RAPPORT DE STAGE DE MASTER 2
MASTER SCIENCES, TECHNOLOGIES, SANTE Mention: Physique
Spécialité: PNANO
Physique et Nanomatériaux
Prénom - Nom : Lei LIU
Titre: Measure of the visco-elastic properties of liquids by use of the picoseconds acoustic technique
Laboratoire d’accueil : Institut des Molecules et des Materiaux du
Mans
Encadrant (s): Thomas PEZERIL
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Année 2012-2013
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Content
1 Introduction ..................................................................................................................4
2 Theory............................................................................................................................7
2.1 Generation of acoustic waves...........................................................................7
2.2 Detection of acoustic waves............................................................................10
2.2.1 Reflectivity change and Brillouin scattering frequency........................10
2.2.2. Interferometry ........................................................................................15
2.2.2.1. Reference Beam Interferometers ..................................................15
2.2.2.2. Self-Referential Interferometers ...................................................15
3. Experiment.................................................................................................................17
3.1. The experimental system...............................................................................17
3.1.1. The AOM crystal ...................................................................................18
3.1.2. Delay line ...............................................................................................19
3.1.3. Brillouin scattering signal......................................................................19
3.1.3.1. Optical derivation by using a piece of glass.................................20
1.1.3.2. Optical derivation by using a moving mirror with a frequency f21
3.1.4 Observation of Newton rings .................................................................22
3.1.5 Acquisition system..................................................................................22
3.2 Sample Design..................................................................................................23
3.2.1 The photo-acoustic transducer ...............................................................23
3.2.2. Liquid cell...............................................................................................24
4 Data analysis...............................................................................................................26
4.1 Measure of the thickness of the liquid..........................................................26
4.2. Measurement of acoustic velocity in the liquid..........................................27
5 Conclusion...................................................................................................................29
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6 Acknowledgements....................................................................................................30
7 References....................................................................................................................31
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1 Introduction
Laser picosecond ultrasonic is a method that uses ultra-short pulsed lasers for generating and detecting acoustic waves in liquids and solids media, it can be widely used for the measurement of mechanical properties of materials. A lot of experiments have been reported on the generation and detection of phonon pulse in a thin film, it has been demonstrated to be an efficient tool in many applied science and medical areas. [1, 2, 3] As showN in figure 1, by using the picosecond ultrasonic technique, the properties of the chip was studied.
FIG. 1. Properties of metal layers inside a silicon
chip are probed by ultrasound. A laser directed at the chip’s surface
heats the chip and generates a pulse of sound. [4]
Ultrasonic phenomenon can often be seen in our daily life, for example, the bats, their echolocation is a perceptual system where ultrasonic sounds are emitted specifically to produce echoes. They can detect frequencies beyond 100 kHz, possibly up to 200 kHz. In the industries, ultrasound is widely used in many areas, such as ultrasonic welding, ultrasonic cleaning, etc, especially in ultrasonic microscopy, but the traditional ultrasonic techniques need that the measuring device and the sample are in direct contact, which is inconvenient in lots of cases. For example, with a hot sample like glowing steel, or some samples where the contact measurement is prohibited by the test specifications, and in those cases, laser ultrasound permits a good way for testing. Compared to the traditional measurement, the laser ultrasonic technique also has other advantages: one of these is the high bandwidth of the
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detectable frequencies. Conventional ultrasonic systems can only generate ultrasonic waves at one certain frequency. The frequency is usually lies below 40 MHz, which is dependent on the capacity and design of the transducer. The temporally short excitation pulse, as emitted by a picosecond laser, leads to the generation of high frequency ultrasonic waves, which can reach the THz region. What's more, detection of the ultrasonic waves with a laser system is not limited by the bandwidth of the photo detector, so the detection in the GHz-THz range is possible. [5] Due to the optical excitation and detection, the frequencies can reach about 1 THz with the current set-ups.
FIG. 2. Basic components of a laser-based ultrasonic device:
The acoustic pulse is generated by the pump in the transducer and
is detected by the probe in the detection substrate.
The sample is exposed in a small spot of short and focused laser pulses and then, the acoustic waves will be generated on the surface, by ablation or by thermoelastic expansion, depending on the power density. Figure 2 shows that pulsed laser beam impinges on the surface of a material and partially penetrate and is absorbed by it, and then the optical power is converted to heat, in a local region, there is rapid temperature increase, that results in a rapid thermal expansion, which leads to generation of ultrasound into the medium.
The detection of ultra-fast waves is also based on laser: detection of the ultrasonic waves is performed by illuminating a point on the sample with a laser. The
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ultrasonic waves lead to small displacements in the order of 100 pm. These displacements lead to a Doppler shift, like changing of the wave length, which can be demodulated. Alternatively the surface displacements can, for example, be observed by the change of reflecitve index.
The techniques can be applied to many types of material. By launching an elastic strain pulse, it can be used to penetrate thin films or nanostructures to measure material mechanical properties [3] or film thickness [6]. With variable delay of the probe beam pulse, the ultrasound detection is performed to measure the slight change of the optical properties of the sample caused by reflected strain pulses as a function of time.
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2 Theory
2.1 Generation of acoustic waves
Generation of acoustic waves in our experiments is based on the photoacoustic effect, which was first discovered by Alexander Graham Bell in his research for a means of wireless communication, and then, laser generation of ultrasound was first demonstrated by White (1963).[7] After that, lasers have been widely used to generate ultrasound in solids, liquids, and gases for a number of applications.[8,9] Lasers provided high intensity light at a tunable frequency, which allowed an increase in sound amplitude and sensitivity. To this end, photoacoustics were able to be applied across a broader range of fields.
FIG. 3. Laser generation of ultrasound (a) at low incident
power density (thermoelastic regime); (b) by vaporizing surface material at high
incident power (ablative regime).[11]
The photoacoustic effect is a conversion between light and acoustic waves due to absorption and localized thermal excitation. When rapid pulses of light are incident on a sample of matter, they can be absorbed and the resulting energy will then be radiated as heat. This heat causes detectable sound waves due to pressure variation in the surrounding medium. The frequency of acoustic waves depends on the frequency of the optical signal, and the intensity is related to the material. Photoacoustic effect can be applied in photoacoustic spectroscopy, photoacoustic microscopy and medical
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imaging technologies. After the laser has been invented, the photoacoustic effect took on new life as an important tool in spectroscopic analysis and continues to be applied in an increasing number of fields. [10]
An ultra-fast laser pulse initiate an acoustic response in the optically absorbing sample by means of two different phenomena: by thermal expansion at low incident power density (thermoelastic effect), and by vaporizing surface material at high incident power (ablation effect), seeing in figure3.
If the optical power is not high enough to make the material melt or ablate, the material expands and generates acoustic waves. In that case, the generation regime is called thermoelastic (see Figure 3(a)). In another case, the optical power is very high and can lead to melting of the material and plasma formation, once again ultrasound is generated, but by momentum transferring due to material ejection (sees Figure 3(b)), and it’s not often used as it consumes the sample, especially for some nondestructive characterization of materials. However, it produces strong bulk wave normal to the surface, so it is useful in some applications. In some cases where a strong ultrasonic signal is needed but ablation is unacceptable, a sacrificial layer (typically a coating or a fluid) is used. It can be either unconstrained on the surface of the test medium or constrained between the medium and an optically transparent plate. The sacrificial layer is then ablated by the laser, again leading to strong ultrasound generation in the medium due to momentum transfer. [11]
In our experiments, the thermoelastic effect was used, with a red laser (800nm) being focused onto the surface of a material (Chromium), which absorbs the photons into a very thin layer at the top, where the acoustic waves were generated. The energy of the photons is initially taken up by electrons, which quickly move a small distance into the material, losing energy when they traverse the material, the temperature of the material near the surface suddenly increases by a few degrees, causing the layer to expand. A sound wave is then launched into the material.
The total energy per unit volume at a distance z into the film will be
� W ( z)=(1−R)QA�
exp(−z / �) (1)
R: the reflectivity index A: the surface of the irradiated area Q: the energy
of the laser pulse ζ: the penetrate distance
And the temperature of the local part will increase
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� T (z )=� W ( z)/ cv (2)
cv : the specific heat of the material
We assume that material is elastically isotropic, then the stress caused by the the thermoelastic effct can be written as
� ( z)=−3K � � T (Z ) (3)
K: the bulk modulus α: the linear expansion coefficient
The stress pulse determines the resulting acoustic wave, as the material is elastically isotropic, we can figure out that the elastic strain η is only depends on z, we can derive the strain η in the z-direction by solving the equations of elasticity [12]
� ( z)=3
1−�1+ �
K � (Z )−3K � �T ( z )
�∂2u(z )
∂ t2 =∂� (z )∂ z
� (z )=∂u (z )∂ z
(4)
n: the Poisson ratio; u(z): the displacements; ρ: the density
At the free surface, the stress σ should be 0, and that gives us the initial condition of the equation, the solution is:
))]()exp(2
1)exp()[exp(
1
1)1(),(
tczsigntcztcz
v
v
cA
QRtz
lll
v
−−
−−−
−+−=
ξξξ
ξαη
(5)
cl :the longitudinal sound velocity
We can see that the strain can be divided into two parts. The first part is a time-independent stain in the region near z=0, and the second part is a pulse which propagates away from the free surface at the speed of cl, see in figure 4.
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FIG. 4. The elastic strain at different time after the pump
pulse has been absorbed.[12]
2.2 Detection of acoustic waves
There are two principal ways to detect the acoustic waves: the first is monitoring a reflected/transmitted probe laser intensity, which was used in our experiments, another is the interferometer measurements. The detection by change of the intensity is based on the coupling of mechanical strain with the laser light through the medium, an effect known as Brillouin Scattering. A blue laser probe pulse relative to the generation pump pulse with a delay time ∆t was used to detect the propagation and attenuation of the acoustic pulse.
2.2.1 Reflectivity change and Brillouin scattering frequency
Based on the photoelastic effect, the information of ultra-sound can be decoded from an optical beam. The photoelastic is the interaction of acoustic waves and light waves in transparent media, and it is effect nature of any homogeneous transparent
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solid under stress that changes the reflective index. By observing the reflected light, we can measure the stress distribution in the material.
When the laser generates an acoustic wave in a material, a probe light beam is sent on the surface to observe the ultrasound. The electric field of such beam can be expressed as
E=Aexp[ i(wt−� )] (6)
A: amplitude w: frequency φ: phase
However, the optical frequency is just too high that the photodetectors can not detect the phase directly, but only the optical intensity (proportional to EE = A2=I and the index of reflectivity r=I/I0) can be directly measured.
In our experiments, a probe pulse with a time delay ∆t was used to detect the acoustic pulse.
FIG. 5. Schematic diagram of Brillouin Scattering: the acoustic wave propagates in the detection substrate at speed cl and reflects the probe in different time, rb: the principal
reflection by the transducer film ra, rc: two beams reflect by the acoustic waves
Here, we only consider about the first order reflections, which include the principal reflection by the transducer film rb and another two beams reflect by the acoustic waves, ra and rc, as demonstrated in figure 5.The information of the acoustic
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waves are contained in ra and rc, and the strain η determines the change of the refractive index δns at the distance z and time t as
),(),( tzn
tzn ss η
ηδ
∂∂
= (7)
Then, the three principal reflections can be written as:
rb=rtrans+ � rtrans
ra (t)=ik o∫0
∞dz �ns(z ,t)exp(−2ikz)
r c( t)=ir trans2 k o∫0
∞dz �ns(z , t)exp(2ikz)
(8)
Here, rtrans is the reflectivity of the sample without a acoustic pulse, as the delay time ∆t changes, the distance of the transducer film and the acoustic wave change, resulting in constructive or destructive interferences. The time dependent part of optical reflectivity is then given by:
cctrtrrrR
rrrrR
catranstrans
transcba
.))()((
22
++=∆−++=∆
δ (9)
As the delay time is changing, the three reflected beam interfere either constructively or destructively, which is known as Brillouin Scattering.
Brillouin scattering is a reflection of the incident wave by the diffraction grating created by thermal phonons. It was first predicted by Leon Brillouin in 1922. After the laser was developed, it turns into a very practical ways to study the acoustic vibration in the gas, liquids and solids. Brillouin scattering is also similar to the Raman Effect, it is subject to a variety of elementary excitations of inelastic scattering of light in the medium and the changes of frequency characterize the energy of elementary excitations.
The Brillouin frequency shift amount is proportional to the sound velocity in the material, while the refractive index and the sound velocity are related to the temperature, the stress and other factors, which makes the Brillouin frequency shift with these parameters. Brillouin scattering is the interaction of the incident light and
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the phonon. The acoustic waves change the density and reflective index of the medium and form a grating.
The moving acoustic waves change the optical index of medium and scatter the incident light, it can be viewed as a Bragg's reflection of the incident wave, as demonstrated in figure 5, so here we have:
nd 0)2/sin(2
λϕ = (10)
The distance between the transducer film and the acoustic pulse is changing with time:
B
lVd
υ= (11)
Then the velocity of the phonon Vl has a form
2/sin20
ϕυλ
nV B
l = (12)
n:the refractive index; Vl:the acoustic velocity; λ:the vacuum wavelength
For back scattering configuration, φ = π, this equation becomes:
nV Bl 2/0νλ= (13)
In another word, we can obtain the acoustic velocity by measuring the Brillouin scattering frequency.
Besides, we can also get the information of the rate of attenuation of the acoustic wave in the medium. The acoustic strain pulse can be written in Fourier form:
�( z , t)=∫ � (k )expi(kz−c l t) (14)
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Equation (7) shows that the amplitude of the acoustic oscillation is proportional with the η (2k), so by Fourier transform of the signal, the decrease of the amplitude of the acoustic oscillation is given by the half width at half maximum:
� ( f )=2� � f
2 (15)
What's more, another way is used in order to measure the velocity of acoustic waves in the liquid in our experiments.
The overall reflection coefficient of the Fabry-Perot type cavity is given by [13]:
ϕierdikrr
dikttrrr =
−−
+=)2exp(1
)2exp(
11210
112211021 (16)
ϕ: the the optical phase shift induced by the cavity; r21, r21 and r10 the optical reflection coefficient [14] from the substrate-liquid, liquid-substrate, and liquid-
transducer interfaces; t12 and t21 are the corresponding optical transmission coefficient
A good approximation for the optical shift is given by: [15]
�≈−2k1d=−2� � l ,B d /V l (17)
v l,B : the Brillouin frequency in the liquid; d: the thickness of the liquid
The total phase change ϕB also includes the acoustic part:
�1=2� �s ,B d /V l (18)
v s,B : the Brillouin frequency in the solid
The detected probe light intensity modulation δI: [16]
� I=I o cos(2� vB t+ � B) (19)
As the thickness change, ϕB will change
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l
BlBsB V
d)(2 ,,1
υυπφφφ
−=+= (20)
By fixing the time, we will get the relation between the thickness d and the intensity I.
BlBs
l
B
VEwith
E
dtII
,,
0 )22cos(
υυ
ππν
−=
+=(21)
The velocity Vl of the acoustic wave in the liquid is obtained by the
measurement of the period E that correlates to a 2π Brillouin phase change.
2.2.2. Interferometry
Another way to decode the information of acoustic waves is interferometry. It's a demodulation scheme used to retrieve phase-encoded information. It can measure independently both phase and amplitude change to an optical probe pulse by splitting a spatially coherent light beam in reference and detected beams.[11] There are a number of optical interferometers that perform this demodulation.
2.2.2.1. Reference Beam Interferometers
In this kind of interferometers, firstly, the laser will separate in two, one of the beams is sent to the test object, and the other is sent to a reference mirror. Upon reflection, the two beams are recombined parallel to each other and made to interfere at the photodetector. As such, they perform best on an optically mirror-polished surface.
2.2.2.2. Self-Referential Interferometers
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Another kind of interferometers widely used for samples with rough surfaces, is self-referential interferometers. It offers significantly improved performance with unpolished surface. A part of the laser reflected form the object contains information about the object displacement, and then it mixes with a wave front-matched reference beam that may or may not contain signal information. Since the two beams are now wave front-matched, it is possible to pull out the signal of interest. Some of the common self-referential interferometers are: (1) time-delay interferometers, (2) Fabry-Perot (FP) interferometers, (3) adaptive holographic interferometers. [11]
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3. Experiment
3.1. The experimental system
The experimental system must perform three primary functions: the generation of laser, the capture of light reflected from the sample, and the analysis of the reflected probe beam.
FIG. 6. Diagram of experimental set up: the output of laser system is separated into two parts, the pump beam (800 nm) and the probe beam (400 nm). With a computer controlled delay line, the detection of signal is allowed at different time delays of
acoustic waves’ propagation.
The generation and detection of acoustic waves in our experiments was realized by using a pump-probe system, as shown in figure 6. A Verdi V5 pump laser was used to perform the experiments, and the laser was tuned to 800 nm. In order to have higher
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pulse energy, a customized MIRA cavity dumper, which is an acousto-optical switch placed inside the femtosecond laser resonator, was used. It increased the pulse energy 4 times and reduce the pulse repetition rate of the modelocked laser system.
A BBO crystal was used for the second harmonic generation, a part of the laser was frequency-doubled, and the 800 nm red laser was used as a pump beam, and the 400nm blue laser was used as the probe beam. The two lasers were separated by a beam splitter, which reflected the blue beam and transmitted the red one.
3.1.1. The AOM crystal
In order to modulate the pump beam, we used an acousto-optic modulator (AOM) crystal in the experiment. AOM uses the acousto-optic effect to diffract of light using sound waves, as shown in figure 7, AOMs consist of a transducer, a crystal and also a circuit to control the input signal.
FIG. 7. Schematic drawing of an AOM: AOMs consist of a transducer, a crystal. The AOM controller put a signal in the transducer and the signal is converted to sound waves in the crystal by the transducer, and the sound waves change the refractive
index and are collimated to form a grating.
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3.1.2. Delay line
The probe pulse with a time delay ∆t was varied with a motorized delay line, as shown in figure 6. A ∆t is changing, the interference of the acoustic waves and the probe laser may occur in the liquid or detection substrate, demonstrated in figure 8, the propagation of acoustic waves was first monitored by the Brillouin scattering in liquid, ant then in the lens. Depending on the thickness of the liquid, the reflection of the probe by the acoustic wave can happen in the liquid or in the detection substrate.
As delay time change, the reflection of the probe laser resulted in constructive or destructive interference and we can observe the Brillouin scattering in that way.
FIG. 8. As delay time changing, the reflection of the probe by the acoustic
waves could occur in liquid or solid.
3.1.3. Brillouin scattering signal
For the delay time system, we can use the numerical derivation to eliminate the baseline and get the Brillouin oscillation, but with the second method (the oscillation by using different thicknesses of liquid) to measure the velocity, the time is fixed, so an optical derivative is needed to eliminate the background line and we can’t perform any numerical derivation in order to get ride of the baseline. We will show in the following how to perform the optical derivation.
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3.1.3.1. Optical derivation by using a piece of glass
FIG. 9. A time delay is introduced by a thin glass and the probe laser was separated
in two part by a mirror after reflection at the sample.
The first way to realize the optical derivative is by using a thin glass, as shown in figure 9, we separated the beam into two parts, one part of the beam passed though the glass, and that led a time delay:
c
nndt ag )( −
=
d: the thickness of the glass; ng: refractive index of glass;
na: refractive index of air.
Then, the two part of the probe laser was separated by a mirror, and we adjusted the two parts to the same intensity, then, each part of a balanced photodiode output the difference of light intensity:
Rofderivation
tRRsignalrecorded
→∆+−= )()( ττ
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In order to verify the possibility of derivation system, we have tested on the sample of chrome with the liquid glycerol, as shown is figure 10, comparing to the electronic signal, we can see that the Brillouin oscillation more clearly from the optical derivative signal, however, the background line still not totally eliminated, that may be caused by the distortion of the light after the lens and the mirror couldn't separate the two parts completely.
FIG. 10. (a)The original signal with a background line; (b) the optical derivative signal eliminated the background line.
1.1.3.2. Optical derivation by using a moving mirror with a frequency f
Another way to realize the optical derivation is by using a moving mirror. The moving mirror was placed before the sample and replaced the mirror III, as shown in figure 6, it was vibrating at the frequency f. The mirror had a little displacement ∆l at frequency f, which modified the time delay ∆l/c. By measuring the reflected signal at frequency f with a lock-in, we obtained the time derivation signal. Iron films were used for the derivative sample, the result is shown in figure 11, and we can see that the Brillouin oscillation from the derivative signal.
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FIG. 11. Signal of iron sample: the optical derivative signal eliminated the
background line by a moving mirror.
3.1.4 Observation of Newton rings
In order to get different liquid thickness, a lens was used in the liquid cell. The thickness would change as the position varied, apparently, the center of the lens could be located by the Newton rings and we adopted a detachable lens in the experiment system to realize that.
3.1.5 Acquisition system
For the data acquisition, a DSP SR830 Lock in amplifiers was used, as demonstrated in figure 6. Generally the signal contained noise at different frequencies. The SR830 multiplies all components of the input signal by a pure sine wave at the reference frequency simultaneously (which is 80 kHz in our experiments). In that way, the amplifier eliminate all the noisy.
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3.2 Sample Design
3.2.1 The photo-acoustic transducer
Chromium is used as the transducer material. It's known as a good photoacoustic transducer. The films were fabricated at university of Hokaido in Japan and deposited by electron beam physical vapor deposition on different substrates, including silicon and silicon dioxide.
After the acoustic waves were generated in the film, there were some echoes in the boundary of the film that also changed the reflection index, therefore, the thickness of the film could be obtained by measuring the distance between two acoustic echoes. As shown in figure 12, the difference of the two echoes time is about 50 ps:
�=t v m
2�=50×10−12×5900/2=150×10−9
vm: the velocity of acoustic waves in chromium
So, we can estimate that the thickness of the film is about 150 nm.
FIG. 12. The acoustic echoes in the sample: the acoustic waves are
reflected several times by the transducer and the detection substrate, and the echoes
change the reflectivity
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3.2.2. Liquid cell
In the experiments, the liquid thickness is ranging from a few nanometres to several microns in order to study the mechanical proprieties via transmission measurements. A lens and a piezo device are used to get access to different thicknesses of liquid, as demonstrated in figure 13.
Glycerol is used in our experiments, it is a colorless, odorless and viscous liquid and widely used in cosmetic industry.
Different liquid thickness was reached in the experiments by two ways: the change of piezo device or different position at the lens.
FIG.13. Schematic of the sample: the transducer was attached on the piezo device, the lens was fixed in a support, the thickness of the liquid could change by the movement
of piezo device or the position of the laser on the lens.
The lens we used in the experiment is Newport KPX124AR.16 BK, a plano-convex lens with a radius of curvature R=516.8 mm, which wass a slightly curved surface. With a 650 to 1000 nm anti-reflection coating, the lens permits the interference of the probe and transmits the pump. There is also another function of the coating, a lens without coating had been used for the experiments, but we found that it's almost impossible to found the Newton rings with the liquid, which we used for locating the center area. That's because the refractive index of the glycerol is 1.4746, and for the lens, the index is almost approaching this value.
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FIG. 14. The experimental setup: a convex lens is placed on top of the sample.
The difference of liquid thickness could be calculated by the radius R and the position x where the laser to focused. As we can see from figure 14, the center of the lens is the most flimsy part of the liquid, and the thickness of the further part can be calculated for:
(R−d )2+ x2=R2
→d =x2
2R
We used a PI E-509.x1 piezo device for modifying the liquid thickness and it is a displacement-sensor and a position-servo-control module for PZT actuators.
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4 Data analysis
4.1 Measure of the liquid thickness
The thin layer of viscous liquids on vertical surfaces involves an important class of problems in fluid mechanics. Many properties of the films are function of their thickness. In the experiments, we have measured the local film thickness between two boundaries, the lens and the transducer.
FIG. 15. The result of detection in two spots x1 and x2:
(a) Reflectivity changes ∆R probes at 400 nm detect dynamic; (b) The derivation of ∆R; (c)Fourier transform of the reflectivity ; (d) The phases of transform
As shown in figure 15(a), two different spots x1 and x2 on the lens have been measured, in figure 15(d), we got their phases by Fourier transform, and by equation (16) we can get the difference of thickness of two spots:
°=∆
∆=∆
13
2
ϕ
πυϕl
B
V
d
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nmd
Vd
B
l
4.5
2
=∆
∆=∆
πυϕ
4.2. Measurement of acoustic velocity in the liquid
The piezo device has a 1.2 nm displacement with an input signal of 2 mV, as demonstrated in figure 16, and the resolution is 0,15 nm. With the piezo device we can change the thickness of the liquid more precisely.
FIG. 16. The piezo device has a 1.2 nm displacement with an input voltage 2 mV.
By fixing the time, we will get the relation between the thickness d and the intensity I. As shown in equation (20), the reflectivity will change as an oscillator, and by measuring the period of the oscillation, we can obtain the acoustic velocity in the liquid.
We can see in figure 17, when the input voltage changes about 0.14 V, the reflectivity R changes a tour. As mentioned before, the piezo device has a 1.2 nm
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displacement with an input signal 2mV. So we can get that the step length of oscillation is 84 nm. From equation (21), we can get:
smV
GHz
GHz
nmV
Ewith
E
dtII
l
Bs
Bl
BlBs
l
B
/1680
20
40
84
)22cos(
,
,
,,
0
=→==
=−
=
+=
υυ
υυ
ππν
FIG.17. when the input of piezo device changes, the reflectivity oscillates with a certain thickness period E.
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5 Conclusion
In that master thesis, we have developed a new way to realize the derivation of signal- the optical derivation. Comparing to the numerical derivation, the new method can be applied to situations in which the time is fixed. Thus some time-dependent variables, like velocity, are also measurable in time-independent experiments. As demonstrated in part 3, the optical derivation can be realized by two methods, the separation of laser by a glass and the vibration of a moving mirror.
Otherwise, for measuring the velocity of acoustic waves in liquid, we change the thickness of liquid instead of fixing the time, and get the relation between thickness d and intensity I. In that way, the velocity Vl of the acoustic wave in the liquid is obtained. The method is examined under two different modes: direct thickness changing by piezo device and lens.
Furthermore, even though velocity of acoustic wave was measured in glycerol, there are some deviations comparing to the result in previous paper [16]. The error may due to the inaccuracy of measurement or the deficiency of theory.
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6 Acknowledgements
I wish to gratefully acknowledge all people who have helped me for the thesis.
First of all, I would like to express my sincere appreciation to my supervisors, Mr Thomas Pezeril, for his patient guidance and valuable comments in every stage of my internship. Without his enlightening instruction, impressive kindness and patience, I could not complete my internship.
I shall extend my thanks to all the teachers and professors who have taught me over the past year of study, they have helped me to develop the fundamental and essential academic competence.
Last but not least, I'd like to thank all my friends, especially my four colleagues, who have offered me quiet situation to compose my thesis and discussed with me about my thesis, I’m very grateful for their encouragement and support.
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7 References
[1] H. Maris, "Picosecond Ultrasonics:Brief Pulsed of High-Frequency Sound Allow Experimenters to Probe Connection insede a Computer chip", Scientific American, (1998)
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M2 stage
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