surface optomechanics: mechanical whispering...
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Surface Optomechanics: Mechanical Whispering Gallery Modes in Microspheres
John Zehnpfennig, Matthew Tomes, Tal CarmonThe University of Michigan Ann Arbor USAThe University of Michigan, Ann Arbor, USA
Various types of Optical ForcesVarious types of Optical Forces
Today, Compressive ForceScattering Force
Poster Session, Gyroscopic Force
Fig credit Goodman dynamics
Gradient Force
g yZhang et. al. , 2010 (In Review)
Qiang Lin, et al., PRL 2009
Adrian Cho
PRL, 2009.
Tomes, et al., PRL, 2009.
Carmon, et al., PRL 2005
Figure Credit: Adrian Cho, Science 2009-2010 (2009).
PRL, 2005.
WGMs schematic descriptionWhispering gallery resonators• Lord Rayleigh – “The problem of the whispering gallery” (1910)
WGMs, schematic description
y g p p g g y ( )• Light is trapped by total internal reflection• The circumference is an integer number of wavelengths
Calculatedh lMechanical
Mode
C l l d
3m
CalculatedOpticalMode
In scaleNot to scale
In scale
Perturbation Speed Governing Eq.
Mechanical Deformation of Sound Stress‐Strain Eq
Optical EM of Light Maxwell’s Eq
WGMs, numerical solutionSolving for mode in whispering galleries
• Mechanical mode solution– Stress strain tensorial equations– Exact equations except for discreatization in space
• Optical mode solutionF ll ectorial sol er for Helmholtz eq ation– Fully vectorial solver for Helmholtz equation
Optical modeMechanical mode, deformation(b)
c) Top View
M. Oxborrow, IEEE Trans. Microwave Theory Tech. 55, 1209 (2007).
SBS Mode Self ConsistencyOptical I
SBS Mode, Self Consistency
Inputωp
|E1+E2|2Ωm= 2 ωp vs n/c
~11 GHz
Optical
Mechanical modeΩm
In silica:vs = 5600 m/sn=1.48
Electrostriction
outputω s
Red D l
Photo elastic effect
Doppler shifted
Effective propagation is 100 meters in a micron scaled deviceA. Yariv, Quantum Electronics (Wiley, New York, 1975).
Experimental results: VibrationExperimental results: Vibration0.81.0
ensit
y
Electrical Spectrum
0.00.20.40.6
orm
alize
d In
te[A
u]
10.964 10.966 10.968 10.97N
Frequency [GHz]
•Main claim: -40
-20
g A
u]
Optical Spectrum11 GHz
•Main claim:– 11 GHz Mechanical vibration rates
-100
-80
-60In
tens
ity [l
og
195.1 195.15 195.2
Frequency [THz]Matthew Tomes and Tal Carmon, Physical Review Letters 102, 20-23 (2009).J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, Opt. Lett. 22, 1129 (1997).S.M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).M. Cai, and K. Vahala, “Highly efficient hybrid fiber taper coupled microsphere laser,” Opt. Lett. 26(12), 884– 886 (2001).
Different Types of Acoustical Waves
• There are several types of acoustical wavesacoustical waves
• Here we look at– Longitudinal– Transverse Polar
Transverse Radial– Transverse Radial– Rayleigh
• Propagation velocities are differentwhile wavelength is fixed
High Radial and Polar Mode OrderHigh Radial and Polar Mode Order• For a 60 micron sphere, there are ~200 acoustical wavelengths
l h i falong the circumference• Transverse and polar directions can also have multiple maxima• Different order modes can vary in frequency as a function of
ph r izsphere size
Mechanical FrequencyMechanical FrequencyResonance frequency Vs sphere radius
11.2
11.3
12.0
13.0Longitudinal Longitudinal
11.1
7 2
7.3
7.4
z]
8 0
9.0
10.0
11.0
Hz] Transverse PolarTransverse Polar
6 9
7.0
7.1
7.2
equ
ency
[G
H5 0
6.0
7.0
8.0
equ
ency
[G
H
Transverse Polar
Transverse Radial
Rayleigh
Transverse Polar
Transverse Radial
6.7
6.8
6.9
15 35 55 75 95
Fre
R di [ m]
3.0
4.0
5.0
1 3 5 7 9
Fre
Rayleigh
Radius [μm]Radius [μm]
Comparison with Others resonatorsComparison with Others resonators
• No notched support is needed no lambda/4 isolators are neededNo notched support is needed, no lambda/4 isolators are needed– Since sound is propagating azimuthally, always far from support
• Can go high frequency irrespective of device miniaturization (fabrication limit)– Since virtual electrodes are written with light (at an optical wavelength scale)
ConclusionConclusion• Electrostrictive forces in optical MEMS
should be able to excite transverse and • Experimental results toRayleigh waves in addition to longitudinal waves.
• Spherical boundary breaks symmetry to
Experimental results to follow soon.
• Spherical boundary breaks symmetry to distinguish transverse polar and transverse radial waves.
• In each family, there exists higher order modes with multiple maxima along the radial and polar directions.
• A wide range of frequencies is achievable due to the different wave velocities.
N t h d t i d d• No notched support is needed as waves are propagating circumferentially
Questions?Questions?