Photothermal Spectroscopy Lecture 1 - Principles Aristides Marcano Olaiola (PhD) Research Professor Department of Physics and Engineering Delaware State University, US
Outlook 1. Photothermal effects: thermal lens and thermal mirror.. Sensitivity of the photothermal methods. 3. Photothermal characteriation of materials. 4. Photothermal spectroscopy a new kind of spectroscopy
Photothermal are those effects that occur in matter due to the generation of heat that follows the absorption of energy from electromagnetic waves.
Photoelastic changes in density due to temperature V V T T Photorefractive change of the refraction index due to temperature n n T T
There are two major characteristics of the photothermal effects: Universality Sensitivity
In any interaction of light and matter there is always a release of heat
Consider one absorbing atom contained in 1 L of water h Consider also that a beam of light illuminates the sample continuously. The atom will absorb one photon and will release the energy of this photon toward the surrounding water molecules (heating) in 10-10 -10-13 s.
Thermal diffusion will remove the generated heat. However, this effect is slow. It will take between tens of ms to seconds to equilibrate the temperatures. During this time the atom will accumulate the energy of 10 8-10 13 photons. This can raise the temperature an average of 10-3 o C.
Photothermal method has a phase character. The signal is in most of the cases proportional to the change of phase L n T T
Photothermal Effects S. E. Bialkowski. Photothermal Spectroscopy Methods for Chemical Analysis. New York: Wiley, 1996.
Thermal lens Focused beam
Photothermal Mirror Effect
Thermal lens act like a phase plate r i Ee E (r) L ( r) Ln(r) n n( r) T ( r) T The change in temperature T is proportional to absorption
To calculate the induced phase we calculate first the distribution of temperature generated thanks to the absorption of a Gaussian beam in the sample.
Excitation Gaussian Beam Intensity
Gaussian Beam Amplitude o o o artg i R r k i a r a a t E t r E ) ( ) ( exp ) / ( ) ( ),, ( / 1 ) ( o o a a R o / ) ( beam spot radius curvature radius / o a o Rayleigh range sample s position
For a given sample s position and for continuous excitation (CW) the intensity of the excitation beam is W ( r, t) P a exp r a o where P o is the total light power This function has axial symmetry. It is convenient to solve the Laplace equation in cylindrical coordinates.
Thermal diffusivity equation Laplace Equation We write the Laplace equation considering axial symmetry T W ( r, t) t D T C p D C p thermal diffusivity coefficient absorption coefficient heat capacity density
In cylindrical coordinates with axial symmetry 1 r r r r We will also neglect the dependence on (thin lens approximation)
The solution of this equation was first obtained by Whinnery in 1973 (add ref here) d d t r G t W C t r T t p 0 0 ),,, ( ), ( ), ( ) ( 4 exp ) ( ) ( / ),, ( D t r D t D t r I t r G o I o is the modified Bessel function of eroth order
Using the table integral I o 0 ( b ) exp We obtain exp b / 4 p p d p 1/(1 t / ) t c T ( r, t) T o 1 (1/ ) exp r / a d where T P / 4 o o t a / 4D c and is the thermal conductivity coefficient
Field of Temperatures generated by the absorption of a beam of light Temperature change ( o K) 0.004 0.003 0.00 0.001 0.000 t=100 s t=10 s t=1 s t=0.1 s -0-10 0 10 0 r/r e For water using a 30 mw of 53 nm light
Refraction index depends on temperature o T T n T T n n n(t) For most of the solvents first order is enough. For example for ethanol T C 10 4 1.3 n(t) 1 o 4
Thermal lens works as a phase plate (thin lens approximation) r E E exp( i(r)) ( r) n ( r ) L T ( r ) T p
The solid samples the thermoelastic effects add an additional term ) ( ) ( r T n T n L r T p Where T is the linear thermo-elastic coefficient
CW excitaion The phase difference with respect to the center of the beam is n(r,, t) n(0,, t) ( r,, t) p Using the results obtained for the temperature ( g, where, t) m( ) a p o ( ) / a 1 1/(1 t / t c ( ) ( )) 1 exp( m( ) g ) d Mode matching coefficient o e dn dt PL p
Single beam photothermal lens (PTL) experiment D Focusing lens Sample Aperture
Pump-probe experiment (m>1) Pump focusing lens Pump filter sample Detector Probe focusing lens Beamsplitter op ob Aperture a p, a b d
Advantages of the pump-probe experiment 1.Higher sensitivity.time dependence experiments possible 3.Spectroscopy possible by using tunable pump sources. 4.Detection technology in the visible. No need of UV or IR detectors. 5.Different experimental configurations possible.
Pump-probe optimied mode-mismatched experiment (m>>1) Pump beam L 1 S A Probe beam F D L B a e d
We define the PTL signal as,0), (,0), ( ),, ( ), ( t W t W t W t S p p p b p p rdr r t E t W 0,,, ( ),, ( where is the sample position, b is the aperture radius.
For the sake of simplicity we can consider the radius of the aperture small (b 0). Then the signal can be calculated as,0,0), (,0,0), ( ),0,, ( ), ( t E t E t E t S p p p
We calculate the probe amplitude at the far field using the Fresnel approximation Plane of the sample Detection plane y R r' y r d-=d x x We suppose r, r << (d-)
Using a Fresnel diffraction approximation we obtain* E p 0 (, t,0, ) exp( (1 iv ) g i( g, t)) dg V p / op op[( p / op) 1] / d op is the Rayleigh range of the probe field, p is the probe beam waist position, d is the detector position ( g,, t) o 1 1/(1 t / t c ( )) 1 exp( m( ) g ) d * Shen J, LoweRD, Snook RD (199) Chem Phys165: 385-396. DOI:10.1016/0301-0104(9)87053-C.
For small phases we can also obtain* c c o t t V m m V t mvt t S / 1 1 / 4 tan ), ( 1 ) ( ) / ( ) ( a a m p p e o dt dn l P D a t c 4 ) / ( ) ( * Marcano A, Loper C, Melikechi N (00) Pump probe mode mismatched Z- scan, J OptSoc Am B 19: 119-14.
0,004 m=1 1 s 0.01 s TL signal 0,000 0.001 s -0,004 - -1 0 1 Sample position (cm) The TL signals were calculated using the following parameters: o =0.01, p =63 nm, e =53 nm, op =0.1 cm, e =0.1 cm, d=00 cm, D=0.891 10-3 cm /s and different time values as indicated.
Optimied mode mis-match experiment 0,0030 1 s TL signal 0,0015 0.01 s 0.1 s 0,0000-0 -10 0 10 0 Sample position (cm) The TL signals were calculated using the following parameters: o =0.01, p =63 nm, e =53 nm, p =100 cm, e =0.1 cm, L=00 cm, a e =0 and D=0.891 10-3 cm /s and different time values as indicated
Mode-mismatched scheme
Probe transmission through the aperture Photocurrent (na) 40 0 T o T(,t) 0 0 5 10 Time (s) Transmitted through the aperture probe light (63 nm) using 50 mw of 53 nm excitation beam of light. The sample is a -mm column of water
Experimental PTL signal S(, t) T ( t) T T o o PTL signal calculated using the data of previous slide. The solid line is the theoretical fitting of the data.
(a) 5000 0 TL signal (arb. units) -5000 0.0 0.5 1.0 (b) 0.5 0.0-0.5 0.0 0.5 1.0 Time (sec) PTL signal as a function of time from the distilled water sample (a) and BK7 optical glass slab (b). The doted line is the pump field time dependence. The signal-to-noise ratio for the PTL is 10 and 75000 for BK7 glass and water, respectively.
Z-scan signal for the distilled water sample (a) and the BK7 optical glass slab (b). 0.0000 (a) -0.0005-0.0010-10 0 10 (b) 1.0x10-7 0.0-10 -5 0 5 10 Sample position (cm) Marcano A., C. Loper and N. Melikechi, Appl. Phys. Lett., 78, 3415-3417 (001).
0.0000 PTL signal -0.000-0.0004 7 H 4 H -0.0006-10 0 10 Sample position (cm) PTL signal from water for two different chopping frequencies : 4 y 7 H.
PTL signal is nearly scattering free PTL Signal 0.6 0.4 0. a T =0 T =8.6 cm -1 T =15 cm -1 0.0 0 4 Time (s) Normalied PTL Signal 1. 0.8 0.4 0.0 b T =0 T =15 cm -1 0 4 Time (s) a- PTL signal as a function of time for samples (water with latex microspheres) with turbidities of 0, 8.6 and 15 cm -1 obtained using 80 mw of 53 nm CW light from the DPSS Nd-YAG laser,b- Normalied PTL signal for T =0 (black) and T =15 cm -1 (light grey) over the stationary values showing the different signal-tonoise ratios.
1 PTL signal 0.1 0.01 1E-3 1E-4 Transmittance 4 6 8 10 Turbidity (cm -1 ) PTL signal as a function of turbidity The solid line is the model prediction. The dependence of transmittance is also plotted for comparison
The signal can be detected in highly turbid samples PTL Signal 0.6 0.3 0.0-0.3 Pump PTL signal Meat mm -0.6 0.0 0.5 1.0 Time (s) PTL Signal 0.1 0.01 Whole milk in water 1 10 Turbidity (cm -1 ) Marcano A., Isaac Basaldua, Aaron Villette, Raymond Ediah, Jinjie Liu, Omar Ziane, and Noureddine Melikechi, Photothermal lens spectrometry measurements in highly turbid media, Appl. Spectros. 67 (9), 1013-1018, 013 (DOI: 10.1366/1-06970).
Photothermal Mirror Method This method involves the detection of the distortion of a probe beam whose reflection profile is affected by the photo-elastic deformation of a polished material surface induced by the absorption of a focused pump field Pump beam Reflected Distorted Beam Photothermal Micromirror
The theoretical model used to explain the PTM method is based on the simultaneous resolution of the thermoelastic equation for the surface deformations and the heat conduction equation. t T D T ( 1 ) u I( r, t) C p u (1 ) T T where is the Poisson ratio, T is the thermo-elastic
Boundary conditions r T (,, t) 0 0 0 0 Normal stress components Initial condition T ( r,,0) 0 The phase difference will be p u ( r,0, t) u (0,0, t)
Scheme of the PTM experiment Pump beam r u(,r,t) Sample
References for PTM theory L. Malacarne, F. Sato, P. R. B. Pedreira, A. C. Bello, R. S. Mendes, M. L. Baesso, N. G. C. Astrath and J. Shen, Nanoscale surface displacement detection in high absorbing solids by time-resolved thermal mirror, Appl. Phys. Lett.9(13), 131903/3 (008). DOI: 10.1063/1.90561. F.Sato,L.C.Malacarne,P.R.B.Pedreira,M.P.Belancon,R.S.Mendes,M. L.Baesso,N.G.AstrathandJ.Shen, Time-resolved thermal mirror method: A theoretical study, J. Appl. Phys.104(5), 05350/9 (008). DOI: 10.1063/1.975997. L. C. Malacarne, N. G. C. Astrath, G. V.B.Lukasievic, E. K. Leni, M. S. Baesso and S. Bialkowski, Time-resolved thermal lens and thermal mirror spectroscopy with sample-fluid heat coupling: A complete model for material characteriation, Appl. Spectros.65(1), 99-104 (011). DOI: 10.1366/10-06096. V. S. Zanuto, L. S. Herculano, M. S. Baesso, G.V.B. Lukaievic, C. Jacinto, L. C. Malacarne and N.G.C. Astrath, Thermal mirror spectrometry: an experimental investigation of optical glasses, Opt. Mat.35(5), 119 1133 (013).DOI: 10.1016/j.optmat.013.01.003. N. G. C. Astrath, L. C. Malacarne, V. S. Zanuto, M. P. Belancon, R. S. Mendes, M. L. Baesso and C. Jacinto, Finite sie effect on the surface deformation thermal mirror method, J. Opt. Soc. Am. B8(7), 1735-1739 (011). DOI:10.1364/JOSAB.8.001735.
For opaque materials ( g, t) o exp ) 0 /8 f (, t J gm d o f (, ) Erfc exp Erf 4 where t / t c ; g r / a Erf(x) is the error function and Erfc(x) is the complementary error function. A. Marcano, G. Gwanmesia, M. King and D. Caballero, Opt. Eng., 53(1), 17101 (014). DOI:10.1117/1.OE.53.1.17101.
P (1 )( ) 1 o T p is thermal quantum yield is the thermal conductivity P is the pump power a t c 4D PTM time build-up
Diffraction theory provides the value of the field amplitude of the center of the probe beam at the detection plane in a similar way it does for the PTL case E p 0 ( t, ) exp( (1 iv ) g i( g, t)) dg S PTM ( t) E p ( t, ) E p E ( t,0) p ( t,0)
PTM Signal 0.3 0. 0.1 =-0.1, p =000 =-0.1, p =100 Normalied PTM Signal 1.0 0.5 =-0.1, p =000 =-0.1, p =100 0.0 0 000 4000 Time (t/t c ) 0.0 0 000 4000 Time (t/t c ) PTM signal for different probe beam Rayleigh ranges
PTM stationary value 1.0 0.5 0.0 0.0 0.5 1.0 PTM signal as a function of PTM phase amplitude
PTM mode-mismatch set-up S A Ampl. DL D Probe laser Osc. B M 3 FL Ref M B 1 SG Pump laser M 1
Normalied PTM Signal 1.0 0.5 0.0 Glass filter 53 nm, 15 mw t c =1.6 10-3 s. S max =0.56 0 500 1000 1500 Time (in t c units)
1. Normalied PTM Signal 1.0 0.5 0.0 Ni, 53 nm, 50 mw t c =1. 10-5 s S stationary =0.091 0 500 1000 1500 000 Time (in t c units) Normalied PTM 1.0 0.8 0.6 0.4 0. 0.0 Glassy carbon 445 nm, 146 mw, 3 H t c =60 10-6 s S stationary =0.35 0 1000 000 3000 t/t c PTM signal from Ni and glassy carbon samples using 53 nm and 445 nm diode lasers
Glass 1000 Dy TiO 5 Quart t c (s) 100 Ti Pt 10 Equation Weight Residual Sum of Squares y = a + b*x No Weighting 0.0141 Pearson's r -0.9971 Adj. R-Square 0.998 Value Standard Error 10-6 s Intercept.7641 0.057 10-6 s Slope -0.98565 0.03746 Ni Sn Cu 1 0.1 1 10 100 D (10-6 m s -1 ) Values of t c versus D
Stationary value versus PTM phase Dy TiO 5 S e /P (W -1 ) 10 1 0.1 Glass Glassy Carbon Ti Dy Ti O 7 Quart Ni Sn Cu 0.01 0.01 0.1 1 10 100 o /P (W -1 )
Conclusions PTL and PTM are versatile and sensitive technique to determine the absorption and photothermal properties of matters. The use of pump-probe configuration allows the implementation of PTL an PTM spectroscopy as new method of analysis.