Thermal Lensing
Thermal lensing or photothermal deflection may be thought of as ultra-sensitive
absorption spectroscopy using a pump laser as the excitation source. It is based upon the
idea that the analyte molecules in a sample will absorb light when the energy of the light
is equal to the energy of a rotational, vibrational, or electronic transition just as in normal
microwave, IR, and UV-Vis spectroscopy. However the thermal lensing technique
makes use of the fact that once the molecules have been excited with the pump laser,
some of them will lose energy through collisions with the surrounding medium much like
in photoacoustic spectroscopy. This leads to a change in the density of the medium in the
region near the focus of the excitation light, again due to the transfer of the excitation
energy to the medium.
The density at the focus is rarified and slightly away from the focus it may be more dense
as the molecules collide and essentially move outward from the focus. The index of
refraction then changes as a function of the time that the laser is focused on the sample
(essentially a temperature change), and on the distance from the laser focus.
The formation of the lens is essentially caused by a change in the index of refraction.
Thus the pump laser which is tuned to the wavelength of light that is absorbed by the
analyte will cause an index gradient or thermal lens in the sample. The index gradient is
from a thermal change due to heating by the absorbed pump laser. This transient thermal
lens can be probed by monitoring how a second probe laser, which is passed through the
focal region of the pump laser, is deflected away from or onto a detector which monitors
the probe beam intensity.
Based on this one would expect the thermal lensing signal to depend on the following:
1)
2)
3)
4)
5)
6)
Lets look at the experimental setup to perform this experiment including a more detailed
look at the focus of the pump and probe beams. This experiment may be accomplished
with a pump beam that is either a chopped cw laser beam or a pulsed laser such as a YAG
pumped dye laser and a stable cw probe laser that is also typically chopped as shown in
the diagram.
Figure of Experimental Layout
Figure of Laser Beam Overlap
Let us also look at some experimental data here first to see if our expectations are true
and then we'll look at the eqn. which predicts the thermal lensing signal which is a ratio
of the signal hitting the photodiode with the pump laser to the signal hitting the
photodiode without the pump laser.
Figure of Thermal lensing signal from 10 Torr NO2 as a function of cell pressure
Figure of Thermal Lensing signal from NO2 as a function of cell pressure and pump laser
power.
Figure of Thermal Lensing signal from 10 Torr NO2 as a function of the solvent gas
pressure and the solvent gas identity
The signal of the themal lens will essentially be tied to the focal length of the induced
thermal lens. For the case of a pulsed pump laser
1/f(t) = 1/fo (1+2t/tc)- 2
1/fo = (4 L D N  h p H) / (k J w1p4 ) (d/dT) (2/)
fo = focal length right after the heating pulse (instant it pulses into the sample)
f(t) = the time dependence of the focal length of the thermal lens
tc is the decay time constant = wp2 /(4D)
w1p is the beam radius of the pump (heating) laser at the sample w1p2 = wop2 (1-z'2 /bp2 )
wop is the beam radius at the beam waist of pump laser
bp is the confocal distance bp=wop2 /p
z' is the sample position from the beam waist of the pump (heating) laser z = z' + zo
z is the distance from the beam waist of the probe laser to the sample
zo is the separation of the beam waist positions of the heating and probe laser
D is the thermal diffusivity D=k/(Cp)
N is the number density such as molecules/cm3
k is the thermal conductivity
 is the density
Cp is the constant pressure specific heat
L is the sample length
p is the frequency of the pump (heating) laser
 is the absorption cross section
H is the total output energy of the pump laser
J is Joules Constant
WHEN the focal length of the thermal lens is long, then the signal intensity is given by:
Sp = -2z / f = [Ip(t =) - Ip(t=t)] / Ip(t=t)
Ip(t=) is the intensity just before the heating pulse
Ip(t=t) is the intensity of the probe beam just after the irradiation pulse
So
Sp = -8LDNhpH /(k J wop4 ) (d/dT) 2/ (1+2t/tc)- 2 z / [1+((z-zo)2 /bp2 )2 ]
Thus for maximum intensity
z = {2zo± [4zo + 3(zo2 +bp2 )]½ } / 3
Using this condition one can find
Sp(t) = Sp(t=0)(1+ 2t/tc)- 2 where Sp(t=0) = 3½ [(hp2 H)/(cwp2 )] {D/k (d/dT)} (LN

Also for pulsed laser [(hp2 H)/(cwp2 )]=Et/(pwop2 ) where Et=pulsed energy of pump laser
So the terms in [ ] are terms that are characteristic of the pump (heating) laser
The terms in { } are the characteristics of the solvent or the medium
D (d/dT) / k = (d/dT) / (Cp)
The last term in the ( ) are characteristic of the analyte and
L N   2.303 where A is the absorbance
The normal UV-Vis signal is given by Suvvis = 2.303 A
So there is an enhancement factor then for the pulsed excitation which is
Enhancement factor pulsed laser Ep=Sp(t=0)/Suvvis = -33 / 2 [Et/(pwop2 )]{1/(Cp)(d/dT)}
The characteristic time constant, tc is obtained by:
tc = wop2 /(3D) = wop2 Cp /(3k)
Calculation of the enhancement factors from the physical parameters provides us
information about the sensitivity of Thermal Lensing.
For a pulse energy of 1 mJ/pulse and a beam waist size of 0.1mm one can calculate the
enhancement factor and also the characteristic time constants.
For a cw system Ec = -Po /(ck) (d/dT)
Po is the output power of the cw pump (heating) laser
c is the wavelength of the probe laser
k is the thermal conductivity
Applications
Trace Detection of Pesticides in Water
Faubel, Schulz et. Al. Jounal de Physique, 1994
Performances of related techniques:
Photoacoustic Spectroscopy
Photothermal Deflection
Photothermal Lensing
were compared with conventional absorbance data taken on a UV-Vis spectrophotometer
for solutions of pesticides in water.
Samples were:
2-methyl-4,6 dinitrophenol (DNOC)
2-sec-butyl-4,6-dinitrophenol (Dinoseb)
2-tert-butyl-4,6-dinitrophenol (dinoterb)
2,4 dinitrophenol (DNP)
in distilled water
The UV-Vis Spectrophotometer used was a Cary 2400.
The photoacoustic system is a single beam instrument using a XeCl excimer laser as the
excitation source to a dye laser. The dye laser produces a beam at 364 nm whih impinges
on a sample solution confined in temp. controlled cell. A piezoelectric transducer is
incontact with the sample and measures the signal amplitude of the resulting
photoacoustic wave. The output is filtered and fed into a preamplifier and a boxcar
integrator.
The thermal lensing system is shown in the figure
A cw UV Ar-ion laser (364nm) pump beam modulated around 10 Hz by a mechanical
chopper impinges on a quartz fluorescence curvet. A HeNe probe laser beam at 632.8
nm is focused to intersect with the Ar-ion pump beam either in a collinear fashion or
perpendicular to the propagation of the pump beam.
In photothermal deflection spectroscopy (PDS) mode, the deflection of the HeNe probe
beam is measured by a two dimensional position sensitive device such as a CCD.
In thermal lensing (TL) mode the position sensitive device is replaced with a photodiode.
In photothermal phase shift (PTPS) molde measurements are performed with the help of
a Mach Zehnder interferometer with the sample cell placed on one arm of the
interferometer.
The following table gives a comparison of the detection limits for DNOC when using the
different techniques.
DNOC
in
μg/kg
Limits of Detection
Cary 2400
PAS
15
PDS
A calibration curve for DNOC using the TL is given in the figure
Similar Results were obtained for the other pesticides.
TL
PTPS
Also a pulsed probe laser was also used and the cw laser performed better by a factor of
about 2.
Note that according to EPA and CEC standards, detection limits of 0.1 μg/kg (0.1 ppb)
for pesticides in drinking water are required.
The experiment was also tried using the PAS and TL detectors after an HPLC
chromatographic instrument. The following table gives a comparison of the detection
limits of DNP and DNOC for the different detector/HPLC combinations.
Specimen
DNP μg/kg
DNOC μg/kg
UV-diode array
11
10
PAS
TL
Note that the TL system gave the best results in both cases and had a detection limit that
was between 10 and 100 times more sensitive than the conventional spectrometer.
Thermal Lensing for Harsh Environments
Supercritical Water
As a result of the high pressures and temperatures necessary for SCW conditions (above
the critical point of water of 22.4 MPa and 374 °C), direct optical spectroscopic analysis
of analytes is difficult. It is necessary to construct sample cells capable of surviving these
extreme conditions that also allow transmission of the optical signal. Optical windows
must be thick and of small diameter. The seating of the windows, and the optical
properties of the window materials, change as the water is heated and pressurized making
alignment especially difficult. Limiting factors for in situ studies include the sensitivity
of the instrumentation and applicability of the wavelengths available. For example,
UV/vis spectroscopy is usable down to a ppm level and applicable to a wide range of
organic compounds, but many compounds only absorb in the deep UV portion of this
spectrum. Absorption measurements in this region require special window materials, and
for supercritical measurements these materials also must have small temperature and
pressure coefficients. In addition, as the windows have to be of small diameter,
absorption measurements are difficult to achieve using a conventional light source.
In contrast, thermal lensing (also called thermal deflection) is a laser-based,
ultrasensitive, UV-vis absorption technique. It has been used to measure and monitor the
concentration of analytes absorbing in the visible and ultraviolet region at the
10-7 absorbance unit level and is more readily employed in a harsh environment. In a
crossed beam arrangement, either pulsed or continuous-wave lasers can be used as the
pump beam, and a stable continuous laser can be used for the probe beam. For
these experiments, the aperature size necessary can be quite small.
Theoretically, the thermal lens signal would be enhanced in supercritical water over the
normal signal expected from UV-Vis absorbance. The enhancement of the thermal lens
depends on several factors and is proportional to the following
Thermal Lensing Signal ~ dη/dT Ep / (λp κ)
where dη/dT is the constant pressure temperature dependence of the refractive index,
Ep
is the pump laser power,
κ
is the sample thermal conductivity, and
λp
is the wavelength of the probe laser.
On the basis of this equation, it can be seen that the lens signal will be greatest for
solvents that have low thermal conductivities, such as organics, but exhibit less
sensitivity in aqueous solution where the thermal conductivity is higher.
Reports of the use of thermal lensing in supercritical CO2 describe a large enhancement
in the signal strength. Because the coefficient of thermal expansion of a fluid diverges at
the critical point, the index of refraction change with temperature should be very large,
and thus the analytical sensitivity of the thermal lensing technique should be greatly
enhanced.
In this study, a supercritical water cell was built. Solutions of benzoic acid in water were
placed in the cell. The fourth harmonic laser beam from a Nd:YAG at 266nm was used
as the pump laser. The extinction coefficient for benzoic acid at this wavelength is about
800 L/(mol cm) at this wavelength.
A schematic of the supercritical water cell is shown here along with a diagram of the TL
experimental setup. Note that an Ar ion laser was used as the probe beam and a
photomultiplier tube with a pinhole in front of it was used as the detector in this
experiment.
signal
-1.00E-06
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
0.00E+00
2.5e-3M
1.25e-3M
2.5e-4M
water
1.00E-06
time (us)
2.00E-06
The signal detected by the photomultiplier tube gave the following results. Integration of
the area under the larger peaks at 800 ns gives the following plot of integrated signal vs
concentration of benzoic acid in water. Note that the detection limits are in the mmol
range.
Thermal Lensing in a Supercooled Jet Expansion
We talked about how CARS, SRG, or SRL could be useful in supercooled jet expansions.
Well one day we were setting up an Inverse Raman experiment to determine the
temperature obtained in a supercooled jet expansion of acetylene and possibly to look for
dimmers and trimers. We were using as a pump laser, the output from a ring dye-laser
using Rhodamine 590 dye. The wavelength was around 570 nm. As a probe, the 568 nm
single-mode output (200 mW, 1MHz bandwidth) of a krypton ion laser was utilized. To
avoid detector damage, this laser was chopped at 10 Hz to produce 100us pulses which
overlapped the 10ns pump pulse.
See the figure of the experimental setup.
The following figure shows the pure rotational Inverse Raman Spectrum that was
obtained.
Well in the process of doing this, we also noticed some other depletion of the probe laser
in the SRL that we could not explain and they had a longer decay time dependence.
What do you think it turned out to be?
The υ2 + 5υ3 vibrational combination band of acetylene at 17518.8 cm-1 or 570.8 nm.
2 = 1973.8 cm- 1
3 = 3287 cm- 1
Thus the geometry used in the SRL experiment turned out to be an excellent setup for
thermal lensing experiments of high lying combination bands.
Interesting, right? To be able to measure combination bands with such good signal
strength and resolution was incredible to us at least.
We use the thermal lensing then to also measure the temperature based on the rotational
structure on the vibrational combination bands.
One may wonder whether energy is released by cascading through the vibrational levels
or if it is primarily through the rotational levels.
Based on the information presented above about the thermal lensing signal, the signal for
a particular J value should be given by:
IJ = Const. x |Er + Ev| gNJ S(J) exp [-EJ/kT]
Er = incremental change in the rotational energy due to the absorption
Ev = incremental change in the vibrational energy due to the absorption
EJ = rotational energy of the level J in the ground state
gNJ = the nuclear spin degeneracy
S(J) = line strength factor for the transition
Const. - contains total concentration of absorbing molecules, the pump laser power,
and instrument factors
A plot of ln [IJ/( Const. x |Er + Ev| gNJ S(J)) ]
vs
EJ
and varying the Ev values gives the following.
When Ev is assumed to be zero a fit of R2 = 0.85 is achieved, but once Ev is above 200
cm- 1 then fits of 0.95 to 0.97 when all 17500 cm- 1 of vibrational energy contribute.
This is the case both in the static cell at 298K and in the jet. Also the slope of the line
give us the temperature and assuming Ev = 200cm- 1 it is calculated to be 316 ±12 K in
the static cell and 125± 6 K in the cooled jet expansion. This is a bit higher than the
temperature of 110 ± 10 calculated from the Inverse Raman spectrum of the cooled jet.
Furthemore, one can get an idea of the collisions that are taking place in the jet from the
bandwidth of the Raman Loss spectrum. The Doppler width for the rotational SRL lines
is very small < 10 MHz and since the bandwidth of the probe and pump lasers that we
were using is about 100 MHz one can use the following eqn. to determine an estimate of
the collisions from the linewidth
See linewidth figure
Assuming a Voigt Profile v for the observed bands and a Lorentzian collisional
linewidth L
v = 0.5 L + [0.25 L2 + (I + Dop)2 ] 0 . 5
I =
Dop =
L =
v =
Value of 10MHz per Torr were determined and from this one calculates that 800
dephasing collisions occur in the static cell
Based on an isentropic expansion one can infer that about
collisions would take place in going from 500 to 750 micron distance from the orifice.
Looking at the linewidth of the thermal lens it is much larger than the Raman loss?