Optomechanical Sensors
Prof. Gaurav Bahl
University of Illinois, Urbana-Champaign
Mechanical Science and Engineering
bahl@illinois.edu
bahl.mechse.illinois.edu
Micro-mechanical systems have harnessed many forces
Energy
source
Actuation method
or “force”
Micro-scale
object
Magnetic
Piezoelectric
Thermal
Electrostatic
Light!
Gradient force
Photo-thermal
Radiation
pressure
Electro-strictive
pressure
2
Vibrational modes in optomechanical resonators
J. Zhu
Flapping mode
in microtoroids
T. Carmon
GHz frequency breathe modes
M. Eichenfield
Mechanical excitation
of zipper cavities
G. Bahl
Surface wave oscillations
in WGRs
G. Bahl
Optomechanofluidics
3
Radiation pressure: Comets
ail
t
dust
Comet Hale Bopp
n
io
ion
tai
l
l
tai
il
ta
t
s
u
d
Direction
to sun
1619 - Johannes Kepler
Observed that comet tails (the bright ones) always opposed the sun
and hypothesized ‘radiation pressure’ as the reason.
4
Quantization of EM energy and momentum (Photons)
At small scales, energy and momentum are quantized
Indeed, most other physical properties as well!
The quantum of light = A photon
A photon is actually the quantum particle of all forms
of electromagnetic radiation!
Momentum
p = k
Energy
E = ω
E = hν
c
E=h
λ
h = 6.63 × 10−34 J · s
h
=
= 1.054 × 10−34 J · s
2π
5
Argument for the existence of radiation pressure
p1
p3
p2
Mirror
(stationary)
Momentum
imparted to
the mirror
m
Momentum conservation must apply
p1 = p3 − p2
Since the mirror velocity is changed
there must have been a force on the mirror
6
Let’s calculate the force
Change in momentum
per photon
= 2k
Photon flux = Optical power / Energy per photon
N = P/ω
(Photons per second)
Total momentum change per second (i.e. Radiation pressure force)
= 2P k/ω
= 2P/c
7
Crookes radiometer (1873)
Absorbing
Reflective
Credit: Wikipedia
Is it moving in the correct direction?
Hint: No. It’s a thermal effect here
8
Brief history of “radiation pressure” experiments
1873 - William Crookes
Experimentally attempted to build a radiometer to
observe radiation pressure.
Failed. Instead gave the world a desk toy.
1899/1900 - Pyotr Lebedev
(Successfully) Experimentally measured the pressure of light
on a solid body.
1901 to 1903 - Ernest Nichols and Gordon Hull
(Successfully) Experimentally measured the pressure of light
on a torsion balance radiometer.
9
Nichols & Hull Radiometer
Not as visually striking as the Crooke’s radiometer.
10
Solar sail
A proposed means of interstellar travel
that uses reflected starlight for propulsion.
Solar sail
Force
Starlight
Images: Wikipedia
IKAROS (Interplanetary Kite-craft Accelerated by Radiation Of the Sun)
First interplanetary solar sail craft launched by Japan (JAXA) in 2010.
Confirmed solar sail acceleration on July 9th 2010.
On its way to Venus.
Passed Venus in Dec 2010.
11
There are other optical forces too!
Gradient force
Electrostrictive force
Used for optical tweezers, optical traps,
waveguide actuation.
Particles get pulled into regions of high
optical intensity.
“Electric field results in constriction.”
Occurs in all dielectrics.
V
Credit: Wikipedia
Basic idea
Force = −∇x E
12
Resonance between mirrors = Fabry-Perot resonator
Two waves end up
propagating opposite
to each other.
Generates standing wave
And there is
constructive interference.
Under what conditions?
2 x Length = integer
wavelengths
13
Resonances are typically periodic
Amplitude of field
Amplitude of field
Reflection and absorption within material and mirrors determine the resonance width.
Mirror reflectivity
R = 0.9
Mirror reflectivity
R = 0.99
FSR
15
10
5
0
5
10
15
15
10
5
Frequency
0
5
10
15
Frequency
Material between mirrors
absorbs and scatters some light
Some light is lost
in reflection
14
Quality factor = Optical storage time
Low-loss mirrors
More energy stored
Lossy mirrors
Less energy stored
Also, more photon
collisions with walls!
stored energy
Q = 2π
energy loss per cycle
νo Optical frequency
Q=
δν
Linewidth
For
more
see Saleh + Teich. Chapter 10.
Learn
more
νo
Q≈
F
νF
15
Finesse = number of round trips
Low-loss mirrors
Lossy mirrors
Important facts
Finesse is inversely proportional to cavity length → So use smaller resonators!
Radiation pressure is magnified by the finesse factor.
Experimental/phenomenological
νF FSR (free spectral range)
Valid when F 1
δν ≈
F Finesse
Linewidth
For
more
see Saleh + Teich. Chapter 10.
Learn
more
16
Nomenclature: Detuning
“Detuning” is defined as the distance from the peak of the resonance.
Measured in wavelength or frequency units (your choice).
Δλ
A signal present here is
on resonance!
A signal present here is
red detuned
Resonance frequency (or wavelength)
A signal present here is
blue detuned
Wavelength
Frequency
17
Energy in the cavity depends on detuning
Coupling
efficiency
Optical
resonance
Wavelength
Poor
coupling
Maximum
intensity inside
resonator
Poor
coupling
18
Analyzing a sinusoidally shifting resonance
Learn more
Schliesser, A., & Kippenberg, T. J. (2010). Cavity Optomechanics with WhisperingGallery Mode Optical Micro-Resonators. Advances In Atomic, Molecular, And
Optical Physics, Vol 58, 58, 207–323. doi:10.1016/S1049-250X(10)05810-6
ωl
is the input laser
frequency
ωl
19
Radiation pressure can induce mechanical oscillation
Resonance
Light in
x=0
Pump
laser
Wavelength
Cavity collapses
Cavity expands
Radiation
pressure
x
Resonance
Pump
laser
Resonance
shifts
Less light in
Wavelength
20
Parametric oscillatory instability
This instability was originally discussed in the context of LIGO in 2001...
LIGO = Laser Interferometer Gravitational-Wave Observatory
Learn more
21
Optomechanical crystals exhibit this instability
Optical modes
Engineered optical
resonators that
exhibit simultaneous
optical and acoustic
modes
Acoustic modes
Eichenfield, M., Chan, J., Camacho, R., Vahala, K. & Painter, O.
Optomechanical crystals. Nature 462, 78–82 (2009).
22
Mathematically describing the opto-mechanical coupling
Coupling of energy in
from acoustic field
Optical field
Detuning
(Optical resonance)
Laser source
Optical
losses
Acoustic field
+ Langevin noise force
(not shown)
Detuning
(Acoustic resonance)
Acoustic
losses
Coupling of energy in
from optical field
G is the opto-mechanical coupling coefficient
related to ...
Cavity deformation causes optical resonance to shift ( dω/dx )
Radiation pressure force is modified when optical resonance shifts relative to laser
More photons create more pressure and more deformation
23
Whispering gallery resonators (WGRs)
Acoustic wave
(speed of sound)
Q > 100,000,000
Finesse = Distance traveled / Circumference
Monochromatic
photons from a laser
Electromagnetic wave
(speed of light)
24
What is the simplest WGR we can build in the lab?
Arc discharge method
Microspheres can be fabricated by reflowing a
broken taper in a fiber splicing tool
Long optical fiber taper
Reflow
Reflow
some
more
~150 um
Q ~ 4×108
25
On chip ultra-high-Q toroid microcavities
Letters to Nature
Nature 421, 925-928 (27 February 2003) | doi:10.1038/nature01371
Ultra-high-Q toroid microcavity on a chip
D. K. Armani, T. J. Kippenberg, S. M. Spillane & K. J. Vahala
26
Fabrication cross-sectional view
Oxide disc on silicon
Disc on pedestal
150 um
4 um
XeF2 etch
CO2 laser
reflow glass
30 um
Ellipsoid
Toroid
more
CO2 laser
reflow
50 um
27
Resonance and FSR for a WGR
Light is confined through total
internal reflection
Dielectric
(think of infinite reflections)
λo /n
Resonance criterion
2
R=Mxλ
λo
Free space wavelength
28
Zipper structures
Optical modes
Acoustic mode
Distance between beams
is an important parameter
Eichenfield, M., Camacho, R., Chan, J., Vahala, K. J. & Painter, O.
A picogram- and nanometre-scale photonic-crystal optomechanical cavity. Nature 459, 550–555 (2009).
29
Optomechanical coupling coefficient
We can define the degree to which the
optical mode shifts upon application of a
mechanical displacement.
gOM
dω
=
dx
Typically 1 GHz/nm - 1 THz/nm
Huge! Compared to 1 MHz - 10 MHz linewidth.
30
Evanescent field region outside a WGR
Real k (surface wave)
Field
strength
Complex k
(evanescent wave)
Quickly decaying
evanescent field
Radial
direction
31
Coupling to a WGR using evanescent fields
Large gap
Evanescent
field
(no propagation)
Resonator
No field here
“Waveguide”
Light “tunnels”
through the “barrier”!
But remember, this is a two-way street
32
How the resonance condition acts on coupled light
On resonance
Off resonance
Lots of light is inside the resonator.
Light escaping the resonator interferes
with light inside the waveguide.
Very little light is inside resonator.
Light in the waveguide
is not affected significantly.
Resonator
“Waveguide”
Resonator
“Waveguide”
Learn more
33
Photograph of tapered optical fiber waveguide
Taper
Hydrogen
torch
Fiber
34
The complete picture
Resonator
Finesse (F)
= # of recirculations
x
Energy stored
= F x (Input x Coupling)
Field gets really high
Optical “input”
Evanescent coupling
35
3rd harmonic generation
Spherical microresonator
3rd harmonic generation
Input IR 㱺 Output green laser
Infra-red
laser in
Green
laser out
~ 1500 nm
~ 500 nm
~150 um
Q~
4×108
3W power
Flicker is due to laser wavelength
being intentionally swept
uW - mW
power
Finesse ~ 105-106
This nonlinear process occurs because the material (silica)
has a nonlinear characteristic (the (3) nonlinearity).
36
Origin of centrifugal radiation pressure
ce
r
o
lf
a
g
u
f
i
r
t
n
Ce
Change in momentum
per photon
Circulating power / energy-per-photon
= energy-through-cross-section-per-second / energy-per-photon
= #-photons-through-cross-section-per-second
Total momentum change per second (i.e. force)
= 2k
N = P/ω
= 2P k/ω
= 2P/c
Now you can perform suitable integrals to determine
force per unit length etc...
37
Radiation pressure can induce mechanical oscillation
Top view of resonator
Toroid resonator
Resonance
Light in
Pump
laser
de
ui
veg
a
W
Wavelength
Cavity expands
Cavity collapses
Mechanical frequency defined by
geometry + materials
Reduced
radiation
pressure
Resonance
Pump
laser
Radiation
pressure
Resonance
shifts
PRL 94, 223902 (2005)
Optics Express 13, 5293 (2005)
Less light in
Wavelength
PRL 95, 033901 (2005)
38
Radiation-pressure driven microtoroids
Pinput
?
More
power
Photodetector
t
Input light
(continuous in
time)
Oscilloscope
Poutput
Effect came as an unexpected surprise
Cavity was not designed to vibrate
Oscillation!
t
39
Mass sensing with optomechanics
Liu, F. & Hossein-Zadeh, M.
Mass Sensing With Optomechanical Oscillation. Sensors Journal, IEEE 13, 146–147 (2013).
Optical devices provide extremely high
measurement sensitivity, especially in
“RF free” zones or harsh environs.
Ultimate limits still defined by Brownian
thermal noise.
Ekinci, K. L. Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems.
J. Appl. Phys. 95, 2682 (2004).
40
Optomechanical Atomic Force Microscope (AFM)
Coupling a vibrating beam to a WGR -light excites the beam, and is also used for readout
Ultimately hit the fundamental
thermal noise limits
want low stiffness, high freq, high Q.
Srinivasan, K., Miao, H., Rakher, M. T., Davanço, M. &
Aksyuk, V.
Optomechanical Transduction of an Integrated Silicon
Cantilever Probe Using a Microdisk Resonator.
Nano Lett 11, 791–797 (2011).
41
Optomechanical accelerometers
Krause, A. G., Winger, M., Blasius, T. D., Lin, Q. & Painter, O. A high-resolution microchip
optomechanical accelerometer. Nature Photonics 6, 768–772 (2012).
Thermal noise (proof mass)
limits accelerometers
Using a zipper resonator and proof mass
to measure acceleration.
42
43
Measuring displacement of a nitride beam
Gavartin, E., Verlot, P. & Kippenberg, T. J.
A hybrid on-chip optomechanical transducer for ultrasensitive force measurements.
Nature Nanotech 7, 509–514 (2012).
74 aN Hz-1/2 at room temperature with a readout stability better than 1% at the minute scale
By applying dissipative feedback (i.e. optomechanical cooling) based on radiation pressure,
force spectral density of just 15 aN Hz-1/2 within 35 s of averaging time
44
Can we build surface-acoustic-wave devices?
(Then we can use the past 60 years of SAW techniques)
45
Acoustic waves through optical electrostriction
Electric fields exert pressure on dielectrics = Electrostriction
V
Electromagnetic waves also generate electrostrictive pressure
Interference of two EM waves can generate pressure that travels at the speed of sound
Speed of sound
Light can generate sound
46
Brillouin scattering: Scattering of light from acoustic waves
The strongest nonlinearity known to optics
Reflection from a stationary mirror
Stationary
mirror
Reflection from a moving mirror
Reflected light is
red-shifted
Moving
mirror
Brillouin light scattering = “Reflection” from a traveling acoustic wave
Sound scatters light
Scattered light is
red-shifted
47
Stimulated Brillouin scattering (SBS) is a feedback process
Light
ht can generate sound
ωP, kP
Speed of sound
ωS, kS
ΩA, kA
Occurs at high input power!
Sound 㲗 Light
“Phase Matching” condition
feedback loop
Brillouin scattering ‘generates’ light
ωP, kP
Energy conservation :: ħωP = ħωS + ħΩA
Momentum conservation :: kP = kS + kA
Speed of sound
ωS, kS
ΩA, kA
Scattered light
R. Chiao, C. Townes, Phys. Rev. Lett., Vol. 12, No. 12, 1964.
48
Lasers were
too new
Good old days!
Before Hz was widely adopted.
cps = cycles per second
49
Experiments in silica
Silica glass
sphere
Continuous light
from 1550 nm
laser (a few mW)
Tapered optical
fiber waveguide
1 µm thick
Electrical
spectrum
analyzer
vsound
11 GHz
acoustic wave
Electrical
signal power, dBm
Detector
ï
ï
Fixed pump laser
frequency
11 GHz
SBS mode
ï
ï
ï
ï
ï
ï
ï
Frequency, MHz
M. Tomes and T. Carmon, Phys. Rev. Lett. 102, 113601 (2009)
50
Generating surface acoustic waves
High frequency
10-12 GHz regime
Low frequency
10 MHz - 2 GHz regime
vsound
vsound
Scientific value
Small mode (~0.5 pg)
Low threshold Brillouin lasers
Scientific value
Larger mode (~10 ng)
Higher quality factors
(longer phonon lifetime)
Greater mechanical amplitude
Surface acoustic wave (SAW)
sensors!
G. Bahl et al, Nature Communications 2:403, doi:10.1038/ncomms1412 (2011)
51
Forward-scattering SBS for lower frequency acoustic waves
B-SBS
F-SBS
G. Bahl et al, Nature Communications 2:403, doi:10.1038/ncomms1412 (2011)
52
Forward Brillouin scattering enables SAW generation
c/n1
Pump
optical
field
vsound
|E1 + E2|2
Electrostriction
Pressure
Acoustic
wave
vsound
Scattered
optical
field
c/n2
Brillouin scattering
G. Bahl et al, Nature Communications 2:403, doi:10.1038/ncomms1412 (2011)
53
Experimental observation
Signal, a.u.
Signal,
AU
SAW-WGM
on silica sphere
1550 nm
infra-red
pump laser
Experimental data
Time,
μs
Time, us
Detector
Oscilloscope
Optical spectrum (95 MHz mode)
Pump
Stokes
95 MHz spacing
Electrical
spectrum
analyzer
Experimental data
16
Measured electrical signal, pW
95 MHz
14
12
10
8
6
4
2
0
95.1
95.15
Frequency, MHz 54
Femtometer-level Brownian vibration can be measured
Mechanical signal
Increasing
pump
power
Maximum amplitude
can reach nanometer-level
with greater input power
Mechanical signal at extremely low input power
=
95 MHz
Rayleigh
SAW-WGM
nsilica = 1.45
G. Bahl et al, Nature Physics, doi:10.1038/nphys2206, Feb 2012
55
Changing laser wavelength changes oscillation frequency
Power, dBm
We generate one oscillation frequency at a time
Or we can scan the laser wavelength to find many frequencies
Frequency, MHz
G. Bahl et al, Nature Communications, 2:403, doi:10.1038/ncomms1412 (2011)
56
There are high transverse order acoustic modes too!
57
Merging optomechanics and microfluidics
Carmon et al, PRL 94 (22), 2005
Rokhsari et al, Opt. Express 13, 2005
Povinelli et al, Opt. Lett. 30, 2005
...
“Dry”
optomechanics
Microfluidics
+
MEMS enabled
bio-sensing
Optical
nanoparticle
sensing
Vollmer et al, Nature Methods 5, 2008
Zhu et al, Nature Photonics 4, 2010
Lu et al, PNAS 108, 2011
...
Burg et al, Nature 446, 2007
Optomechanical
bio/chemical sensors?
58
Opto-Mechano-Fluidic Sensors
Bottle shape enables simultaneous
confinement of optical and acoustic WGMs
Optical
and
acoustic
WGR
Qmechanical = 4700
Qoptical = 160 million
(with liquid core)
70 um
Tapered
fiber
Micro-capillary
G. Bahl et al, Nature Communications, 4:1994, doi:10.1038/ncomms2994 (2013)
59
OMFR system
Fiber
OMFR
Taper
Hydrogen
torch
Fiber
60
Cavity optomechanics on microfluidic resonators
Interferometric
detection
Fluid
analyte
reservoir
eguide
Silica wav
CW pump
at 1.5 microns
(NIR diode laser)
Silica
microfluidic
resonator
Scattered light
(beat note)
RF signal
measures
mechanical
mode
Outlet
K.H. Kim, G. Bahl, et al
arXiv:1205.5477
G. Bahl et al
Nat Comms
4:1994
2013
Radiation-pressure driven
breathing mode
Qmechanical = 2170
with liquid core
at 19 MHz
Qmechanical = 4700
with liquid core
at 100 MHz
G. Bahl et al, Nature Communications, 4:1994, doi:10.1038/ncomms2994 (2013)
61
Capillary whispering-gallery acoustic modes
Bahl, G., Fan, X. & Carmon, T.
Acoustic whispering-gallery modes in optomechanical shells.
New Journal of Physics 14, 115026 (2012).
Rayleigh-Lamb mode
Rayleigh wave
Transverse mode
Longitudinal mode
Lamb wave
62
Acoustic WGMs
Experiments With water
ï
ï
H1
ï
ï
ï
H2
ï
ï
ï
ï
ï
M = 14
SAW-WGM
169 MHz
ï
ï
ï
ï
ï
ï
ï
ï
ï
M = 24
SAW-WGM
277 MHz
861 MHz
ï
ï
ï
M = 79
SAW-WGM
ï
ï
ï
ï
M=8
SAW-WGM
99 MHz
M=2
Wineglass
mode
7.4 MHz
11.3 GHz
Extremely high order
SAW-WGM
ï
ï
ï
ï
ï
ï
ï
G. Bahl et al, Nature Communications, 4:1994, doi:10.1038/ncomms2994 (2013)
63
Testing with sucrose solutions
Optomechanical interaction can be sustained
even when -• Motional mass is high
(i.e. high density liquid)
• Fluid-related acoustic energy losses are high
(i.e. high viscosity)
Non-monotonic trend may be explained by multi-parameter
variation. (1) Density (2) Viscosity (3) Speed of sound.
1.15
1.1
1.05
Known trend
Experiment
1700
Acoustic velocity in solution (m/s)
Increasing viscosity
Density (g/ml)
1.2
1
0
10
20
30
40
Sucrose concentration (% w/w)
Known trend
1650
1600
1550
1500
0
10
20
30
40
Sucrose concentration (% w/w)
G. Bahl et al, Nature Communications, 4:1994, doi:10.1038/ncomms2994 (2013)
64
Sensing with radiation pressure modes
K.H. Kim, G. Bahl, et al
arXiv:1205.5477
to appear in Light: Science
& Applications, Nov 2013
Radiation-pressure driven
breathing mode
65
Optomechanical viscometer
Extract viscosity by measuring
thermal mechanical fluctuations
(Brownian noise)
Water
Active
region
Distilled water
Air
Sucrose solution 60% w/w
"
'$!"#!$#
OMFR
CF = 11.6 MHz
Q = 1977
Power, a.u.
%!$
Power, a.u.
Increased damping
ï
CF =12.4 MHz
Q = 712
!"
Frequency offset, kHz
ï
! $&'
Frequency offset, kHz
66
Rapid screening of cells
OMFR
Water
Active
region
Taper
(background)
Air
Fibroblast
OMFR
1
2
3
Transit of a single monkey kidney fibroblast
stay tuned...
67
Optomechanical pressure sensor
K. Han, J. Kim, G. Bahl
“Aerostatically tunable optomechanical
oscillators”
In review, 2013
68
Dual mode (RP + SBS) pressure sensing
Potential for f1-f2
self-referencing!
69
Putting some challenges out there
Fiber is virtually free. $0.08/meter.
Sensors in harsh
environments
High temperature
Electromagnetic
interference
Silica, LiNbO3, CaF2 are high temperature materials
Photons behave linearly in most media
Distributed fiber-SAW sensors
Fiber-tip optomechanical sensors
Optical
input
Fib
er
Mechanical
interaction
Input:
Interfering
optical
modes
Lamb waves
Love waves
Optical
read-out
Surface
wave
Optomechanical temperature sensor /
hydrogen sensor / pressure sensor.
Surface
mechanical
interaction
Output:
Optical signals
70
Sources of noise
71
Equipartition theorem - Thermal mechanical fluctuations
At thermal equilibrium, the average kinetic energy contained in
any degree of freedom is 1/2 kBT at any non-zero temperature T.
kB = 1.38 x 10-23 J/K
Therefore, at any non-zero temperature, a mass-spring-damper system has some “thermal
occupation”, i.e. its average kinetic energy is not zero.
x(t)
x=0
x(t)
t
1
1
kB T = kx2zpf 2
2 “Zero point fluctuations”
Lowering temperature lowers the thermal mechanical noise. x2zpf 72
Estimating magnitude of thermal motion
Example --G. Bahl et al, Nature Physics,Vol. 8, No. 3, pp. 203-207 (2012)
G. Bahl et al, Nature Physics, doi:10.1038/nphys2206, Feb 2012
73
Photon shot noise
We can use light to measure the position of an object very accurately.
Source
Detector noise
+
Signal of interest
Incident beam
Detector
Reflection
Measurement
gets better with
increasing input
power
To do a good job in measurement, we want to overcome the noise of our
detector, so we increase the power at the source.
But if we pretend that detector noise is zero, we still have photon shot noise.
Photons are discrete particles
Detector noise
+
Photon shot noise
+
Signal of interest
Source
Detector
Measurement
gets better with
increasing input
power
We can also average out this randomness in arrival times by turning up the power.
74
Radiation pressure shot noise
Simultaneously, we must also remember that light exerts radiation pressure.
Since photon arrival times are erratic, radiation pressure shot noise is
generated.
Photon shot noise
+
Radiation pressure
shot noise
+
Signal of interest
Source
Object position
and momentum get
perturbed
Detector
Each photon reflection creates a tiny
radiation pressure related momentum kick.
The more photons we use to probe, the more significant these
momentum kicks are!
Measurement
gets worse with
increasing input
power
75
Standard quantum limit
There is an optimum point where the total noise drops to its
minimum value.
This minimum value is called the standard quantum limit.
Noise in
measuring
position
Standard quantum
limit
Me
asu
rem
RP
ent
noi
se
ise
s
no
hot
Learn more There exist techniques to beat this!
Power of source
Anetsberger, G. et al. Measuring nanomechanical motion with an imprecision below the standard
quantum limit. Phys. Rev. A 82, 061804 (2010).
Teufel, J. D., Donner, T., Castellanos-Beltran, M. A., Harlow, J. W. & Lehnert, K. W. Nanomechanical
motion measured with animprecision below that at the standardquantum limit. Nature Nanotech 4, 820–
823 (2009).
76
Thermorefractive noise in optical devices
The variance of temperature fluctuations u in volume V is
where T is the temperature of the heat bath, k is the Boltzmann constant,
ρ is density, and C is specific heat capacity.
Thermorefractive noise in silica microsphere resonator
V = 10-9 cm3
ρ = 2.2 g/cm3
Radius = 50 um
dn/dT = 1.45 x 10-5 K-1 (coeff. of thermal refraction)
i.e. 6x104 Hz optical frequency fluctuation for a 197 THz (telecom infrared) optical mode.
Learn more
Gorodetsky and Grudinin
77
Thermal effects in optical resonators
What happens to an optical resonator when the temperature is changed?
dn
dT
Consider a WGR
Refractive index change
Resonance
frequency
c/n
fr =
2πR/M
Speed of light
Wavelength
α
Thermal expansion coeff.
78
Thermal effects in mechanical resonators
What happens to a mechanical resonator when the temperature is changed?
dE
dT
vs ∝ f
Stiffness change (TCE)
dρ
dT
vs ∝
E
ρ
α
Thermal expansion coeff.
Geometric effect
Strained anchors/tethers
79
Heating and cooling processes are symmetric
Heating
Pump
photon
x(t)
Cooling
Stokes
photon
Pump
photon
Phonon
Thermal
phonon
When the mirror moves away,
momentum conservation causes the
reflected light to be red-shifted
Mirror velocity
incoming
wave
standing
wave
anti-Stokes
photon
When the mirror moves inwards,
momentum conservation causes the
reflected light to be blue-shifted
Mirror velocity
Green
Green
Red
Blue
Energy conservation:
Vibration energy increases
Energy conservation:
Vibration energy decreases
80
Asymmetry in vibration-scattered light
The optical resonance can tilt this energy balance (optical “density of states”)
higher order terms
anti-Stokes
vibration
amplitude
Stokes
detuning
a0 (t)
a0 (t)
a1 (t) Anti-Stokes
Stokes a1 (t)
Ωm
Ωm
Stokes a1 (t)
a1 (t) Anti-Stokes
Ωm
Frequency
Ωm
Frequency
81
2004: Photothermal cooling of a cantilever
The device can be made to self-oscillate (S)
or cool (C)
depending on chosen laser detuning.
-λ/25 detuned
(anti-damping)
+λ/25 detuned
(damping)
Tune optical
resonances by
modifying cavity
length z.
82
This experiment used the photothermal “force”
“The photon-induced force, which is assumed proportional to the light
intensity stored in the cavity, includes of course the radiation pressure but more
generally all the n independent light-induced contributions, such as the photothermal
(bolometric), radiometric and photo-elastic pressure to name just a few. For instance,
a bolometric force FB results from the differential thermal expansion between the
silicon lever and the thin gold film.”
Au
+ ΔT
Si
local heating
due to
photon absorption
ΔL
Bending occurs due to different
coefficient of thermal expansion.
Changes cavity length.
... the essence of cooling is based on the fact that the optically induced forces
acting on the lever are delayed with respect to a sudden change in the lever
position.
83
Measuring effective temperature
Main message
The area under the Lorentzian
curves is most important measurement
for determining temperature
Use equipartition
theorem to
determine temperature
84
Radiation pressure cooling demonstrated in 2006
85
We can also cool using Brillouin scattering
Pump
resonance
OP
Anti-Stokes
resonance
Frequency
Find candidate optical modes
OaS
95 MHz spacing
Momentum
Mechanical signal (linear scale)
Mechanical signal (log scale)
19 K
Increasing
pump
power
95 MHz
SAW-WGM
Increasing pump power
8 kHz
120 kHz
Acoustical
mode FEM
G. Bahl et al, Nature Physics, Vol. 8, No. 3, p. 203, doi:10.1038/nphys2206 (2012)
86
There is potential for cooled mechanical sensors
PSD
Brownian vibrations in sensors need to be suppressed
Sensor bandwidth
Signal of interest
Noise + Brownian modes
Frequency
Background
“noise” signal
k
m
Sensor
readout
b
Brownian thermal
vibration
Some stochastic background “noise” is present because of Brownian occupation
Time
Background
“noise” signal
Cooling on
Event of interest
(e.g. rotation signal in gyro)
Time
87
Thank you!
Optomechanical
pressure
sensing
Aerostatically tunable optomechanical oscillators
Microfluidic
optomechanics
Brillouin cavity optomechanics with microfluidic devices
RP-driven microfluidic
optomechanics
Acoustic WGMs
on shells
Brillouin
cooling
Surface-wave
optomechanics
K. Han, J. Kim, G. Bahl
in review
G. Bahl, K.H. Kim, W. Lee, J. Liu, X. Fan, T. Carmon
Nature Communications, 4:1994 (2013)
Cavity optomechanics on a microfluidic resonator
K.H. Kim, G. Bahl, W. Lee, J. Liu, M. Tomes, X. Fan, T. Carmon
Light: Science & Applications, (to appear)
Preview: arXiv:1205.5477
Acoustic whispering-gallery modes in optomechanical shells
G. Bahl, X. Fan, T. Carmon
New. J. Phys. 14, 115026 (2012).
Observation of spontaneous Brillouin cooling
G. Bahl, M. Tomes, F. Marquardt, T. Carmon
Nature Physics, Vol.8, doi:10.1038/nphys2206 (2012)
Stimulated optomechanical excitation of surface acoustic waves in a microdevice
G. Bahl, J. Zehnpfennig, M. Tomes, T. Carmon
Nature Communications, 2:403 (2011)
Optical
and
acoustic
WGR
97