Abstract

Measuring optical rotations in materials is a useful tool in many experimental studies. Research may be limited by the ability to measure small rotations due to weak interactions. We propose a novel scheme wherein we use a coupled waveguide and ring resonator to amplify the effects of optical rotation, potentially opening new avenues for investigation. Our proposed device can increase the resulting optical rotation by up to six orders of magnitude.

© 2015 Optical Society of America

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References

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  1. Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the spin hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
    [Crossref] [PubMed]
  2. J. M. Kikkawa and D. D. Awschalom, “Resonant spin amplification in n-type GaAs,” Phys. Rev. Lett. 80(19), 4313–4316 (1998).
    [Crossref]
  3. H. Kitzerow and C. Bahr, eds., Chirality in Liquid Crystals (Springer 2001).
  4. Y. Q. Li, D. W. Steuerman, J. Berezovsky, D. S. Seferos, G. C. Bazan, and D. D. Awschalom, “Cavity enhanced Faraday rotation of semiconductor quantum dots,” Appl. Phys. Lett. 88(19), 193126 (2006).
    [Crossref]
  5. R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
    [Crossref]
  6. J. M. Choi, R. K. Lee, and A. Yariv, “Control of critical coupling in a ring resonator-fiber configuration: application to wavelength-selective switching, modulation, amplification, and oscillation,” Opt. Lett. 26(16), 1236–1238 (2001).
    [Crossref] [PubMed]
  7. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
    [Crossref]
  8. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Wispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289 (1992).
    [Crossref]
  9. C. J. Trowbridge, B. M. Norman, J. Stephens, A. C. Gossard, D. D. Awschalom, and V. Sih, “Electron spin polarization-based integrated photonic devices,” Opt. Express 19(16), 14845–14851 (2011).
    [Crossref] [PubMed]
  10. A. Yariv, “Critical coupling and its ccntrol in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
    [Crossref]
  11. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321 (2000).
    [Crossref]
  12. J. K. Doylend, O. Cohen, M. R. Lee, O. Raday, S. Xu, V. Sih, H. Rong, and M. Paniccia, “Tunable ring resonators for silicon Raman laser and amplifier applications,” Proc. SPIE 6896, 68960Q (2008).
    [Crossref]

2012 (1)

R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
[Crossref]

2011 (1)

2008 (1)

J. K. Doylend, O. Cohen, M. R. Lee, O. Raday, S. Xu, V. Sih, H. Rong, and M. Paniccia, “Tunable ring resonators for silicon Raman laser and amplifier applications,” Proc. SPIE 6896, 68960Q (2008).
[Crossref]

2006 (1)

Y. Q. Li, D. W. Steuerman, J. Berezovsky, D. S. Seferos, G. C. Bazan, and D. D. Awschalom, “Cavity enhanced Faraday rotation of semiconductor quantum dots,” Appl. Phys. Lett. 88(19), 193126 (2006).
[Crossref]

2004 (1)

Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the spin hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
[Crossref] [PubMed]

2002 (1)

A. Yariv, “Critical coupling and its ccntrol in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[Crossref]

2001 (1)

2000 (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321 (2000).
[Crossref]

1998 (1)

J. M. Kikkawa and D. D. Awschalom, “Resonant spin amplification in n-type GaAs,” Phys. Rev. Lett. 80(19), 4313–4316 (1998).
[Crossref]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Wispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289 (1992).
[Crossref]

Awschalom, D. D.

C. J. Trowbridge, B. M. Norman, J. Stephens, A. C. Gossard, D. D. Awschalom, and V. Sih, “Electron spin polarization-based integrated photonic devices,” Opt. Express 19(16), 14845–14851 (2011).
[Crossref] [PubMed]

Y. Q. Li, D. W. Steuerman, J. Berezovsky, D. S. Seferos, G. C. Bazan, and D. D. Awschalom, “Cavity enhanced Faraday rotation of semiconductor quantum dots,” Appl. Phys. Lett. 88(19), 193126 (2006).
[Crossref]

Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the spin hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
[Crossref] [PubMed]

J. M. Kikkawa and D. D. Awschalom, “Resonant spin amplification in n-type GaAs,” Phys. Rev. Lett. 80(19), 4313–4316 (1998).
[Crossref]

Bazan, G. C.

Y. Q. Li, D. W. Steuerman, J. Berezovsky, D. S. Seferos, G. C. Bazan, and D. D. Awschalom, “Cavity enhanced Faraday rotation of semiconductor quantum dots,” Appl. Phys. Lett. 88(19), 193126 (2006).
[Crossref]

Berezovsky, J.

Y. Q. Li, D. W. Steuerman, J. Berezovsky, D. S. Seferos, G. C. Bazan, and D. D. Awschalom, “Cavity enhanced Faraday rotation of semiconductor quantum dots,” Appl. Phys. Lett. 88(19), 193126 (2006).
[Crossref]

Bloch, J.

R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
[Crossref]

Choi, J. M.

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Cohen, O.

J. K. Doylend, O. Cohen, M. R. Lee, O. Raday, S. Xu, V. Sih, H. Rong, and M. Paniccia, “Tunable ring resonators for silicon Raman laser and amplifier applications,” Proc. SPIE 6896, 68960Q (2008).
[Crossref]

Cronenberger, S.

R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
[Crossref]

Doylend, J. K.

J. K. Doylend, O. Cohen, M. R. Lee, O. Raday, S. Xu, V. Sih, H. Rong, and M. Paniccia, “Tunable ring resonators for silicon Raman laser and amplifier applications,” Proc. SPIE 6896, 68960Q (2008).
[Crossref]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Giri, R.

R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
[Crossref]

Glazov, M. M.

R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
[Crossref]

Gossard, A. C.

C. J. Trowbridge, B. M. Norman, J. Stephens, A. C. Gossard, D. D. Awschalom, and V. Sih, “Electron spin polarization-based integrated photonic devices,” Opt. Express 19(16), 14845–14851 (2011).
[Crossref] [PubMed]

Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the spin hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
[Crossref] [PubMed]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Kato, Y. K.

Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the spin hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
[Crossref] [PubMed]

Kavokin, K. V.

R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
[Crossref]

Kikkawa, J. M.

J. M. Kikkawa and D. D. Awschalom, “Resonant spin amplification in n-type GaAs,” Phys. Rev. Lett. 80(19), 4313–4316 (1998).
[Crossref]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Lee, M. R.

J. K. Doylend, O. Cohen, M. R. Lee, O. Raday, S. Xu, V. Sih, H. Rong, and M. Paniccia, “Tunable ring resonators for silicon Raman laser and amplifier applications,” Proc. SPIE 6896, 68960Q (2008).
[Crossref]

Lee, R. K.

Lemaître, A.

R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
[Crossref]

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Wispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289 (1992).
[Crossref]

Li, Y. Q.

Y. Q. Li, D. W. Steuerman, J. Berezovsky, D. S. Seferos, G. C. Bazan, and D. D. Awschalom, “Cavity enhanced Faraday rotation of semiconductor quantum dots,” Appl. Phys. Lett. 88(19), 193126 (2006).
[Crossref]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Wispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289 (1992).
[Crossref]

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Wispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289 (1992).
[Crossref]

Myers, R. C.

Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the spin hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
[Crossref] [PubMed]

Nawrocki, M.

R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
[Crossref]

Norman, B. M.

Paniccia, M.

J. K. Doylend, O. Cohen, M. R. Lee, O. Raday, S. Xu, V. Sih, H. Rong, and M. Paniccia, “Tunable ring resonators for silicon Raman laser and amplifier applications,” Proc. SPIE 6896, 68960Q (2008).
[Crossref]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Wispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289 (1992).
[Crossref]

Raday, O.

J. K. Doylend, O. Cohen, M. R. Lee, O. Raday, S. Xu, V. Sih, H. Rong, and M. Paniccia, “Tunable ring resonators for silicon Raman laser and amplifier applications,” Proc. SPIE 6896, 68960Q (2008).
[Crossref]

Rong, H.

J. K. Doylend, O. Cohen, M. R. Lee, O. Raday, S. Xu, V. Sih, H. Rong, and M. Paniccia, “Tunable ring resonators for silicon Raman laser and amplifier applications,” Proc. SPIE 6896, 68960Q (2008).
[Crossref]

Scalbert, D.

R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
[Crossref]

Seferos, D. S.

Y. Q. Li, D. W. Steuerman, J. Berezovsky, D. S. Seferos, G. C. Bazan, and D. D. Awschalom, “Cavity enhanced Faraday rotation of semiconductor quantum dots,” Appl. Phys. Lett. 88(19), 193126 (2006).
[Crossref]

Sih, V.

C. J. Trowbridge, B. M. Norman, J. Stephens, A. C. Gossard, D. D. Awschalom, and V. Sih, “Electron spin polarization-based integrated photonic devices,” Opt. Express 19(16), 14845–14851 (2011).
[Crossref] [PubMed]

J. K. Doylend, O. Cohen, M. R. Lee, O. Raday, S. Xu, V. Sih, H. Rong, and M. Paniccia, “Tunable ring resonators for silicon Raman laser and amplifier applications,” Proc. SPIE 6896, 68960Q (2008).
[Crossref]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Wispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289 (1992).
[Crossref]

Stephens, J.

Steuerman, D. W.

Y. Q. Li, D. W. Steuerman, J. Berezovsky, D. S. Seferos, G. C. Bazan, and D. D. Awschalom, “Cavity enhanced Faraday rotation of semiconductor quantum dots,” Appl. Phys. Lett. 88(19), 193126 (2006).
[Crossref]

Trowbridge, C. J.

Vladimirova, M.

R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
[Crossref]

Xu, S.

J. K. Doylend, O. Cohen, M. R. Lee, O. Raday, S. Xu, V. Sih, H. Rong, and M. Paniccia, “Tunable ring resonators for silicon Raman laser and amplifier applications,” Proc. SPIE 6896, 68960Q (2008).
[Crossref]

Yariv, A.

A. Yariv, “Critical coupling and its ccntrol in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[Crossref]

J. M. Choi, R. K. Lee, and A. Yariv, “Control of critical coupling in a ring resonator-fiber configuration: application to wavelength-selective switching, modulation, amplification, and oscillation,” Opt. Lett. 26(16), 1236–1238 (2001).
[Crossref] [PubMed]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321 (2000).
[Crossref]

Appl. Phys. Lett. (2)

Y. Q. Li, D. W. Steuerman, J. Berezovsky, D. S. Seferos, G. C. Bazan, and D. D. Awschalom, “Cavity enhanced Faraday rotation of semiconductor quantum dots,” Appl. Phys. Lett. 88(19), 193126 (2006).
[Crossref]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Wispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289 (1992).
[Crossref]

Electron. Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321 (2000).
[Crossref]

IEEE Photon. Technol. Lett. (1)

A. Yariv, “Critical coupling and its ccntrol in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[Crossref]

J. Lightwave Technol. (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

R. Giri, S. Cronenberger, M. Vladimirova, D. Scalbert, K. V. Kavokin, M. M. Glazov, M. Nawrocki, A. Lemaître, and J. Bloch, “Giant photoinduced Faraday rotation due to the spin-polarized electron gas in an n-GaAs microcavity,” Phys. Rev. B 85(19), 195313 (2012).
[Crossref]

Phys. Rev. Lett. (1)

J. M. Kikkawa and D. D. Awschalom, “Resonant spin amplification in n-type GaAs,” Phys. Rev. Lett. 80(19), 4313–4316 (1998).
[Crossref]

Proc. SPIE (1)

J. K. Doylend, O. Cohen, M. R. Lee, O. Raday, S. Xu, V. Sih, H. Rong, and M. Paniccia, “Tunable ring resonators for silicon Raman laser and amplifier applications,” Proc. SPIE 6896, 68960Q (2008).
[Crossref]

Science (1)

Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Observation of the spin hall effect in semiconductors,” Science 306(5703), 1910–1913 (2004).
[Crossref] [PubMed]

Other (1)

H. Kitzerow and C. Bahr, eds., Chirality in Liquid Crystals (Springer 2001).

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Figures (7)

Fig. 1
Fig. 1 Schematic of ring resonator with coupling and interaction regions.
Fig. 2
Fig. 2 Device output polarization as a function of field rotation in the interaction region at critical coupling (t = α).
Fig. 3
Fig. 3 Amplification of the polarization rotation when (a) far off critical coupling and (b) close to critical coupling (δ = α -t).
Fig. 4
Fig. 4 Amplification as a function of offset from critical coupling for ϕ = 10−6 rad.
Fig. 5
Fig. 5 (a) Amplification when off resonance depending on offset from critical coupling for α = 0.999 and ϕ = 10−6 rad and (b) The width of the amplitude curve as a function of offset for different α
Fig. 6
Fig. 6 Polarization amplification as a function of (a) α and (b) 1-α for ϕ = 10−6 rad.
Fig. 7
Fig. 7 Amplification as a function of transmission coefficient for different combinations of αx and αy. Values for constant parameters are (a) αy = 0.999, δy = 10−3 and (b) αx = 0.999, δx = 10−3.

Equations (12)

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

( b 1 b 2 )=( t κ κ t * )=( a 1 a 2 )
| t | 2 + | κ | 2 =1
a 2 =α e iθ b 2 + a inj
b 1 = tα e iθ 1 t * α e iθ a 1 + κ 1 t * α e iθ a inj
b 1,crit = a inj κ = a inj 1 t 2
B=( b 1x b 2x b 1y b 2y )=( t x κ x 0 0 κ x * t x * 0 0 0 0 t y κ y 0 0 κ y * κ y * )( a 1x a 2x a 1y a 2y )=CA
A=( 0 0 0 0 0 cosϕ 0 sinϕ 0 0 0 0 0 sinϕ 0 cosϕ )( α x 0 0 0 0 α x 0 0 0 0 α y 0 0 0 0 α y ) e iθ B+( a 1x 0 a 1y 0 )=RB+ A 0
B=CA=C( RB+ A 0 ) B= ( 1CR ) 1 C A 0
b 1x = α x e iθ cosϕ t y * α x α y e 2iθ + t x t y * α y e iθ cosϕ t x t x * α x e iθ cosϕ+ t y * α y e iθ cosϕ t x * t y * α x α y e 2iθ 1
b 1y = κ x * κ y α x e iθ sinϕ t x * α x e iθ cosϕ+ t y * α y e iθ cosϕ t x * t y * α x α y e 2iθ 1
t x,opt = α x t y α y cosϕ t y α y cosϕ1 α x ( 1+ 1 2 t y α y +1 t y α y 1 ϕ 2 )
t y,opt = α y α x t x cosϕ α x cosϕ t x α y ( 1+ 1 2 α x + t x α x t x ϕ 2 )

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