Abstract

We propose a new type of amplitude modulator for integrated optics based on phase-controllable coherent perfect loss (CPL) from a resonant cavity. Temporal coupled-mode theory is employed to derive a simple set of equations that describe the device operation, and finite-difference time-domain simulations are used to verify these equations. Two examples of CPL modulators are described with this formalism: a ring resonator and a 1D photonic crystal cavity. We show that internal resonator loss, and thus critical coupling, are not strict requirements for CPL operation. These devices are simple to design and can act as compact switches and modulators for integrated optics.

© 2013 Optical Society of America

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References

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  1. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  2. H. A. Haus, M. A. Popović, and M. R. Watts, IEEE Photon. Technol. Lett. 18, 1137 (2006).
    [CrossRef]
  3. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
    [CrossRef]
  4. F. Wang, X. Wang, H. Zhou, Q. Zhou, Y. Hao, X. Jiang, M. Wang, and J. Yang, Opt. Express 17, 7708 (2009).
    [CrossRef]
  5. T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
    [CrossRef]
  6. L. Zhou and A. W. Poon, Opt. Lett. 32, 781 (2007).
    [CrossRef]
  7. L. Zhou and A. W. Poon, Opt. Express 15, 9194 (2007).
    [CrossRef]
  8. M. E. Solmaz, Y. Zhou, and C. K. Madsen, IEEE J. Lightwave Technol. 28, 2951 (2010).
    [CrossRef]
  9. W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
    [CrossRef]
  10. A. Mock, IEEE Photon. J. 4, 2229 (2012).
    [CrossRef]
  11. Z. Zhang and M. Qiu, J. Opt. Soc. Am. B 23, 104 (2006).
    [CrossRef]
  12. R. R. Grote, K. Padmaraju, B. Souhan, J. B. Driscoll, K. Bergman, and R. M. Osgood, IEEE Photon. Technol. Lett. 25, 67 (2013).
    [CrossRef]
  13. H. Liu and A. Yariv, Opt. Express 20, 9249 (2012).
    [CrossRef]
  14. R. R. Grote, J. B. Driscoll, C. G. Biris, N. C. Panoiu, and R. M. Osgood, Opt. Express 19, 26406 (2011).
    [CrossRef]

2013 (2)

T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
[CrossRef]

R. R. Grote, K. Padmaraju, B. Souhan, J. B. Driscoll, K. Bergman, and R. M. Osgood, IEEE Photon. Technol. Lett. 25, 67 (2013).
[CrossRef]

2012 (2)

2011 (2)

R. R. Grote, J. B. Driscoll, C. G. Biris, N. C. Panoiu, and R. M. Osgood, Opt. Express 19, 26406 (2011).
[CrossRef]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

2010 (1)

M. E. Solmaz, Y. Zhou, and C. K. Madsen, IEEE J. Lightwave Technol. 28, 2951 (2010).
[CrossRef]

2009 (1)

2007 (2)

2006 (2)

H. A. Haus, M. A. Popović, and M. R. Watts, IEEE Photon. Technol. Lett. 18, 1137 (2006).
[CrossRef]

Z. Zhang and M. Qiu, J. Opt. Soc. Am. B 23, 104 (2006).
[CrossRef]

1999 (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Bergman, K.

R. R. Grote, K. Padmaraju, B. Souhan, J. B. Driscoll, K. Bergman, and R. M. Osgood, IEEE Photon. Technol. Lett. 25, 67 (2013).
[CrossRef]

Biris, C. G.

Cao, H.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Chong, Y.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Driscoll, J. B.

R. R. Grote, K. Padmaraju, B. Souhan, J. B. Driscoll, K. Bergman, and R. M. Osgood, IEEE Photon. Technol. Lett. 25, 67 (2013).
[CrossRef]

R. R. Grote, J. B. Driscoll, C. G. Biris, N. C. Panoiu, and R. M. Osgood, Opt. Express 19, 26406 (2011).
[CrossRef]

Fan, S.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Ge, L.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Grote, R. R.

R. R. Grote, K. Padmaraju, B. Souhan, J. B. Driscoll, K. Bergman, and R. M. Osgood, IEEE Photon. Technol. Lett. 25, 67 (2013).
[CrossRef]

R. R. Grote, J. B. Driscoll, C. G. Biris, N. C. Panoiu, and R. M. Osgood, Opt. Express 19, 26406 (2011).
[CrossRef]

Hao, Y.

Haus, H. A.

H. A. Haus, M. A. Popović, and M. R. Watts, IEEE Photon. Technol. Lett. 18, 1137 (2006).
[CrossRef]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

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

Hu, T.

T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
[CrossRef]

Jiang, X.

T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
[CrossRef]

F. Wang, X. Wang, H. Zhou, Q. Zhou, Y. Hao, X. Jiang, M. Wang, and J. Yang, Opt. Express 17, 7708 (2009).
[CrossRef]

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Khan, M. J.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Liu, H.

Madsen, C. K.

M. E. Solmaz, Y. Zhou, and C. K. Madsen, IEEE J. Lightwave Technol. 28, 2951 (2010).
[CrossRef]

Manolatou, C.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Mock, A.

A. Mock, IEEE Photon. J. 4, 2229 (2012).
[CrossRef]

Noh, H.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Osgood, R. M.

R. R. Grote, K. Padmaraju, B. Souhan, J. B. Driscoll, K. Bergman, and R. M. Osgood, IEEE Photon. Technol. Lett. 25, 67 (2013).
[CrossRef]

R. R. Grote, J. B. Driscoll, C. G. Biris, N. C. Panoiu, and R. M. Osgood, Opt. Express 19, 26406 (2011).
[CrossRef]

Padmaraju, K.

R. R. Grote, K. Padmaraju, B. Souhan, J. B. Driscoll, K. Bergman, and R. M. Osgood, IEEE Photon. Technol. Lett. 25, 67 (2013).
[CrossRef]

Panoiu, N. C.

Poon, A. W.

Popovic, M. A.

H. A. Haus, M. A. Popović, and M. R. Watts, IEEE Photon. Technol. Lett. 18, 1137 (2006).
[CrossRef]

Qiu, C.

T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
[CrossRef]

Qiu, H.

T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
[CrossRef]

Qiu, M.

Solmaz, M. E.

M. E. Solmaz, Y. Zhou, and C. K. Madsen, IEEE J. Lightwave Technol. 28, 2951 (2010).
[CrossRef]

Souhan, B.

R. R. Grote, K. Padmaraju, B. Souhan, J. B. Driscoll, K. Bergman, and R. M. Osgood, IEEE Photon. Technol. Lett. 25, 67 (2013).
[CrossRef]

Stone, A. D.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Wan, W.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Wang, F.

T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
[CrossRef]

F. Wang, X. Wang, H. Zhou, Q. Zhou, Y. Hao, X. Jiang, M. Wang, and J. Yang, Opt. Express 17, 7708 (2009).
[CrossRef]

Wang, M.

Wang, X.

Watts, M. R.

H. A. Haus, M. A. Popović, and M. R. Watts, IEEE Photon. Technol. Lett. 18, 1137 (2006).
[CrossRef]

Yang, J.

T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
[CrossRef]

F. Wang, X. Wang, H. Zhou, Q. Zhou, Y. Hao, X. Jiang, M. Wang, and J. Yang, Opt. Express 17, 7708 (2009).
[CrossRef]

Yang, M.

T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
[CrossRef]

Yariv, A.

Yu, H.

T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
[CrossRef]

Yu, P.

T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
[CrossRef]

Zhang, Z.

Zhou, H.

Zhou, L.

Zhou, Q.

Zhou, Y.

M. E. Solmaz, Y. Zhou, and C. K. Madsen, IEEE J. Lightwave Technol. 28, 2951 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

T. Hu, P. Yu, C. Qiu, H. Qiu, F. Wang, M. Yang, X. Jiang, H. Yu, and J. Yang, Appl. Phys. Lett. 102, 011112 (2013).
[CrossRef]

IEEE J. Lightwave Technol. (1)

M. E. Solmaz, Y. Zhou, and C. K. Madsen, IEEE J. Lightwave Technol. 28, 2951 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

IEEE Photon. J. (1)

A. Mock, IEEE Photon. J. 4, 2229 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

H. A. Haus, M. A. Popović, and M. R. Watts, IEEE Photon. Technol. Lett. 18, 1137 (2006).
[CrossRef]

R. R. Grote, K. Padmaraju, B. Souhan, J. B. Driscoll, K. Bergman, and R. M. Osgood, IEEE Photon. Technol. Lett. 25, 67 (2013).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (4)

Opt. Lett. (1)

Science (1)

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Other (1)

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) Power loss and transmission from the CPL modulator as a function of phase shift, (b) frequency response of the CPL modulator in the on and off states, (c) RR and (d) 1D PhC CPL modulators, (e) transmitted and scattered power out of an MZI as a function of phase shift, and (f) an MZI modulator.

Fig. 2.
Fig. 2.

Complex transmission and loss coefficients for (a) on-resonance CPL modulator and (b) phase-matched MZI modulator.

Fig. 3.
Fig. 3.

Field profiles for (a) an unloaded RR, and a CPL-I RR in the (b) off and (c) on states. (d) An unloaded 1D PhC, and a CPL-E 1D PhC in the (e) off state and (f) on states. White arrows indicate source positions.

Fig. 4.
Fig. 4.

(a) Power spectrum out of port A in the on and off states, (b) step response, and (c) amplitude modulation of outputs calculated using TCMT and FDTD for RR CPL-I modulator. (d)–(f) are the same quantities for PhC CPL-E modulator. FDTD calculated values in (c),(f) are denoted with squares for PT and circles for PL.

Equations (10)

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da(t)dt=jω0a12γtota+γc2(1+ejΔφ)s0,
a(ω)=γc2(1+ejΔφ)s012γtot+jΔω,
sA=12s0γca,
sB=12s0ejΔφγca.
ΓA=sAs0=12(γL2γcejΔφ)+jΔω12γtot+jΔω,
ΓB=sBs0=12(γL2ejΔφγc)+jΔωejΔφ12γtot+jΔω,
ΓL=γLas0=12γcγL(1+ejΔφ)12γtot+jΔω.
PL(ω)=γL|a|2=P02γcγLcos2(Δφ2)14γtot2+Δω2,
PL(t)=PL(ω)(12e12γtott+eγtott),
PA,B(t)=12(P0ddtPL(t)γLPL(t)),

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