Photothermal Spectroscopy Lecture 1 - Principles Aristides Marcano - PowerPoint PPT Presentation

Winter College on Optics Photothermal Spectroscopy Lecture 1 - Principles Aristides Marcano Olaizola (PhD) Research Professor Department of Chemistry Delaware State University, US

Outlook 1. Photothermal effects: thermal lens and thermal mirror. 2. Sensitivity of the photothermal methods. 3. Photothermal characterization of materials. Photothermal spectroscopy – a new 4. 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 m L of water h w 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       2 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 ( r ) E E e z L   2 n      ( r ) L n ( r ) 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       2 2 E ( t ) r i k r z           o E ( z , r , t ) exp i artg    2   a ( z ) / a a ( z ) 2 R ( z ) z   o o 2 /   beam spot radius 2 a ( z ) a 1 z z o o   z 2   2 curvature radius R ( z ) z z o /   2 / 2 z a Rayleigh range o o sample’s position z

For a given sample’s position z and for continuous excitation (CW) the intensity of the excitation beam is   2 2 P 2 r   o   W ( r , t ) exp  2 2   a a 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 )     2 D T    t C p thermal diffusivity coefficient D  absorption coefficient C heat capacity p  density

In cylindrical coordinates with axial symmetry      2 1      2 r      2 r r r z We will also neglect the dependence on z (thin lens approximation)

The solution of this equation was first obtained by Whinnery in 1973 (add ref here)   t             T ( r , t ) W ( , t ) G ( r , , t , ) d d  C p 0 0          2 2 I r / 2 D ( t ) r      o G ( r , , t ) exp         2 ( ) 4 ( ) D t D t I o is the modified Bessel function of zeroth order

Using the table integral      2 2 exp b / 4 p           2 2 I o ( b ) exp p d 2 2 p 0 We obtain  1 /( 1 2 / )   t t c  2 /        2 T ( r , t ) T ( 1 / ) exp 2 r a d o 1  T    2 where t c a / 4 D P / 4 o o and  is the thermal conductivity coefficient

Field of Temperatures generated by the absorption of a beam of light t=100 s 0.004 o K) Temperature change ( t=10 s 0.003 t=1 s 0.002 t=0.1 s 0.001 0.000 -20 -10 0 10 20 r/r e For water using a 30 mW of 532 nm light

Refraction index depends on temperature       2 n n            2  n ( T ) n T T     o   2   T T For most of the solvents first order is enough. For example for ethanol        4 o 1 n ( T ) 1 . 3 4 10 C T

Thermal lens works as a phase plate  (thin lens approximation) r      E exp( i ( r )) E (   r )     2 n      ( ) ( ) r L T r   T p

The solid samples the thermoelastic effects add an additional term       2 n          ( r ) L n T ( r )   T   T p Where  T is the linear thermo-elastic coefficient

CW excitaion The phase difference with respect to the center of the beam is          ( r , z , t ) 2 n ( r , z , t ) n ( 0 , z , t ) p Using the results obtained for the temperature      1 1 exp( 2 m ( z ) g )       ( g , z , t ) d  o  1 /( 1 2 t / t ( z )) c where  2 2 m ( z ) a ( z ) / a ( z ) Mode matching coefficient p         P L dn dT 2 o e p

Single beam photothermal lens (PTL) experiment D Sample Focusing Aperture lens

Pump-probe experiment (m>1) Pump focusing lens Pump filter sample Detector Beamsplitter z op Aperture Probe focusing lens z ob a p z, a b d

Advantages of the pump-probe experiment 1.Higher sensitivity 2.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 optimized mode-mismatched experiment (m>>1) Pump beam L 1 S A Probe F D beam B L 2 a e z d

We define the PTL signal as   ( , , ) ( , , 0 ) W t z W z t  p p ( , ) S z t W ( z , t , 0 ) p b 2 2       W ( z , t , ) E ( z , t , r , rdr p p 0 where z 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 2 2   E ( z , t , 0 , ) E ( z , t , 0 , 0 )  p p S ( z , t ) 2 E ( z , t , 0 , 0 ) p

We calculate the probe amplitude at the far field using the Fresnel approximation Plane of the sample Detection plane   y’ r ' R y  j ’ d- z=d’ r j x’ x We suppose r, r’ << (d-z)

Using a Fresnel diffraction approximation we obtain*         E p ( z , t , 0 , ) exp( ( 1 iV ) g i ( g , t )) dg 0 2    V z / z z [( z / z ) 1 ] / d p op op p op z op is the Rayleigh range of the probe field, z p is the probe beam waist position, d is the detector position      1 1 exp( 2 m ( z ) g )       ( g , z , t ) d  o  1 /( 1 2 t / t ( z )) c * Shen J, LoweRD, Snook RD (1992) Chem Phys165: 385-396. DOI:10.1016/0301- 0104(92)87053-C.

For small phases we can also obtain*   4 mVt / t    1     c S ( z , t ) tan        o 2 2 2   V 1 2 m 1 2 m V 2 t / t c         P l dn dT o e p  2 2 m ( z ) a ( z ) / a ( z ) p  2 t c ( z ) a ( z ) / 4 D * Marcano A, Loper C, Melikechi N (2002) Pump probe mode mismatched Z- scan, J OptSoc Am B 19: 119-124.

m=1 1 s 0,004 0.01 s TL signal 0.001 s 0,000 -0,004 -2 -1 0 1 2 Sample position (cm) The TL signals were calculated using the following parameters:  o =0.01,  p =632 nm,  e =532 nm, z op =0.1 cm, z e =0.1 cm, d=200 cm, D=0.891 10 -3 cm 2 /s and different time values as indicated.