. Joannopoulos, and M. Soljacic, Nat. Photonics 8, 822 (2014).

Johnson, S. G.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

Jones, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubio, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[Crossref]

Koos, C.

Kubota, K.

K. Kubota, J. Noda, and O. Mikami, IEEE J. Quantum Electron. 16, 754 (1980).
[Crossref]

Kundert, K. S.

K. S. Kundert and A. Sangiovanni-Vincentelli, IEEE Trans. Microwave Theory Tech. 5, 521 (1986).

Lanzillotti-Kimura, N. D.

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, Nanophotonics 1, 17 (2012).
[Crossref]

Leuthold, J.

Lewen, R.

S. Irmscher, R. Lewen, and U. Eriksson, IEEE Photon. Technol. Lett. 14, 923 (2002).
[Crossref]

Li, G. L.

G. L. Li, C. K. Sun, S. A. Pappert, W. X. Chen, and P. K. L. Yu, IEEE Trans. Microwave Theory Tech. 47, 1177 (1999).
[Crossref]

Liao, L.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubio, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[Crossref]

Liertzer, M.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

Lipson, M.

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[Crossref]

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[Crossref]

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, Opt. Express 15, 430 (2007).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[Crossref]

C. A. Barrios, V. R. Almeida, R. Panepucci, and M. Lipson, J. Lightwave Technol. 21, 2332 (2003).
[Crossref]

Lira, H.

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[Crossref]

Liu, A.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubio, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[Crossref]

Liu, D.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

Lu, L.

L. Lu, J. D. Joannopoulos, and M. Soljacic, Nat. Photonics 8, 822 (2014).

Ma, R.

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, Nanophotonics 1, 17 (2012).
[Crossref]

Makris, K.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

Manipatruni, S.

Marris-Morini, D.

Mashanovich, G.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
[Crossref]

Melenk, J. M.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

Mikami, O.

K. Kubota, J. Noda, and O. Mikami, IEEE J. Quantum Electron. 16, 754 (1980).
[Crossref]

Nachtigal, N.

R. Freund and N. Nachtigal, Numerische Mathematik 60, 315 (1991).
[Crossref]

Nicolaescu, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubio, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[Crossref]

Noda, J.

K. Kubota, J. Noda, and O. Mikami, IEEE J. Quantum Electron. 16, 754 (1980).
[Crossref]

Ozawa, T.

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: from optical isolation to 4D quantum Hall physics,” arXiv:1510.03910 (2015).

Panepucci, R.

Paniccia, M.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubio, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[Crossref]

Pappert, S. A.

G. L. Li, C. K. Sun, S. A. Pappert, W. X. Chen, and P. K. L. Yu, IEEE Trans. Microwave Theory Tech. 47, 1177 (1999).
[Crossref]

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[Crossref]

Preble, S. F.

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[Crossref]

Price, H. M.

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: from optical isolation to 4D quantum Hall physics,” arXiv:1510.03910 (2015).

Rasigade, G.

Reed, G. T.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
[Crossref]

Rooks, M. J.

Rotter, S.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

Rubio, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubio, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[Crossref]

Samara-Rubio, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubio, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[Crossref]

Sandhu, S.

Sangiovanni-Vincentelli, A.

K. S. Kundert and A. Sangiovanni-Vincentelli, IEEE Trans. Microwave Theory Tech. 5, 521 (1986).

Schmidt, B.

Sekaric, L.

Shakya, J.

Shi, Y.

L. Yuan, Y. Shi, and S. Fan, Opt. Lett. 41, 741 (2016).
[Crossref]

Y. Shi and S. Fan, Appl. Phys. Lett. 108, 021110 (2016).
[Crossref]

Shin, W.

W. Shin and S. Fan, Opt. Express 21, 22578 (2013).
[Crossref]

W. Shin and S. Fan, J. Comput. Phys. 231, 3406 (2012).
[Crossref]

Soljacic, M.

L. Lu, J. D. Joannopoulos, and M. Soljacic, Nat. Photonics 8, 822 (2014).

Sorace-Agaskar, C. M.

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. Watts, Nat. Commun. 5, 4008 (2014).
[Crossref]

Sorger, V. J.

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, Nanophotonics 1, 17 (2012).
[Crossref]

Sounas, D. L.

Y. Hadad, D. L. Sounas, and A. Alu, Proc. Natl. Acad. Sci. USA 113, 3471 (2016).
[Crossref]

Y. Hadad, D. L. Sounas, and A. Alu, Phys. Rev. B 92, 100304(R) (2015).
[Crossref]

Stone, A. D.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

Sun, C. K.

G. L. Li, C. K. Sun, S. A. Pappert, W. X. Chen, and P. K. L. Yu, IEEE Trans. Microwave Theory Tech. 47, 1177 (1999).
[Crossref]

Sun, J.

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. Watts, Nat. Commun. 5, 4008 (2014).
[Crossref]

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Thomson, D. J.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
[Crossref]

Timurdogan, E.

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. Watts, Nat. Commun. 5, 4008 (2014).
[Crossref]

Troyanovsky, B.

B. Troyanovsky, Z. Yu, and R. W. Dutton, J Comput. Methods Appl. Mech. Eng. 181, 467 (2000).
[Crossref]

Veronis, G.

G. Veronis, R. W. Dutton, and S. Fan, Opt. Letters 29, 2288 (2004).
[Crossref]

Vivien, L.

Vlasov, Y.

Waldow, M.

Watts, M.

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. Watts, Nat. Commun. 5, 4008 (2014).
[Crossref]

Xu, Q.

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, Opt. Express 15, 430 (2007).
[Crossref]

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[Crossref]

Yee, K.

K. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[Crossref]

Yu, P. K. L.

G. L. Li, C. K. Sun, S. A. Pappert, W. X. Chen, and P. K. L. Yu, IEEE Trans. Microwave Theory Tech. 47, 1177 (1999).
[Crossref]

Yu, Z.

K. Fang, Z. Yu, and S. Fan, Nat. Photonics 6, 782 (2012).
[Crossref]

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[Crossref]

K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
[Crossref]

Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009).
[Crossref]

B. Troyanovsky, Z. Yu, and R. W. Dutton, J Comput. Methods Appl. Mech. Eng. 181, 467 (2000).
[Crossref]

Yuan, L.

Zhang, X.

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, Nanophotonics 1, 17 (2012).
[Crossref]

Ziebell, M.

Zilberberg, O.

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: from optical isolation to 4D quantum Hall physics,” arXiv:1510.03910 (2015).

ACM Trans. Math. Software (1)

T. A. Davis, ACM Trans. Math. Software 30, 196 (2004).
[Crossref]

Appl. Phys. Lett. (1)

Y. Shi and S. Fan, Appl. Phys. Lett. 108, 021110 (2016).
[Crossref]

IEEE J. Quantum Electron. (2)

K. Kubota, J. Noda, and O. Mikami, IEEE J. Quantum Electron. 16, 754 (1980).
[Crossref]

R. Alferness, IEEE J. Quantum Electron. 17, 946 (1981).
[Crossref]

IEEE Photon. Technol. Lett. (1)

S. Irmscher, R. Lewen, and U. Eriksson, IEEE Photon. Technol. Lett. 14, 923 (2002).
[Crossref]

IEEE Trans. Antennas Propag. (1)

K. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[Crossref]

IEEE Trans. Microwave Theory Tech. (2)

K. S. Kundert and A. Sangiovanni-Vincentelli, IEEE Trans. Microwave Theory Tech. 5, 521 (1986).

G. L. Li, C. K. Sun, S. A. Pappert, W. X. Chen, and P. K. L. Yu, IEEE Trans. Microwave Theory Tech. 47, 1177 (1999).
[Crossref]

J Comput. Methods Appl. Mech. Eng. (1)

B. Troyanovsky, Z. Yu, and R. W. Dutton, J Comput. Methods Appl. Mech. Eng. 181, 467 (2000).
[Crossref]

J. Comput. Phys. (3)

N. J. Champagne, J. G. Berryman, and H. M. Buettner, J. Comput. Phys. 170, 830 (2001).
[Crossref]

W. Shin and S. Fan, J. Comput. Phys. 231, 3406 (2012).
[Crossref]

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[Crossref]

J. Lightwave Technol. (1)

Math. Comput. (1)

J. Bunch and J. Hopcroft, Math. Comput. 28, 231 (1974).
[Crossref]

Nanophotonics (1)

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, Nanophotonics 1, 17 (2012).
[Crossref]

Nat. Commun. (1)

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. Watts, Nat. Commun. 5, 4008 (2014).
[Crossref]

Nat. Photonics (5)

Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009).
[Crossref]

K. Fang, Z. Yu, and S. Fan, Nat. Photonics 6, 782 (2012).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljacic, Nat. Photonics 8, 822 (2014).

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[Crossref]

Nature (2)

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubio, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[Crossref]

Numerische Mathematik (1)

R. Freund and N. Nachtigal, Numerische Mathematik 60, 315 (1991).
[Crossref]

Opt. Express (7)

Opt. Lett. (1)

Opt. Letters (1)

G. Veronis, R. W. Dutton, and S. Fan, Opt. Letters 29, 2288 (2004).
[Crossref]

Phys. Rev. A (1)

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014).
[Crossref]

Phys. Rev. B (1)

Y. Hadad, D. L. Sounas, and A. Alu, Phys. Rev. B 92, 100304(R) (2015).
[Crossref]

Phys. Rev. Lett. (2)

K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
[Crossref]

H. Lira, Z. Yu, S. Fan, and M. Lipson, Phys. Rev. Lett. 109, 033901 (2012).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

Y. Hadad, D. L. Sounas, and A. Alu, Proc. Natl. Acad. Sci. USA 113, 3471 (2016).
[Crossref]

Other (5)

R. Fletcher, Numerical Analysis, Vol. 506 of Lecture Notes in Mathematics (Springer-Verlag, 1976), pp. 73–89.

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: from optical isolation to 4D quantum Hall physics,” arXiv:1510.03910 (2015).

A. Taflove and S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley-IEEE, 2002).

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Supplementary Material (1)

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» Supplement 1: PDF (1098 KB)      Coupled mode theory results used in Fig. 2.

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Figures (3)

Fig. 1.
Fig. 1. (a) Schematic of the waveguide structure with the source location and modulation region indicated. In the modulation region, the top and bottom halves of the waveguide are modulated with a relative phase difference of π . (b), (c) Modal profiles of the TE 0 and TE 1 modes of the waveguide at λ 0 = 1.55    μm and λ 1 = 1.50    μm , respectively. Both modes carry a guided power normalized to 1    W / μm .
Fig. 2.
Fig. 2. (a) Plot of maximum field amplitude that exists in each frequency sideband as indexed with n . The field amplitude decreases exponentially with n . (b) (left) Field profiles of frequency components with n [ 2 , 2 ] and (right) comparison of the MF-FDFD results with coupled mode theory (CMT).
Fig. 3.
Fig. 3. (a) Schematic of the ring resonator geometry. (b) At λ = 1564.55    nm , the TE 0 mode from the waveguide is critically coupled to the ring resonator. (c), (d) Field profiles for waves at the n = 1 , 2 sidebands, respectively. The power inside the ring at these sidebands is coupled to the waveguide and can be detected at the probe. (e) Power amplitude at the probe at each frequency. (f) Plot of power at the probe as a function of time.

Equations (7)

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× μ ( ω ) 1 × E ( ω ) ω 2 ϵ s ( ω ) E ( ω ) ω 2 P ( ω ) = i ω J ( ω ) .
A e = i ω j ,
ϵ ( t ) = ϵ s + δ cos ( Ω t + φ ) = ϵ s + δ 2 e i Ω t + i φ + δ 2 e i Ω t i φ ,
P ˜ ( t ) = ( δ 2 e i Ω t + i φ + δ 2 e i Ω t i φ ) E ˜ ( t ) .
P ( ω ) = δ 2 e i φ E ( ω Ω ) + δ 2 e i φ E ( ω + Ω ) .
E ˜ ( t ) = Re { n E ( ω n ) e i ω n t } ,
× μ ( ω n ) 1 × E ( ω n ) ω n 2 ϵ s ( ω n ) E ( ω n ) 1 2 ω n 2 δ e i φ E ( ω n 1 ) 1 2 ω n 2 δ e i φ E ( ω n + 1 ) = i ω J ( ω 0 ) δ n 0 ,

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