Abstract

A critical issue that hinders the development of chip-scale optical gyroscopes is the size dependence of the Sagnac effect, which manifests as a rotation-induced phase shift or frequency splitting between two counterpropagating waves or resonances, and is proportional to the size of the optical system. We show numerically and theoretically that the far-field emission patterns (FFPs) of optical microdisk cavities depend strongly on rotation and can therefore provide an alternative approach. At low rotation speed where resonant frequencies barely shift with rotation (i.e., a negligible Sagnac effect), the FFPs already exhibit a significant rotation-induced asymmetry, which increases linearly with the rotation speed. We further identify the basic requirements to maximize this effect, including distinct output directions for the clockwise and counterclockwise waves in a cavity mode, as well as a vanishing frequency splitting between one such mode and its symmetry related partner mode. Based on these requirements, we propose several microcavity shapes that display orders of magnitude enhancement of the emission sensitivity to rotation and could stimulate a new generation of optical gyroscopes with small footprints and on-chip integrability.

© 2015 Optical Society of America

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    [Crossref]
  34. C. Kim, Y.-J. Kim, E.-S. Jang, G.-C. Yi, H. H. Kim, “Whispering-gallery-modelike-enhanced emission from ZnO nanodisk,” Appl. Phys. Lett. 88, 093104 (2006).
    [Crossref]
  35. D. J. Gargas, M. C. Moore, A. Ni, S.-W. Chang, Z. Y. Zhang, S.-L. Chuang, P. D. Yang, “Whispering gallery mode lasing from zinc oxide hexagonal nanodisks,” ACS Nano 4, 3270–3276 (2010).
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    [Crossref]

2014 (2)

L. Ge, R. Sarma, H. Cao, “Rotation-induced asymmetry of far-field emission from optical microcavities,” Phys. Rev. A 90, 013809 (2014).
[Crossref]

B. Redding, L. Ge, Q. H. Song, G. S. Solomon, H. Cao, “Manipulation of high-order scattering processes in ultrasmall optical resonators to control far-field emission,” Phys. Rev. Lett. 112, 163902 (2014).
[Crossref]

2013 (4)

R. Novitski, J. Scheuer, B. Z. Steinberg, “Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect,” Phys. Rev. E 87, 023303 (2013).
[Crossref]

L. Ge, Q. H. Song, B. Redding, H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87, 023833 (2013).
[Crossref]

L. Ge, Q. Song, B. Redding, A. Eberspächer, J. Wiersig, H. Cao, “Controlling multimode coupling by boundary-wave scattering,” Phys. Rev. A 88, 043801 (2013).
[Crossref]

C. Tessarek, G. Sarau, M. Kiometzis, S. Christiansen, “High quality factor whispering gallery modes from self-assembled hexagonal GaN rods grown by metal-organic vapor phase epitaxy,” Opt. Express 21, 2733–2740 (2013).
[Crossref]

2012 (4)

B. Redding, L. Ge, Q. H. Song, J. Wiersig, G. S. Solomon, H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref]

C. Sorrentino, J. R. E. Toland, C. P. Search, “Ultra-sensitive chip scale Sagnac gyroscope based on periodically modulated coupling of a coupled resonator optical waveguide,” Opt. Express 20, 354–363 (2012).
[Crossref]

R. Novitski, B. Z. Steinberg, J. Scheuer, “Losses in rotating degenerate cavities and a coupled-resonator optical-waveguide rotation sensor,” Phys. Rev. A 85, 023813 (2012).
[Crossref]

R. Sarma, H. Cao, “Wavelength-scale microdisks as optical gyroscopes: a finite-difference time-domain simulation study,” J. Opt. Soc. Am. B 29, 1648–1654 (2012).
[Crossref]

2010 (3)

C. Ciminelli, F. Dell’Olio, C. E. Campanella, M. N. Armenise, “Photonic technologies for angular velocity sensing,” Adv. Opt. Photon. 2, 370–404 (2010).

D. J. Gargas, M. C. Moore, A. Ni, S.-W. Chang, Z. Y. Zhang, S.-L. Chuang, P. D. Yang, “Whispering gallery mode lasing from zinc oxide hexagonal nanodisks,” ACS Nano 4, 3270–3276 (2010).
[Crossref]

Q. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 103902 (2010).
[Crossref]

2009 (1)

M. Terrel, M. J. F. Digonnet, S. Fan, “Performance comparison of slow-light coupled-resonator optical gyroscopes,” Laser Photon. Rev. 3, 452–465 (2009).

2008 (3)

S. Sunada, S. Tamura, K. Inagaki, T. Harayama, “Ring-laser gyroscope without the lock-in phenomenon,” Phys. Rev. A 78, 053822 (2008).
[Crossref]

J. Wiersig, M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
[Crossref]

R. Dubertrand, E. Bogomolny, N. Djellali, M. Lebental, C. Schmit, “Circular dielectric cavity and its deformations,” Phys. Rev. A 77, 013804 (2008).
[Crossref]

2007 (4)

2006 (3)

J. Scheuer, A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96, 053901 (2006).
[Crossref]

S. Sunada, T. Harayama, “Sagnac effect in resonant microcavities,” Phys. Rev. A 74, 021801(R) (2006).
[Crossref]

C. Kim, Y.-J. Kim, E.-S. Jang, G.-C. Yi, H. H. Kim, “Whispering-gallery-modelike-enhanced emission from ZnO nanodisk,” Appl. Phys. Lett. 88, 093104 (2006).
[Crossref]

2005 (1)

B. Z. Steinberg, “Rotating photonic crystals: a medium for compact optical gyroscopes,” Phys. Rev. E 71, 056621 (2005).
[Crossref]

2004 (2)

2000 (1)

K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, T. Maeda, “Fabrication and characterization of low defect density GaN using facet-controlled epitaxial lateral overgrowth (FACELO),” J. Cryst. Growth 221, 316–326 (2000).
[Crossref]

1998 (1)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

1997 (1)

J. U. Nöckel, A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
[Crossref]

1985 (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[Crossref]

1967 (1)

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–493 (1967).
[Crossref]

Armenise, M. N.

Aronowitz, F.

F. Aronowitz, “The laser gyro,” in Laser Applications (Academic, 1971), pp. 113–200.

Ben-Messaoud, T.

Boag, A.

Bogomolny, E.

R. Dubertrand, E. Bogomolny, N. Djellali, M. Lebental, C. Schmit, “Circular dielectric cavity and its deformations,” Phys. Rev. A 77, 013804 (2008).
[Crossref]

Campanella, C. E.

Cao, H.

L. Ge, R. Sarma, H. Cao, “Rotation-induced asymmetry of far-field emission from optical microcavities,” Phys. Rev. A 90, 013809 (2014).
[Crossref]

B. Redding, L. Ge, Q. H. Song, G. S. Solomon, H. Cao, “Manipulation of high-order scattering processes in ultrasmall optical resonators to control far-field emission,” Phys. Rev. Lett. 112, 163902 (2014).
[Crossref]

L. Ge, Q. H. Song, B. Redding, H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87, 023833 (2013).
[Crossref]

L. Ge, Q. Song, B. Redding, A. Eberspächer, J. Wiersig, H. Cao, “Controlling multimode coupling by boundary-wave scattering,” Phys. Rev. A 88, 043801 (2013).
[Crossref]

R. Sarma, H. Cao, “Wavelength-scale microdisks as optical gyroscopes: a finite-difference time-domain simulation study,” J. Opt. Soc. Am. B 29, 1648–1654 (2012).
[Crossref]

B. Redding, L. Ge, Q. H. Song, J. Wiersig, G. S. Solomon, H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref]

Q. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 103902 (2010).
[Crossref]

Capasso, F.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

Chang, R. K.

Chang, S.-W.

D. J. Gargas, M. C. Moore, A. Ni, S.-W. Chang, Z. Y. Zhang, S.-L. Chuang, P. D. Yang, “Whispering gallery mode lasing from zinc oxide hexagonal nanodisks,” ACS Nano 4, 3270–3276 (2010).
[Crossref]

Cho, A. Y.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

Chow, W. W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[Crossref]

Christiansen, S.

Chuang, S.-L.

D. J. Gargas, M. C. Moore, A. Ni, S.-W. Chang, Z. Y. Zhang, S.-L. Chuang, P. D. Yang, “Whispering gallery mode lasing from zinc oxide hexagonal nanodisks,” ACS Nano 4, 3270–3276 (2010).
[Crossref]

Ciminelli, C.

Dell’Olio, F.

Digonnet, M. J. F.

M. Terrel, M. J. F. Digonnet, S. Fan, “Performance comparison of slow-light coupled-resonator optical gyroscopes,” Laser Photon. Rev. 3, 452–465 (2009).

Djellali, N.

R. Dubertrand, E. Bogomolny, N. Djellali, M. Lebental, C. Schmit, “Circular dielectric cavity and its deformations,” Phys. Rev. A 77, 013804 (2008).
[Crossref]

Dubertrand, R.

R. Dubertrand, E. Bogomolny, N. Djellali, M. Lebental, C. Schmit, “Circular dielectric cavity and its deformations,” Phys. Rev. A 77, 013804 (2008).
[Crossref]

Eberspächer, A.

L. Ge, Q. Song, B. Redding, A. Eberspächer, J. Wiersig, H. Cao, “Controlling multimode coupling by boundary-wave scattering,” Phys. Rev. A 88, 043801 (2013).
[Crossref]

Faist, J.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

Fan, S.

M. Terrel, M. J. F. Digonnet, S. Fan, “Performance comparison of slow-light coupled-resonator optical gyroscopes,” Laser Photon. Rev. 3, 452–465 (2009).

Fang, W.

Q. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 103902 (2010).
[Crossref]

Gargas, D. J.

D. J. Gargas, M. C. Moore, A. Ni, S.-W. Chang, Z. Y. Zhang, S.-L. Chuang, P. D. Yang, “Whispering gallery mode lasing from zinc oxide hexagonal nanodisks,” ACS Nano 4, 3270–3276 (2010).
[Crossref]

Ge, L.

B. Redding, L. Ge, Q. H. Song, G. S. Solomon, H. Cao, “Manipulation of high-order scattering processes in ultrasmall optical resonators to control far-field emission,” Phys. Rev. Lett. 112, 163902 (2014).
[Crossref]

L. Ge, R. Sarma, H. Cao, “Rotation-induced asymmetry of far-field emission from optical microcavities,” Phys. Rev. A 90, 013809 (2014).
[Crossref]

L. Ge, Q. Song, B. Redding, A. Eberspächer, J. Wiersig, H. Cao, “Controlling multimode coupling by boundary-wave scattering,” Phys. Rev. A 88, 043801 (2013).
[Crossref]

L. Ge, Q. H. Song, B. Redding, H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87, 023833 (2013).
[Crossref]

B. Redding, L. Ge, Q. H. Song, J. Wiersig, G. S. Solomon, H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref]

Q. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 103902 (2010).
[Crossref]

Gea-Banacloche, J.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[Crossref]

Gmachl, C.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

Harayama, T.

S. Sunada, S. Tamura, K. Inagaki, T. Harayama, “Ring-laser gyroscope without the lock-in phenomenon,” Phys. Rev. A 78, 053822 (2008).
[Crossref]

S. Sunada, T. Harayama, “Design of resonant microcavities: application to optical gyroscopes,” Opt. Express 15, 16245–16254 (2007).
[Crossref]

S. Sunada, T. Harayama, “Sagnac effect in resonant microcavities,” Phys. Rev. A 74, 021801(R) (2006).
[Crossref]

Hentschel, M.

J. Wiersig, M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
[Crossref]

Hiramatsu, K.

K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, T. Maeda, “Fabrication and characterization of low defect density GaN using facet-controlled epitaxial lateral overgrowth (FACELO),” J. Cryst. Growth 221, 316–326 (2000).
[Crossref]

Ilchenko, V. S.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004).
[Crossref]

Inagaki, K.

S. Sunada, S. Tamura, K. Inagaki, T. Harayama, “Ring-laser gyroscope without the lock-in phenomenon,” Phys. Rev. A 78, 053822 (2008).
[Crossref]

Iyechika, Y.

K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, T. Maeda, “Fabrication and characterization of low defect density GaN using facet-controlled epitaxial lateral overgrowth (FACELO),” J. Cryst. Growth 221, 316–326 (2000).
[Crossref]

Jang, E.-S.

C. Kim, Y.-J. Kim, E.-S. Jang, G.-C. Yi, H. H. Kim, “Whispering-gallery-modelike-enhanced emission from ZnO nanodisk,” Appl. Phys. Lett. 88, 093104 (2006).
[Crossref]

Kim, C.

C. Kim, Y.-J. Kim, E.-S. Jang, G.-C. Yi, H. H. Kim, “Whispering-gallery-modelike-enhanced emission from ZnO nanodisk,” Appl. Phys. Lett. 88, 093104 (2006).
[Crossref]

Kim, H. H.

C. Kim, Y.-J. Kim, E.-S. Jang, G.-C. Yi, H. H. Kim, “Whispering-gallery-modelike-enhanced emission from ZnO nanodisk,” Appl. Phys. Lett. 88, 093104 (2006).
[Crossref]

Kim, Y.-J.

C. Kim, Y.-J. Kim, E.-S. Jang, G.-C. Yi, H. H. Kim, “Whispering-gallery-modelike-enhanced emission from ZnO nanodisk,” Appl. Phys. Lett. 88, 093104 (2006).
[Crossref]

Kiometzis, M.

Lebental, M.

R. Dubertrand, E. Bogomolny, N. Djellali, M. Lebental, C. Schmit, “Circular dielectric cavity and its deformations,” Phys. Rev. A 77, 013804 (2008).
[Crossref]

Li, Z.

Maeda, T.

K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, T. Maeda, “Fabrication and characterization of low defect density GaN using facet-controlled epitaxial lateral overgrowth (FACELO),” J. Cryst. Growth 221, 316–326 (2000).
[Crossref]

Maleki, L.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004).
[Crossref]

Matsko, A. B.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004).
[Crossref]

Miyake, H.

K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, T. Maeda, “Fabrication and characterization of low defect density GaN using facet-controlled epitaxial lateral overgrowth (FACELO),” J. Cryst. Growth 221, 316–326 (2000).
[Crossref]

Mizutani, H.

K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, T. Maeda, “Fabrication and characterization of low defect density GaN using facet-controlled epitaxial lateral overgrowth (FACELO),” J. Cryst. Growth 221, 316–326 (2000).
[Crossref]

Moore, M. C.

D. J. Gargas, M. C. Moore, A. Ni, S.-W. Chang, Z. Y. Zhang, S.-L. Chuang, P. D. Yang, “Whispering gallery mode lasing from zinc oxide hexagonal nanodisks,” ACS Nano 4, 3270–3276 (2010).
[Crossref]

Motogaito, A.

K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, T. Maeda, “Fabrication and characterization of low defect density GaN using facet-controlled epitaxial lateral overgrowth (FACELO),” J. Cryst. Growth 221, 316–326 (2000).
[Crossref]

Narimanov, E. E.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

Narukawa, M.

K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, T. Maeda, “Fabrication and characterization of low defect density GaN using facet-controlled epitaxial lateral overgrowth (FACELO),” J. Cryst. Growth 221, 316–326 (2000).
[Crossref]

Ni, A.

D. J. Gargas, M. C. Moore, A. Ni, S.-W. Chang, Z. Y. Zhang, S.-L. Chuang, P. D. Yang, “Whispering gallery mode lasing from zinc oxide hexagonal nanodisks,” ACS Nano 4, 3270–3276 (2010).
[Crossref]

Nishiyama, K.

K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, T. Maeda, “Fabrication and characterization of low defect density GaN using facet-controlled epitaxial lateral overgrowth (FACELO),” J. Cryst. Growth 221, 316–326 (2000).
[Crossref]

Nöckel, J. U.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

J. U. Nöckel, A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
[Crossref]

Novitski, R.

R. Novitski, J. Scheuer, B. Z. Steinberg, “Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect,” Phys. Rev. E 87, 023303 (2013).
[Crossref]

R. Novitski, B. Z. Steinberg, J. Scheuer, “Losses in rotating degenerate cavities and a coupled-resonator optical-waveguide rotation sensor,” Phys. Rev. A 85, 023813 (2012).
[Crossref]

Onishi, M.

K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, T. Maeda, “Fabrication and characterization of low defect density GaN using facet-controlled epitaxial lateral overgrowth (FACELO),” J. Cryst. Growth 221, 316–326 (2000).
[Crossref]

Pedrotti, L. M.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[Crossref]

Peng, C.

Post, E. J.

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–493 (1967).
[Crossref]

Redding, B.

B. Redding, L. Ge, Q. H. Song, G. S. Solomon, H. Cao, “Manipulation of high-order scattering processes in ultrasmall optical resonators to control far-field emission,” Phys. Rev. Lett. 112, 163902 (2014).
[Crossref]

L. Ge, Q. H. Song, B. Redding, H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87, 023833 (2013).
[Crossref]

L. Ge, Q. Song, B. Redding, A. Eberspächer, J. Wiersig, H. Cao, “Controlling multimode coupling by boundary-wave scattering,” Phys. Rev. A 88, 043801 (2013).
[Crossref]

B. Redding, L. Ge, Q. H. Song, J. Wiersig, G. S. Solomon, H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref]

Rex, N. B.

Sanders, V. E.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[Crossref]

Sarau, G.

Sarma, R.

L. Ge, R. Sarma, H. Cao, “Rotation-induced asymmetry of far-field emission from optical microcavities,” Phys. Rev. A 90, 013809 (2014).
[Crossref]

R. Sarma, H. Cao, “Wavelength-scale microdisks as optical gyroscopes: a finite-difference time-domain simulation study,” J. Opt. Soc. Am. B 29, 1648–1654 (2012).
[Crossref]

Savchenkov, A. A.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004).
[Crossref]

Scheuer, J.

R. Novitski, J. Scheuer, B. Z. Steinberg, “Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect,” Phys. Rev. E 87, 023303 (2013).
[Crossref]

R. Novitski, B. Z. Steinberg, J. Scheuer, “Losses in rotating degenerate cavities and a coupled-resonator optical-waveguide rotation sensor,” Phys. Rev. A 85, 023813 (2012).
[Crossref]

J. Scheuer, “Direct rotation-induced intensity modulation in circular Bragg micro-lasers,” Opt. Express 15, 15053–15059 (2007).
[Crossref]

B. Z. Steinberg, J. Scheuer, A. Boag, “Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B 24, 1216–1224 (2007).
[Crossref]

J. Scheuer, A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96, 053901 (2006).
[Crossref]

Schleich, W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[Crossref]

Schmit, C.

R. Dubertrand, E. Bogomolny, N. Djellali, M. Lebental, C. Schmit, “Circular dielectric cavity and its deformations,” Phys. Rev. A 77, 013804 (2008).
[Crossref]

Schwefel, H. G.

Scully, M. O.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[Crossref]

Search, C. P.

Shim, J.-B.

Q. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 103902 (2010).
[Crossref]

Sivco, D. L.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

Solomon, G. S.

B. Redding, L. Ge, Q. H. Song, G. S. Solomon, H. Cao, “Manipulation of high-order scattering processes in ultrasmall optical resonators to control far-field emission,” Phys. Rev. Lett. 112, 163902 (2014).
[Crossref]

B. Redding, L. Ge, Q. H. Song, J. Wiersig, G. S. Solomon, H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref]

Q. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 103902 (2010).
[Crossref]

Song, Q.

L. Ge, Q. Song, B. Redding, A. Eberspächer, J. Wiersig, H. Cao, “Controlling multimode coupling by boundary-wave scattering,” Phys. Rev. A 88, 043801 (2013).
[Crossref]

Q. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 103902 (2010).
[Crossref]

Song, Q. H.

B. Redding, L. Ge, Q. H. Song, G. S. Solomon, H. Cao, “Manipulation of high-order scattering processes in ultrasmall optical resonators to control far-field emission,” Phys. Rev. Lett. 112, 163902 (2014).
[Crossref]

L. Ge, Q. H. Song, B. Redding, H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87, 023833 (2013).
[Crossref]

B. Redding, L. Ge, Q. H. Song, J. Wiersig, G. S. Solomon, H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref]

Sorrentino, C.

Steinberg, B. Z.

R. Novitski, J. Scheuer, B. Z. Steinberg, “Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect,” Phys. Rev. E 87, 023303 (2013).
[Crossref]

R. Novitski, B. Z. Steinberg, J. Scheuer, “Losses in rotating degenerate cavities and a coupled-resonator optical-waveguide rotation sensor,” Phys. Rev. A 85, 023813 (2012).
[Crossref]

B. Z. Steinberg, J. Scheuer, A. Boag, “Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B 24, 1216–1224 (2007).
[Crossref]

B. Z. Steinberg, “Rotating photonic crystals: a medium for compact optical gyroscopes,” Phys. Rev. E 71, 056621 (2005).
[Crossref]

Stone, A. D.

Q. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 103902 (2010).
[Crossref]

H. G. Schwefel, N. B. Rex, H. E. Türeci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B 21, 923–934 (2004).
[Crossref]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

J. U. Nöckel, A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
[Crossref]

Sunada, S.

S. Sunada, S. Tamura, K. Inagaki, T. Harayama, “Ring-laser gyroscope without the lock-in phenomenon,” Phys. Rev. A 78, 053822 (2008).
[Crossref]

S. Sunada, T. Harayama, “Design of resonant microcavities: application to optical gyroscopes,” Opt. Express 15, 16245–16254 (2007).
[Crossref]

S. Sunada, T. Harayama, “Sagnac effect in resonant microcavities,” Phys. Rev. A 74, 021801(R) (2006).
[Crossref]

Tamura, S.

S. Sunada, S. Tamura, K. Inagaki, T. Harayama, “Ring-laser gyroscope without the lock-in phenomenon,” Phys. Rev. A 78, 053822 (2008).
[Crossref]

Terrel, M.

M. Terrel, M. J. F. Digonnet, S. Fan, “Performance comparison of slow-light coupled-resonator optical gyroscopes,” Laser Photon. Rev. 3, 452–465 (2009).

Tessarek, C.

Toland, J. R. E.

Türeci, H. E.

Unterhinninghofen, J.

Q. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 103902 (2010).
[Crossref]

Wiersig, J.

L. Ge, Q. Song, B. Redding, A. Eberspächer, J. Wiersig, H. Cao, “Controlling multimode coupling by boundary-wave scattering,” Phys. Rev. A 88, 043801 (2013).
[Crossref]

B. Redding, L. Ge, Q. H. Song, J. Wiersig, G. S. Solomon, H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref]

Q. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 103902 (2010).
[Crossref]

J. Wiersig, M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
[Crossref]

Xu, A.

Yang, P. D.

D. J. Gargas, M. C. Moore, A. Ni, S.-W. Chang, Z. Y. Zhang, S.-L. Chuang, P. D. Yang, “Whispering gallery mode lasing from zinc oxide hexagonal nanodisks,” ACS Nano 4, 3270–3276 (2010).
[Crossref]

Yariv, A.

J. Scheuer, A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96, 053901 (2006).
[Crossref]

Yi, G.-C.

C. Kim, Y.-J. Kim, E.-S. Jang, G.-C. Yi, H. H. Kim, “Whispering-gallery-modelike-enhanced emission from ZnO nanodisk,” Appl. Phys. Lett. 88, 093104 (2006).
[Crossref]

Zhang, Z. Y.

D. J. Gargas, M. C. Moore, A. Ni, S.-W. Chang, Z. Y. Zhang, S.-L. Chuang, P. D. Yang, “Whispering gallery mode lasing from zinc oxide hexagonal nanodisks,” ACS Nano 4, 3270–3276 (2010).
[Crossref]

Zyss, J.

ACS Nano (1)

D. J. Gargas, M. C. Moore, A. Ni, S.-W. Chang, Z. Y. Zhang, S.-L. Chuang, P. D. Yang, “Whispering gallery mode lasing from zinc oxide hexagonal nanodisks,” ACS Nano 4, 3270–3276 (2010).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (1)

C. Kim, Y.-J. Kim, E.-S. Jang, G.-C. Yi, H. H. Kim, “Whispering-gallery-modelike-enhanced emission from ZnO nanodisk,” Appl. Phys. Lett. 88, 093104 (2006).
[Crossref]

J. Cryst. Growth (1)

K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, T. Maeda, “Fabrication and characterization of low defect density GaN using facet-controlled epitaxial lateral overgrowth (FACELO),” J. Cryst. Growth 221, 316–326 (2000).
[Crossref]

J. Opt. Soc. Am. B (3)

Laser Photon. Rev. (1)

M. Terrel, M. J. F. Digonnet, S. Fan, “Performance comparison of slow-light coupled-resonator optical gyroscopes,” Laser Photon. Rev. 3, 452–465 (2009).

Nature (1)

J. U. Nöckel, A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
[Crossref]

Opt. Commun. (1)

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004).
[Crossref]

Opt. Express (5)

Phys. Rev. A (7)

R. Novitski, B. Z. Steinberg, J. Scheuer, “Losses in rotating degenerate cavities and a coupled-resonator optical-waveguide rotation sensor,” Phys. Rev. A 85, 023813 (2012).
[Crossref]

L. Ge, Q. H. Song, B. Redding, H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87, 023833 (2013).
[Crossref]

L. Ge, Q. Song, B. Redding, A. Eberspächer, J. Wiersig, H. Cao, “Controlling multimode coupling by boundary-wave scattering,” Phys. Rev. A 88, 043801 (2013).
[Crossref]

R. Dubertrand, E. Bogomolny, N. Djellali, M. Lebental, C. Schmit, “Circular dielectric cavity and its deformations,” Phys. Rev. A 77, 013804 (2008).
[Crossref]

S. Sunada, T. Harayama, “Sagnac effect in resonant microcavities,” Phys. Rev. A 74, 021801(R) (2006).
[Crossref]

S. Sunada, S. Tamura, K. Inagaki, T. Harayama, “Ring-laser gyroscope without the lock-in phenomenon,” Phys. Rev. A 78, 053822 (2008).
[Crossref]

L. Ge, R. Sarma, H. Cao, “Rotation-induced asymmetry of far-field emission from optical microcavities,” Phys. Rev. A 90, 013809 (2014).
[Crossref]

Phys. Rev. E (2)

B. Z. Steinberg, “Rotating photonic crystals: a medium for compact optical gyroscopes,” Phys. Rev. E 71, 056621 (2005).
[Crossref]

R. Novitski, J. Scheuer, B. Z. Steinberg, “Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect,” Phys. Rev. E 87, 023303 (2013).
[Crossref]

Phys. Rev. Lett. (5)

J. Scheuer, A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96, 053901 (2006).
[Crossref]

J. Wiersig, M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
[Crossref]

Q. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105, 103902 (2010).
[Crossref]

B. Redding, L. Ge, Q. H. Song, J. Wiersig, G. S. Solomon, H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref]

B. Redding, L. Ge, Q. H. Song, G. S. Solomon, H. Cao, “Manipulation of high-order scattering processes in ultrasmall optical resonators to control far-field emission,” Phys. Rev. Lett. 112, 163902 (2014).
[Crossref]

Rev. Mod. Phys. (2)

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–493 (1967).
[Crossref]

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[Crossref]

Science (1)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

Other (4)

F. Aronowitz, “The laser gyro,” in Laser Applications (Academic, 1971), pp. 113–200.

R. K. Chang, A. J. Campillo, eds., Optical Processes in Microcavities, Advanced Series in Applied Physics (World Scientific, 1996).

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

http://www.mermig-space.eu/ , accessed 2/22/15.

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Figures (3)

Fig. 1.
Fig. 1.

Near-field and far-field intensity patterns of a nonrotating limaçon cavity. (a) Near-field intensity pattern in the logarithmic scale and (b) far-field intensity pattern in the polar coordinates of a symmetric resonance ψeven at kevenR33.78. The cavity deformation is ε=0.41, and the refractive index is n=3. The resonance is concentrated near the cavity boundary, similar to a whispering-galley mode. Its emission is directional, with the main direction centered in θ=0° and the secondary peaks in θ138° and 138°=222°. The CW wave component of this resonance is separated and plotted in (c) and (d). Its mirror image about the horizontal axis gives the CCW wave (not shown).

Fig. 2.
Fig. 2.

Rotation-induced changes in resonance frequency and far-field emission pattern of a limaçon cavity. (a) Far-field intensity pattern of the resonance shown in Fig. 1 when the dimensionless rotation speed Ω¯=108 (thick line), 109 (medium line), and 1010 (thin line). The maximum intensity is normalized to 1 for each curve. Rotation enhances the emission peak at θcw and reduces the one at θccw. (b) Dimensionless frequency splitting Δ of the quasi-degenerate resonances as a function of the normalized rotation speed Ω¯. Δ remains nearly constant below Ω¯c109 (marked by the vertical dashed line), marking a “dead zone” for the Sagnac effect. The diamonds represent the numerical data, and the solid line shows the result of the coupled-mode theory, Eq. (4). (c) Rotation-induced FFP asymmetry χ as a function of Ω¯. χ increases linearly with Ω¯ inside the “dead zone.”

Fig. 3.
Fig. 3.

Enhanced sensitivity of far-field emission pattern to rotation in a D3 cavity with R=5μm and n=3. (a) Near-field intensity plot of the CW wave in a whispering-gallery-like resonance at kevenR33.80 in the logarithmic scale. The dominant angular components of this resonance are m=±94. (b) Distinct FFPs in the polar coordinates of CW (solid) and CCW (dotted) waves at rest. (c) Far-field intensity pattern at Ω¯=1013 (thick line), 1014 (medium line), and 1015 (thin line). (d) Dimensionless frequency splitting Δ as a function of the normalized rotation speed Ω¯, showing a linear increase due to the vanishing “dead zone”. The diamonds represent the numerical data, and the solid line shows the result of the coupled-mode theory, Eq. (4). (e) Rotation-induced FFP asymmetry χ of the ψeven resonance as a function of Ω¯. θcw=254°, θccw=226° (equivalent to the one at 254°), and σ=15° are used in calculating χ(Ω¯) from Eq. (3).

Equations (5)

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

[2+n(r⃗)2ω2c2+2iωcΩcθ]ψ(r⃗)=0
Am(r)={αmHm+(k¯mr)+βmHm(k¯mr),r<ρ(θ),γmHm+(k˜mr),r>ρ(θ).
χ(Ω¯)=θcwσ/2θcw+σ/2IFFP(θ;Ω¯)dθθccwσ/2θccw+σ/2IFFP(θ;Ω¯)dθ1,
Δ(Ω¯)[Δ02+g2Ω¯2]12.
ξ(Ω¯)±iΩ2Ωc,

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