Abstract

We look into the use of the intracavity backscattering in twin-coupled traveling wave microresonators (TWMRs) to generate enhanced coupled-resonator-induced transparency (CRIT) and optical Fano resonance (OFR). Intracavity backscattering makes it possible to either generate a single CRIT peak or a pair of CRIT peaks within one free spectral range in the transmission spectrum. The distance between the twin-CRIT peaks can be tuned by controlling the intracavity backscattering strength. Also, the use of intracavity backscattering allows the simultaneous production of both fast and slow light effects. In addition, it is found that the symmetric CRIT peaks can be reshaped into asymmetric OFR line shapes either by using TWMRs with different intracavity backscattering strengths when one input is launched into the circuit or by modulating the phase/amplitude difference between the dual contrapropagating inputs, which are launched into the circuit in the presence of intracavity backscattering. These allow switching between CRIT and OFR to be realized in the absence of gain or phase tuning elements in the cavities, unlike conventional twin-coupled TWMR systems.

© 2012 Optical Society of America

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    [CrossRef]
  17. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (2)

2009 (6)

J. G. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photon. 4, 46–49 (2009).
[CrossRef]

Q. Li, Z. Zhang, J. Wang, M. Qiu, and Y. Su, “Fast light in silicon ring resonator with resonance-splitting,” Opt. Express 17, 933–940 (2009).
[CrossRef]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef]

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef]

M. Tomita, K. Totsuka, R. Hanamura, and T. Matsumoto, “Tunable Fano interference effect in coupled-microsphere resonator-induced transparency,” J. Opt. Soc. Am. B 26, 813–818 (2009).
[CrossRef]

Y. F. Xiao, L. He, J. Zhu, and L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009).
[CrossRef]

2008 (1)

R. W. Boyd, “Slow light now and then,” Nat. Photon. 2, 454–455 (2008).
[CrossRef]

2007 (4)

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[CrossRef]

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced-transparency,” Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

C. Peng, Z. Li, and A. Xu, “Optical gyroscope based on a coupled resonator with the all-optical analogous property of electromagnetically induced transparency,” Opt. Express 15, 3864–3875 (2007).
[CrossRef]

L. Zhou and A. W. Poon, “Fano resonance-based electrically reconfigurable add–drop filters in silicon microring resonator-coupled Mach–Zehnder interferometers,” Opt. Lett. 32, 781–783 (2007).
[CrossRef]

2006 (2)

Y. Lu, L. Xu, Y. Yu, P. Wang, and J. Yao, “Double-wavelength Fano resonance and enhanced coupled-resonator-induced transparency in a double-microcavity resonator system,” J. Opt. Soc. Am. A 23, 1718–1721 (2006).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

2005 (3)

2004 (2)

L. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, “Tunable delay line with interacting whispering-gallery-mode resonators,” Opt. Lett. 29, 626–628 (2004).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

2003 (1)

C. Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527–1529 (2003).
[CrossRef]

2001 (1)

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef]

1999 (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add–drop filtering,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

1998 (2)

S. A. Backes and J. R. A. Cleaver, “Microdisk laser structures for mode control and directional emission,” J. Vac. Sci. Technol. B 16, 3817–3820 (1998).
[CrossRef]

B. E. Little, S. T. Chu, and H. A. Haus, “Second-order filtering and sensing with partially coupled traveling waves in a single resonator,” Opt. Lett. 23, 1570–1572 (1998).
[CrossRef]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Ang, T. Y. L.

Backes, S. A.

S. A. Backes and J. R. A. Cleaver, “Microdisk laser structures for mode control and directional emission,” J. Vac. Sci. Technol. B 16, 3817–3820 (1998).
[CrossRef]

Borselli, M.

Boyd, R. W.

R. W. Boyd, “Slow light now and then,” Nat. Photon. 2, 454–455 (2008).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Chang, H.

H. Chang and D. D. Smith, “Gain-assisted superluminal propagation in coupled optical resonators,” J. Opt. Soc. Am. B 22, 2237–2241 (2005).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Chao, C. Y.

C. Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527–1529 (2003).
[CrossRef]

Chen, D.-R.

J. G. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photon. 4, 46–49 (2009).
[CrossRef]

Chen, Y. L.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Chu, S. T.

Cleaver, J. R. A.

S. A. Backes and J. R. A. Cleaver, “Microdisk laser structures for mode control and directional emission,” J. Vac. Sci. Technol. B 16, 3817–3820 (1998).
[CrossRef]

Fan, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add–drop filtering,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef]

Fuller, K. A.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Giessen, H.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef]

Guo, G. C.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Guo, L. J.

C. Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527–1529 (2003).
[CrossRef]

Hanamura, R.

Harris, S. E.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Haus, H. A.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add–drop filtering,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

B. E. Little, S. T. Chu, and H. A. Haus, “Second-order filtering and sensing with partially coupled traveling waves in a single resonator,” Opt. Lett. 23, 1570–1572 (1998).
[CrossRef]

He, L.

J. G. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photon. 4, 46–49 (2009).
[CrossRef]

Y. F. Xiao, L. He, J. Zhu, and L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009).
[CrossRef]

Ilchenko, V. S.

Imamoglu, A.

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef]

Jiang, W.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add–drop filtering,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Johnson, T.

Kästel, J.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef]

Khan, M. J.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add–drop filtering,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Kimerling, L. C.

Kivshar, Y. S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Kobayashi, N.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced-transparency,” Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

Kwong, D. L.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef]

Langguth, L.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef]

Li, L.

J. G. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photon. 4, 46–49 (2009).
[CrossRef]

Li, Q.

Li, Z.

Lipson, M.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Little, B. E.

Liu, N.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef]

Lu, Y.

Lukin, M. D.

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef]

Maleki, L.

Manolatou, C.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add–drop filtering,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Matsko, A. B.

Matsumoto, T.

Matsuo, S.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “All-optical switch involving Fano resonance in ultrasmall photonic crystal nanocavities,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMV5.

Miroshnichenko, A. E.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Ngo, N. Q.

Notomi, M.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “All-optical switch involving Fano resonance in ultrasmall photonic crystal nanocavities,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMV5.

Nozaki, K.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “All-optical switch involving Fano resonance in ultrasmall photonic crystal nanocavities,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMV5.

Ozdemir, S. K.

J. G. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photon. 4, 46–49 (2009).
[CrossRef]

Painter, O.

Peng, C.

Pfau, T.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef]

Poon, A. W.

Povinelli, M. L.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Qiu, M.

Rosenberger, A. T.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Sandhu, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Sato, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “All-optical switch involving Fano resonance in ultrasmall photonic crystal nanocavities,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMV5.

Savchenkov, A. A.

Shakya, J.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Shinya, A.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “All-optical switch involving Fano resonance in ultrasmall photonic crystal nanocavities,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMV5.

Smith, D. D.

H. Chang and D. D. Smith, “Gain-assisted superluminal propagation in coupled optical resonators,” J. Opt. Soc. Am. B 22, 2237–2241 (2005).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Sparacin, D. K.

Spector, S. J.

Su, Y.

Tanabe, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “All-optical switch involving Fano resonance in ultrasmall photonic crystal nanocavities,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMV5.

Taniyama, H.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “All-optical switch involving Fano resonance in ultrasmall photonic crystal nanocavities,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMV5.

Tomita, M.

Totsuka, K.

Vahala, K. J.

K. J. Vahala, Optical Microcavities, Vol. 5 of Advanced Series in Applied Physics (World Scientific, 2004).

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add–drop filtering,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Wang, J.

Wang, P.

Weiss, T.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef]

Wong, C. W.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of the proposed twin-coupled-MR structure, in which periodic surface perturbations like grating ridges are intentionally introduced on the cavities.

Fig. 2.
Fig. 2.

Evolution in the transmission at the through port of the twin-coupled MRs with Qint,1=5.0e4, Qint,2=6.0e8, and Qext=5.0e4 as the resonator-to-resonator coupling (controlled by Qcou) changes in the presence of different intracavity backscattering strength (controlled by Qmut). The two MRs have equal Qmut, i.e., Qmut=Qmut,1=Qmut,2. In each row, Qcou is varied while Qmut is fixed. Insets show the blown-up regions marked by “X”.

Fig. 3.
Fig. 3.

Evolution in the transmission at the reflection port of the twin-coupled MRs with Qint,1=5.0e4, Qint,2=6.0e8, and Qext=5.0e4 as the resonator-to-resonator coupling (controlled by Qcou) changes in the presence of different intracavity backscattering strength (controlled by Qmut). The two resonators have equal Qmut, i.e., Qmut=Qmut,1=Qmut,2. In each row, Qcou is varied while Qmut is fixed. Insets show the blown-up regions marked by “X”.

Fig. 4.
Fig. 4.

The transmission, effective phase shift, and group delay responses of the twin-coupled MRs with Qint,1=5.0e4, Qint,2=6.0e8, Qext=5.0e4, and Qcou=1.5e5, using different intracavity backscattering strength (quantified by Qmut). Adjusting Qmut tunes the separation distance between the CRIT peaks. In all the graphs, the spectra move in the direction of the arrows as Qmut increases, where Qmut=Qmut,1=Qmut,2.

Fig. 5.
Fig. 5.

Reshaping of the symmetric CRIT peaks in the transmission TT at the through port (first column) and the Lorentzian dips in the transmission TR at the reflection port (second column) of the twin-coupled MRs with Qint,1=5.0e4, Qint,2=6.0e8, Qext=4.0e2, and Qcou=1.2e3. In (a) and (b), Qmut,1 is adjusted, while fixing Qmut,2 at 1.0e2. Different asymmetric Fano-like line shapes are produced, with the spectral location of each Fano-like line shape fixed in this case in (a) and (b). On the other hand, in (c) and (d), Qmut,2 is adjusted, while fixing Qmut,1 at 1.0e2. Different asymmetric Fano-like line shapes are produced like those in (a) and (b). However, the spectral location of each Fano-like line shape changes with Qmut,2 in (c) and (d).

Fig. 6.
Fig. 6.

Evolution of the transmission TT spectrum at the through port (first column) and the transmission TR spectrum at the reflection port (second column) of the twin-coupled MRs with Qint,1=5.0e4, Qint,2=6.0e8, Qext=4.0e2, Qcou=1.2e3, and Qmut,1=Qmut,2=Qmut=4.1e3 as dual inputs are employed to interact with the intracavity backscattering. Tuning the phase difference θ between the dual inputs allows active switching between the symmetric CRIT peaks and the asymmetric OFR line shapes.

Tables (1)

Tables Icon

Table 1. Comparisons of the CRIT and OFR Features between Different Twin-Coupled-MR Schemes

Equations (5)

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dEccw,1dt=(jΔω1Γnet,1)Eccw,1jumut,1Ecw,1jk0S+1,dEcw,1dt=(jΔω1Γnet,1)Ecw,1jumut,1Eccw,1jk0S+2,dEccw,2dt=(jΔω2Γnet,2)Eccw,2jumut,2Ecw,2jk1Ecw,1,dEcw,2dt=(jΔω2Γnet,2)Ecw,2jumut,2Eccw,2jk1Eccw,1,
S1=ejβwL(S+2jk0Ecw),S2=ejβwL(S+1jk0Eccw),
ξT=1k02B1{jΔω03(Γ1+2Γ2jAumut,1)Δω02[Γ2(2jΓ1+jΓ2+2Aumut,1)+jumut,22+jk12]Δω0+[Γ2(k12+Γ1Γ2)+Γ1umut,22]+jA(k12umut,2umut,1umut,22umut,1Γ22)},ξR=Ak02B1{jAΔω03+(jumut,1AΓ12AΓ2)Δω02+[jA(k12+umut,22+Γ22+2Γ1Γ2)+2unet,1Γ2]Δω0j(um,1Γ22umut,2k12+umut,1um,22)+A(Γ1umut,22+Γ2k12+Γ1Γ22)},whereB1=[Δω02+j(Γ1+Γ2+jumut,1+jumut,2)Δω0j(umut,1Γ2+umut,2Γ1)k12Γ1Γ2+umut,1umut,2]×[Δω02+j(Γ1+Γ2jumut,1jumut,2)Δω0+j(umut,1Γ2+umut,2Γ1)k12Γ1Γ2+umut,1umut,2].
ωspc±ω0±k12Γnet,22.
ωspc±1ω0±um+u12Γnet,22,ωspc±2ω0±umu12Γnet,22,

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