Abstract

Using a combination of resist reflow to form a highly circular etch mask pattern and a low-damage plasma dry etch, high-quality-factor silicon optical microdisk resonators are fabricated out of silicon-oninsulator (SOI) wafers. Quality factors as high as Q=5×106 are measured in these microresonators, corresponding to a propagation loss coefficient as small as α~0.1 dB/cm. The different optical loss mechanisms are identified through a study of the total optical loss, mode coupling, and thermally-induced optical bistability as a function of microdisk radius (5-30 µm). These measurements indicate that optical loss in these high-Q microresonators is limited not by surface roughness, but rather by surface state absorption and bulk free-carrier absorption.

© 2005 Optical Society of America

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References

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Appl. Phys. Lett.

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

M. Haverlag, D. Vender, and G. S. Oehrlein, �??Ellipsometric study of silicon surface damage in electron cyclotron resonance plasma etching using CF4 and SF6,�?? Appl. Phys. Lett. 61, 2875�??2877 (1992).
[CrossRef]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, �??Loss characterization in microcavities using the thermal bistability effect,�?? Appl. Phys. Lett. 85, 3029�??3031 (2004).
[CrossRef]

IEEE J. Quan. Elec.

M. Kuznetsov and H. A. Haus, �??Radiation Loss in Dielectric Waveguide Structures by the Volume Current Method,�?? IEEE J. Quan. Elec. 19, 1505�??1514 (1983).
[CrossRef]

R. A. Soref and B. R. Bennett, �??Electrooptical effects in silicon,�?? IEEE J. Quan. Elec. 23, 123�??129 (1987).
[CrossRef]

J. Opt. Soc. Am. B

Nature

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, �??Ultra-high-Q toroid microcavity on a chip,�?? Nature 421, 925�??928 (2003).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, �??A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,�?? Nature 427, 615�??618 (2004).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, �??All-optical control of light on a silicon chip,�?? Nature 431, 1081�??1084 (2004).
[CrossRef] [PubMed]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, �??A continuous-wave Raman silicon laser,�?? Nature 433, 725�??728 (2005).
[CrossRef] [PubMed]

OFC 2003

B. E. Little, �??A VLSI Photonics Platform,�?? in Optical Fiber Communication Conference (2003).

Opt. Express

Opt. Lett.

Phys. Rev. B

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, 081306(R) (2004).
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, D. L. Allara, C. C. Chang, T. Gmitter, and T. B. Bright, �??Unusually Low Surface-Recombination Velocity on Silicon and Germanium Surfaces,�?? Phys. Rev. Lett. 57, 249�??252 (1986).
[CrossRef] [PubMed]

M. Cai, O. Painter, and K. Vahala, �??Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,�?? Phys. Rev. Lett. 85, 74�??77 (2000).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, �??Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,�?? Phys. Rev. Lett. 91, 043,902 (2003).
[CrossRef]

Other

J. D. Joannopoulos, R. D. Meade, and J. N.Winn, Photonic Crystals (Princeton University Press, Princeton, New Jersey, 1995).

H. A. Haus, Waves and Fields in Optoelectronics, 1st ed. (Prentice-Hall, Englewood Cliffs, New Jersey 07632, 1984).

L. Pavesi and D. Lockwood, Silicon Photonics (Springer-verlag, New York, 2004).

G. Reed and A. Knights, Silicon Photonics: An Introduction (John Wiley, West Sussex, 2004).
[CrossRef]

K. Okamoto, Fundamentals of optical waveguides (Academic Press, San Diego, 2000).

A. Yariv, Optical Electronics, 4th ed. (Saunder College Publishing, a division of Holt, Rinehart and Winston, Inc., Orlando, Florida, 1991).

S. Spillane (2004). Private communication.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic representation of a fabricated silicon microdisk. (a) Top view showing ideal disk (red) against disk with roughness. (b) Top view close-up illustrating the surface roughness, Δr(s), and surface reconstruction, ξ. Also shown are statistical roughness parameters, σ r and Lc , of a typical scatterer. (c) Side view of a fabricated SOI microdisk highlighting idealized SiO2 pedestal.

Fig. 2.
Fig. 2.

Taper transmission versus wavelength showing a high-Q doublet mode for the R=30 µm disk. Qcλ 0/δλ c and Qsλ 0/δλ s are the unloaded quality factors for the long and short wavelength modes respectively, where δλ c and δλ s are resonance linewidths. Also shown is the doublet splitting, Δλ, and normalized splitting quality factor, Qβλ 0λ.

Fig. 3.
Fig. 3.

Normalized doublet splitting (Qβ ) versus disk radius. (inset) Taper transmission data and fit of deeply coupled doublet demonstrating 14 dB coupling depth.

Fig. 4.
Fig. 4.

Measured intrinsic quality factor, Qi , versus disk radius and resulting breakdown of optical losses due to: surface scattering (Qss ), bulk doping and impurities (Qb ), and surface absorption (Qsa ).

Fig. 5.
Fig. 5.

Plot showing absorbed power versus intra-cavity energy for a R=5 µm disk to deduce linear, quadratic, and cubic loss rates. (inset) normalized data selected to illustrate bistability effect on resonance.

Equations (57)

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1 Q i = 1 Q r + 1 Q s s + 1 Q s a + 1 Q b ,
Q β λ 0 Δ λ = 1 2 π 3 4 ξ ( V d V s ) ,
ξ = n ̅ 2 ( n d 2 n 0 2 ) n d 2 ( n ̅ 2 n 0 2 ) .
Q s s = 3 λ 0 3 8 π 7 2 n 0 δ n 2 ξ ( V d V s 2 ) ,
Q s a = π c ( n ̅ 2 n 0 2 ) R λ 0 n ̅ 2 γ s a ζ ,
R th = h ped ( κ Si O 2 π r max r min ) .
Δ λ 0 n Si λ 0 Δ n ( d n d T ) Si 1 Δ T R th 1 P abs ,
P abs = κ SiO 2 π r max r min n S i h ped d n d T Si λ 0 Δ λ 0 .
U c = Q i ω P L = Q i ω ( 1 T min ) P in ,
· D ( r , t ) = 0 × E ( r , t ) = B ( r , t ) t · B ( r , t ) = 0 × H ( r , t ) = D ( r , t ) t ,
2 F n 2 ( r ) c 2 2 F t 2 = 0 ,
( 2 ρ 2 + 1 ρ ρ + 1 ρ 2 2 ϕ 2 + 2 z 2 + ( ω c ) 2 n 2 ( r ) ) F ( r ) = 0 .
1 W ( 2 W ρ 2 + 1 ρ W ρ + 1 ρ 2 2 W ϕ 2 ) + 1 Z d 2 Z d z 2 + k 0 2 n 2 ( r ) = 0 ,
( 2 W ρ 2 + 1 ρ W ρ + 1 ρ 2 2 W ϕ 2 ) + k 0 2 n ̅ 2 ( ρ ) W = 0
d 2 Z d z 2 + k 0 2 ( n 2 ( z ) n ̅ 2 ) Z = 0 ,
2 Ψ ρ 2 + 1 ρ Ψ ρ + ( k 0 2 n ̅ 2 ( ρ ) m 2 ρ 2 ) Ψ = 0
2 Ω ϕ 2 + m 2 Ω = 0 .
k 0 n ̅ ( k 0 ) J m + 1 ( k 0 n ̅ ( k 0 ) R ) = ( m R + η α ) J m ( k 0 n ̅ ( k 0 ) R ) ,
Ψ ( ρ ) { J m ( k 0 n ̅ ρ ) ρ R J m ( k 0 n ̅ R ) exp ( α ( ρ R ) ) ρ > R .
J = i ω δ ε E 0 .
δ ε = ε 0 δ n 2 h Δ r ( ϕ ) δ ( r R ) δ ( z ) ,
A rad ( r ) = μ 0 4 π ( e i k 1 r r ) J ( r ) e i k 1 r ̂ · r d r ,
A rad ( r ) = i μ 0 ω h δ n 2 ε 0 E m ( R , 0 ) R 4 π ( e i k 1 r r ) 0 2 π Δ r ( ϕ ) e i m ϕ exp ( i k 1 R sin θ cos ϕ ) d ϕ .
A rad ( r ) · A rad ( r ) * = μ 0 ω h δ n 2 ε 0 E m ( R , 0 ) 4 π 2 ( R r ) 2 Θ
Θ 0 2 π 0 2 π C ( ϕ ϕ ) exp ( i m ϕ ϕ ) exp [ i k 1 R sin θ ( cos ϕ cos ϕ ) ] d ϕ d ϕ ,
Θ = 2 π 0 2 π C ( t ) exp ( i m t ) J 0 [ 2 k 1 R sin θ sin ( t 2 ) ] d t .
Θ = 2 π R π R π R σ R 2 exp ( s 2 L c 2 + i m R s ) J 0 [ 2 k 1 R sin θ sin ( s R 2 ) ] d s 2 π 3 2 σ R 2 L c R ,
S rad = r ̂ ω k 0 2 μ 0 r ̂ × A rad 2 = r ̂ ω k 1 3 n 0 ( δ n 2 ) 2 V s 2 ε 0 E m ( R , 0 ) 2 16 π r ̂ × e ̂ 2 r 2 ,
P rad = ( S · r ̂ ) r 2 d Ω = η ̂ π 7 2 ω n 0 ( δ n 2 ) 2 V s 2 ε 0 E m ( R , 0 ; η ̂ ) 2 G ( η ̂ ) λ 0 3 ,
Q ss = λ 0 3 π 7 2 n 0 ( δ n 2 ) 2 V s 2 Σ η ̂ u s ¯ ( η ̂ ) G ( η ̂ ) ,
u ¯ s ( η ̂ ) = ε 0 E 0 ( η ̂ ) s , avg 2 1 2 ε 0 ( r ) E 0 2 d r .
2 E μ 0 ( ε 0 + δ ε ) 2 E t 2 = 0 ,
2 E j 0 ( r ) + μ 0 ε 0 ( r ) ω j 2 E j 0 ( r ) = 0 .
E ( r , t ) = exp ( i ω 0 t ) j a j ( t ) E j 0 ( r ) .
j ( 2 i ω 0 ε 0 d a j d t + δ ε ω 0 2 a j ε 0 ( ω j 2 ω 0 2 ) a j ) E j 0 ( r ) = 0 .
d a k d t + i Δ ω k a k ( t ) = i j β j k a j ,
with β j k = ω 0 2 δ ε ( E j 0 ( r ) ) * E k 0 ( r ) d r ε 0 E k 0 ( r ) 2 d r ,
d a c w d t = i Δ ω a c w + i β a c c w
d a c c w d t = i Δ ω a c c w + i β a c w ,
β = ω 0 4 U c ε 0 δ n 2 h Δ r ( s ) δ ( r R ) δ ( z ) ( E c w ( r ) ) * E c c w ( r ) d r .
β = ω 0 δ n 2 h R ε 0 E m ( R , 0 ) 2 4 U c ϒ
ϒ = 0 2 π Δ r ( ϕ ) e i 2 m ϕ d ϕ .
ϒ 2 = 2 π R π R π R σ R 2 exp ( s 2 L c 2 + i 2 m R s ) 2 π 3 2 σ R 2 L c R .
d a c w d t = ( γ t 2 + i Δ ω ) a c w + i β a c c w + κ s
d a c c w d t = ( γ t 2 + i Δ ω ) a c c w + i β a c w ,
Q β = 2 π 3 4 δ n 2 V s u s ¯ .
γ ̅ s a = γ s a ( r ) n 2 ( r ) E ( r ) 2 d r n 2 ( r ) E ( r ) 2 d r ,
γ ̅ s a = γ s a n S i 2 δ V s a E ( r ) 2 d r n 2 ( r ) E ( r ) 2 d r = 1 2 γ s a n S i 2 u s ¯ δ V s a .
Q s a = 4 π c λ 0 γ s a n S i 2 u s ¯ δ V s a .
E s , avg 2 = 1 δ V R δ r R + δ r h 2 h 2 0 2 π ρ d ρ d ϕ d z E 2 ,
U c = 1 2 ε 0 ( r ) E 2 d r 1 2 ε 0 n d 2 0 R h 2 h 2 0 2 π ρ d ρ d ϕ d z E 2 .
u s ̅ ( Z ̂ ) = 2 n d 2 δ V R δ r R + δ r ρ d ρ [ J m ( k 0 n ̅ ρ ) ] 2 0 R ρ d ρ [ J m ( k 0 n ̅ p ) ] 2 .
u s ̅ ( Z ̂ ) = [ J m ( k 0 n ̅ R ) ] 2 π h n d 2 0 R ρ d ρ [ J m ( k 0 n ̅ ρ ) ] 2 2 n ̅ 2 V d n d 2 ( n ̅ 2 n 0 2 ) ,
Q s s = 3 λ 0 3 8 π 7 2 n 0 δ n 2 ξ ( V d V s 2 ) ,
Q β = 1 2 π 3 4 ξ ( V d V s ) ,
Q s a = π c ( n ̅ 2 n 0 2 ) R λ 0 n ̅ 2 γ s a ζ ,
ξ = n ̅ 2 ( n d 2 n 0 2 ) n d 2 ( n ̅ 2 n 0 2 ) .

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