Subwavelength silicon microcavities

doi:10.1364/OE.17.023323

Subwavelength silicon microcavities

Jeffrey Shainline, Stuart Elston, Zhijun Liu, Gustavo Fernandes, Rashid Zia, and Jimmy Xu »View Author Affiliations

Optics Express, Vol. 17, Issue 25, pp. 23323-23331 (2009)
http://dx.doi.org/10.1364/OE.17.023323

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Abstract

We present a study of the first silicon microdisk resonators which are smaller than the free-space resonant wavelength in all spatial dimensions. Spectral details of whispering gallery modes with azimuthal mode number m = 4-7 are measured in microdisks with diameters between 1.35 and 1.89μm and are studied at wavelengths from 1.52 to 1.62μm. For the structures considered here, m = 5 is the highest azimuthal mode order in a subwavelength cavity and has measured Q = 1250. These results agree well with theoretical calculations using a finite difference frequency domain method and fit an exponential scaling law relating Q to disk radius via m.

OCIS Codes
(230.5750) Optical devices : Resonators
(130.3990) Integrated optics : Micro-optical devices

ToC Category:
Integrated Optics

History
Original Manuscript: October 5, 2009
Revised Manuscript: November 6, 2009
Manuscript Accepted: November 25, 2009
Published: December 4, 2009

Citation
Jeffrey Shainline, Stuart Elston, Zhijun Liu, Gustavo Fernandes, Rashid Zia, and Jimmy Xu, "Subwavelength silicon microcavities," Opt. Express 17, 23323-23331 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-23323

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References

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992). [CrossRef]
A. F. J. Levi, R. E. Slusher, S. L. McCall, T. Tanbun-Ek, D. L. Coblentz, and S. J. Pearton, “Room temperature operation of microdisc lasers with submilliamp threshold current,” Electron. Lett. 28(11), 1010–1012 (1992). [CrossRef]
A. F. J. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Room temperature operation of submicrometre radius disk laser,” Electron. Lett. 29(18), 1666–1667 (1993). [CrossRef]
M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007). [CrossRef]
Q. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavelength microdisk lasers,” Appl. Phys. Lett. 94(6), 061109 (2009). [CrossRef]
C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron. 44(5), 435–447 (2008). [CrossRef]
Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express 16(6), 4309–4315 (2008). [CrossRef] [PubMed]
K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber-based measurement of an ultrasmall volume high- Q photonic crystal microcavity,” Phys. Rev. B 70(8), 081306 (2004). [CrossRef]
M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009). [CrossRef] [PubMed]
M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling and optical loss in silicon microdisks,” Appl. Phys. Lett. 85(17), 3693–3695 (2004). [CrossRef]
M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005). [CrossRef] [PubMed]
K. Srinivasan, M. Borselli, O. Painter, A. Stintz, and S. Krishna, “Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots,” Opt. Express 14(3), 1094–1105 (2006). [CrossRef] [PubMed]
K. Zhang, and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics (Springer, 1998).
J. E. Heebner, T. C. Bond, and J. S. Kallman, “Generalized formulation for performance degradations due to bending and edge scattering loss in microdisk resonators,” Opt. Express 15(8), 4452–4473 (2007). [CrossRef] [PubMed]
Amnon Yariv, Quantum Electronics (John Wiley and Sons, 1989), Chap. 22.
Jens Uwe Nöckel, “Resonances in nonintegrable open systems,” Ph.D. thesis (Yale University, 1997) pp 91–105.
R. P. Wang and M.-M. Dumitrescu, “Optical modes in semiconductor microdisk lasers,” IEEE J. Quantum Electron. 34(10), 1933–1937 (1998). [CrossRef]
N. C. Frateschi and A. F. J. Levi, “The spectrum of microdisk lasers,” J. Appl. Phys. 80(2), 644 (1996). [CrossRef]
P. Lusse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12(3), 487–494 (1994). [CrossRef]
R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71(16), 165431 (2005). [CrossRef]
H. Benisty, J.-M. Gerard, R. Houdre, J. Rarity, and C. Weisbuch, eds., Confined Photon Systems (Springer, New York, 1998).
B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009). [CrossRef] [PubMed]
A. C. F. Hoole, M. E. Welland, and A. N. Broers, “Negative PMMA as a high-resolution resist—the limits and possibilities,” Semicond. Sci. Technol. 12(9), 1166–1170 (1997). [CrossRef]
L. Deych, and J. Rubin, “Rayleigh scattering of whispering gallery modes of microspheres due to a single scatterer: myths and reality.” arXiv:0812.4404v1 [physics.optics] 23 Dec 2008.

Barclay, P. E.
Beausoleil, R. G.
Bond, T. C.
Borselli, M.
Broers, A. N.
Brongersma, M. L.
Camacho, R.
Cao, H.
Chan, J.
Coblentz, D. L.
de Vries, T.
de Waardt, H.
Dumitrescu, M.-M.
Eichenfield, M.
Eijkemans, T. J.
Fattal, D.
Frateschi, N. C.
Geluk, E. J.
Heebner, J. E.
Hill, M. T.
Ho, S. T.
Hoole, A. C. F.
Johnson, T. J.
Kallman, J. S.
Krishna, S.
Kwon, S.-H.
Lee, Y.-H.
Levi, A. F. J.
Logan, R. A.
Lusse, P.
Manolatou, C.
McCall, S. L.
Min, B.
Nötzel, R.
Oei, Y.-S.
Ostby, E.
Painter, O.
Pearton, S. J.
Rana, F.
Schule, J.
Selker, M. D.
Slusher, R. E.
Smalbrugge, B.
Smit, M. K.
Solomon, G. S.
Song, Q.
Sorger, V.
Srinivasan, K.
Stintz, A.
Stuwe, P.
Tanbun-Ek, T.
Turkiewicz, J. P.
Ulin-Avila, E.
Unger, H.-G.
Vahala, K.
Vahala, K. J.
van Otten, F. W. M.
van Veldhoven, P. J.
Wang, R. P.
Welland, M. E.
Xu, Q.
Yang, L.
Zhang, X.
Zhu, Y.
Zia, R.

Appl. Phys. Lett.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992). [CrossRef]
Q. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavelength microdisk lasers,” Appl. Phys. Lett. 94(6), 061109 (2009). [CrossRef]
M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling and optical loss in silicon microdisks,” Appl. Phys. Lett. 85(17), 3693–3695 (2004). [CrossRef]

Electron. Lett.

A. F. J. Levi, R. E. Slusher, S. L. McCall, T. Tanbun-Ek, D. L. Coblentz, and S. J. Pearton, “Room temperature operation of microdisc lasers with submilliamp threshold current,” Electron. Lett. 28(11), 1010–1012 (1992). [CrossRef]
A. F. J. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Room temperature operation of submicrometre radius disk laser,” Electron. Lett. 29(18), 1666–1667 (1993). [CrossRef]

IEEE J. Quantum Electron.

C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron. 44(5), 435–447 (2008). [CrossRef]
R. P. Wang and M.-M. Dumitrescu, “Optical modes in semiconductor microdisk lasers,” IEEE J. Quantum Electron. 34(10), 1933–1937 (1998). [CrossRef]

J. Appl. Phys.

N. C. Frateschi and A. F. J. Levi, “The spectrum of microdisk lasers,” J. Appl. Phys. 80(2), 644 (1996). [CrossRef]

J. Lightwave Technol.

P. Lusse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12(3), 487–494 (1994). [CrossRef]

Nat. Photonics

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007). [CrossRef]

Nature

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009). [CrossRef] [PubMed]
M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009). [CrossRef] [PubMed]

Opt. Express

Phys. Rev. B

R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71(16), 165431 (2005). [CrossRef]
K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber-based measurement of an ultrasmall volume high- Q photonic crystal microcavity,” Phys. Rev. B 70(8), 081306 (2004). [CrossRef]

Semicond. Sci. Technol.

A. C. F. Hoole, M. E. Welland, and A. N. Broers, “Negative PMMA as a high-resolution resist—the limits and possibilities,” Semicond. Sci. Technol. 12(9), 1166–1170 (1997). [CrossRef]

Other

L. Deych, and J. Rubin, “Rayleigh scattering of whispering gallery modes of microspheres due to a single scatterer: myths and reality.” arXiv:0812.4404v1 [physics.optics] 23 Dec 2008.
Amnon Yariv, Quantum Electronics (John Wiley and Sons, 1989), Chap. 22.
Jens Uwe Nöckel, “Resonances in nonintegrable open systems,” Ph.D. thesis (Yale University, 1997) pp 91–105.
H. Benisty, J.-M. Gerard, R. Houdre, J. Rarity, and C. Weisbuch, eds., Confined Photon Systems (Springer, New York, 1998).
K. Zhang, and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics (Springer, 1998).

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[1] S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992). [CrossRef]

[2] A. F. J. Levi, R. E. Slusher, S. L. McCall, T. Tanbun-Ek, D. L. Coblentz, and S. J. Pearton, “Room temperature operation of microdisc lasers with submilliamp threshold current,” Electron. Lett. 28(11), 1010–1012 (1992). [CrossRef]

[3] A. F. J. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Room temperature operation of submicrometre radius disk laser,” Electron. Lett. 29(18), 1666–1667 (1993). [CrossRef]

[4] M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007). [CrossRef]

[5] Q. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavelength microdisk lasers,” Appl. Phys. Lett. 94(6), 061109 (2009). [CrossRef]

[6] C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron. 44(5), 435–447 (2008). [CrossRef]

[7] Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express 16(6), 4309–4315 (2008). [CrossRef] [PubMed]

[8] K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber-based measurement of an ultrasmall volume high- Q photonic crystal microcavity,” Phys. Rev. B 70(8), 081306 (2004). [CrossRef]

[9] M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009). [CrossRef] [PubMed]

[10] M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling and optical loss in silicon microdisks,” Appl. Phys. Lett. 85(17), 3693–3695 (2004). [CrossRef]

[11] M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005). [CrossRef] [PubMed]

[12] K. Srinivasan, M. Borselli, O. Painter, A. Stintz, and S. Krishna, “Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots,” Opt. Express 14(3), 1094–1105 (2006). [CrossRef] [PubMed]

[13] K. Zhang, and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics (Springer, 1998).

[14] J. E. Heebner, T. C. Bond, and J. S. Kallman, “Generalized formulation for performance degradations due to bending and edge scattering loss in microdisk resonators,” Opt. Express 15(8), 4452–4473 (2007). [CrossRef] [PubMed]

[15] Amnon Yariv, Quantum Electronics (John Wiley and Sons, 1989), Chap. 22.

[16] Jens Uwe Nöckel, “Resonances in nonintegrable open systems,” Ph.D. thesis (Yale University, 1997) pp 91–105.

[17] R. P. Wang and M.-M. Dumitrescu, “Optical modes in semiconductor microdisk lasers,” IEEE J. Quantum Electron. 34(10), 1933–1937 (1998). [CrossRef]

[18] N. C. Frateschi and A. F. J. Levi, “The spectrum of microdisk lasers,” J. Appl. Phys. 80(2), 644 (1996). [CrossRef]

[19] P. Lusse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12(3), 487–494 (1994). [CrossRef]

[20] R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71(16), 165431 (2005). [CrossRef]

[21] H. Benisty, J.-M. Gerard, R. Houdre, J. Rarity, and C. Weisbuch, eds., Confined Photon Systems (Springer, New York, 1998).

[22] B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009). [CrossRef] [PubMed]

[23] A. C. F. Hoole, M. E. Welland, and A. N. Broers, “Negative PMMA as a high-resolution resist—the limits and possibilities,” Semicond. Sci. Technol. 12(9), 1166–1170 (1997). [CrossRef]

[24] L. Deych, and J. Rubin, “Rayleigh scattering of whispering gallery modes of microspheres due to a single scatterer: myths and reality.” arXiv:0812.4404v1 [physics.optics] 23 Dec 2008.

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Subwavelength silicon microcavities

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References

Appl. Phys. Lett.

Electron. Lett.

IEEE J. Quantum Electron.

J. Appl. Phys.

J. Lightwave Technol.

Nat. Photonics

Nature

Opt. Express

Phys. Rev. B

Semicond. Sci. Technol.

Other

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