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?