Abstract

We characterize planar microcavities in whispering-gallery mode optical resonances. The microcavity consists of a waveguide and a microdisk, and a nanoscale gap separates the waveguide and the microdisk. The devices can be fabricated on Si-based thin films by using conventional microelectronics techniques. To characterize these types of cavity, we study a broad range of resonator configuration parameters including the size of the microdisk, the width of the gap, and the waveguide dimensions. The finite-element method is used for solving Maxwell's equations. The electric fields and the energy density distributions are obtained and compared between the on-resonance and off-resonance situations. A brilliant ring with a strong electric field and a high-energy density is found inside the periphery of the microdisk under first-order resonance. While under second-order resonance, there are two bright rings, and the light intensity in the inner ring is stronger than that in the outer ring. The resonant frequencies and their free spectral ranges are predominantly determined by the size of the microdisk. The gap effect on the resonant frequencies is observable, although it is minor. The gap strongly affects the full width at half-maximum (FWHM), finesse, and quality factor of the resonances. With an increase in the gap width from 100 to 300nm, both the Q value and finesse increase substantially, while the FWHM decreases. The waveguide width has a visible influence on the Q value, FWHM, and finesse as well.

© 2006 Optical Society of America

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References

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2005 (1)

H. Quan and Z. Guo, "Simulation of whispering-gallery-mode resonance shifts for optical miniature biosensors," J. Quant. Spectrosc. Radiat. Transfer 93, 231-243 (2005).
[CrossRef]

2003 (2)

2002 (1)

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

2001 (4)

2000 (1)

1997 (2)

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

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and T. J. A. Popma, "Experimental study of integrated-optics micro-cavity resonators: Toward an all-optical switching device," Appl. Phys. Lett. 71, 747-749 (1997).
[CrossRef]

1995 (1)

1991 (1)

1969 (1)

P. P. Silvester, "Finite element solution of homogeneous waveguide problems," Alta Freq. 38, 313-317 (1969).

Arnold, S.

Barber, P. W.

P. W. Barber and P. K. Chang, Optical Effects Associated with Small Particles (World Scientific, 1988).

Blair, S.

Blom, F. C.

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and T. J. A. Popma, "Experimental study of integrated-optics micro-cavity resonators: Toward an all-optical switching device," Appl. Phys. Lett. 71, 747-749 (1997).
[CrossRef]

Boyd, R. W.

Braun, D.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

Byer, R. L.

Cai, M.

Chang, P. K.

P. W. Barber and P. K. Chang, Optical Effects Associated with Small Particles (World Scientific, 1988).

Chen, Y.

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, 998-1005 (1997).
[CrossRef]

Driessen, A.

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and T. J. A. Popma, "Experimental study of integrated-optics micro-cavity resonators: Toward an all-optical switching device," Appl. Phys. Lett. 71, 747-749 (1997).
[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, 998-1005 (1997).
[CrossRef]

Griffel, G.

Guo, Z.

H. Quan and Z. Guo, "Simulation of whispering-gallery-mode resonance shifts for optical miniature biosensors," J. Quant. Spectrosc. Radiat. Transfer 93, 231-243 (2005).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

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, 998-1005 (1997).
[CrossRef]

Heebner, J. E.

Hoekstra, H. J.

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and T. J. A. Popma, "Experimental study of integrated-optics micro-cavity resonators: Toward an all-optical switching device," Appl. Phys. Lett. 71, 747-749 (1997).
[CrossRef]

Hsu, T. R.

T. R. Hsu, MEMS & Microsystems Design and Manufacture (McGraw-Hill, 2002).

Khoshsima, M.

S. Arnold, M. Khoshsima, I. Teraoka, and F. Vollmer, "Shift of whispering-gallery modes in microspheres by protein adsorption," Opt. Lett. 28, 272-274 (2003).

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

Kovetz, A.

A. Kovetz, The Principles of Electromagnetic Theory (Cambridge U. Press, 1990).

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, 998-1005 (1997).
[CrossRef]

Libchaber, A.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[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, 998-1005 (1997).
[CrossRef]

Modest, M. F.

M. F. Modest, Radiative Heat Transfer, 2nd ed. (Academic, 2003).

Painter, Q.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Popma, T. J. A.

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and T. J. A. Popma, "Experimental study of integrated-optics micro-cavity resonators: Toward an all-optical switching device," Appl. Phys. Lett. 71, 747-749 (1997).
[CrossRef]

Quan, H.

H. Quan and Z. Guo, "Simulation of whispering-gallery-mode resonance shifts for optical miniature biosensors," J. Quant. Spectrosc. Radiat. Transfer 93, 231-243 (2005).
[CrossRef]

Schiller, S.

Sercel, P. C.

Serpenguzel, A.

Silvester, P. P.

P. P. Silvester, "Finite element solution of homogeneous waveguide problems," Alta Freq. 38, 313-317 (1969).

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Teraoka, I.

Vahala, K. J.

van Dijk, D. R.

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and T. J. A. Popma, "Experimental study of integrated-optics micro-cavity resonators: Toward an all-optical switching device," Appl. Phys. Lett. 71, 747-749 (1997).
[CrossRef]

Vollmer, F.

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University Press, 1997).

Alta Freq. (1)

P. P. Silvester, "Finite element solution of homogeneous waveguide problems," Alta Freq. 38, 313-317 (1969).

Am. Sci. (1)

S. Arnold, "Microspheres, photonic atoms and the physics of nothing," Am. Sci. 89, 414-421 (2001).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and T. J. A. Popma, "Experimental study of integrated-optics micro-cavity resonators: Toward an all-optical switching device," Appl. Phys. Lett. 71, 747-749 (1997).
[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, 998-1005 (1997).
[CrossRef]

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

J. Quant. Spectrosc. Radiat. Transfer (1)

H. Quan and Z. Guo, "Simulation of whispering-gallery-mode resonance shifts for optical miniature biosensors," J. Quant. Spectrosc. Radiat. Transfer 93, 231-243 (2005).
[CrossRef]

Opt. Lett. (4)

Other (7)

M. F. Modest, Radiative Heat Transfer, 2nd ed. (Academic, 2003).

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University Press, 1997).

A. Kovetz, The Principles of Electromagnetic Theory (Cambridge U. Press, 1990).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

T. R. Hsu, MEMS & Microsystems Design and Manufacture (McGraw-Hill, 2002).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

P. W. Barber and P. K. Chang, Optical Effects Associated with Small Particles (World Scientific, 1988).

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Figures (8)

Fig. 1
Fig. 1

Sketch of a waveguide–microdisk coupling WGM resonator.

Fig. 2
Fig. 2

SEM photos of a fabricated WGM microcavity.

Fig. 3
Fig. 3

Electric fields under (a) the first-order resonance, (b) the second-order resonance, and (c) off resonance.

Fig. 4
Fig. 4

Energy distributions under (a) the first-order resonance, (b) the second-order resonance, and (c) off resonance.

Fig. 5
Fig. 5

Scattering spectra for different microdisk sizes of d = 10 , 12.5 , and 15 µm , respectively.

Fig. 6
Fig. 6

Comparisons between analytically estimated resonant frequencies and numerically predicted resonant frequencies.

Fig. 7
Fig. 7

Effects of the gap on the resonant quality factor Q and finesse F.

Fig. 8
Fig. 8

Effects of the waveguide width on the resonant quality factor Q and FWHM.

Tables (1)

Tables Icon

Table 1 Resonance Data From the Scattering Spectra

Equations (10)

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1 μ 2 E ¯ + ω 2 ε c E ¯ = 0 ,
1 μ 2 H ¯ + ω 2 ε c H ¯ = 0 ,
E ¯ ( x , y , t ) = E z ( x , y ) e ̄ z exp ( i ω t ) ,
H ¯ ( x , y , t ) = [ H x ( x , y ) e ̄ x + H y ( x , y ) e ̄ y ] exp ( i ω t ) .
n ¯ × H ¯ = 0.
e ̄ z · n ¯ × μ H ¯ + ε E z = 0.
E 0 z = 1 2 ε ( e ¯ z · n ¯ × μ H ¯ + ε E z ) .
Q = ω 0 / Δω = 2 π ω 0 τ ,
S ( E ¯ × H ¯ ) · n ¯ d S = - V ( E ¯ · D ¯ t + H ¯ · B ¯ t ) d V V J ¯ · E ¯ d V ,
f = c 0 2 r n sin ( π / m ) .

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