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

Photothermal Spectroscopy Lecture 1 - Principles Winter College on Optics

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. 4. Photothermal spectroscopy – a new kind of spectroscopy

Photothermal are those effects that

• ccur in matter due to the generation
• f heat that follows the absorption of

energy from electromagnetic waves.

Photoelastic – changes in density due to temperature Photorefractive – change of the refraction index due to temperature

T V V

T

     

T T n n      

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 mL

• f water

hw

Consider also that a beam of light illuminates the sample continuously. The atom will absorb

• ne 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 108-1013 photons. This can raise the temperature an average of 10-3 oC.

Photothermal method has a phase

• character. The signal is in most of the

cases proportional to the change of phase T T n L              2

• S. E. Bialkowski. “Photothermal Spectroscopy Methods for

Chemical Analysis”. New York: Wiley, 1996.

Photothermal Effects

Thermal lens Focused beam

Photothermal Mirror Effect

Thermal lens act like a phase plate

E 

) r ( i

e E





r z

) r ( n L 2 ) r (     

L

) ( ) ( r T T n r n    

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

                      

• z

z artg i z R r k i z a r a z a t E t r z E ) ( 2 ) ( exp / ) ( ) ( ) , , (

2 2 2

2 2 /

1 ) (

• z

z a z a  

  z

z z z R

• /

) (

2 2 



beam spot radius curvature radius 2 /

2

• a

z   Rayleigh range z sample’s position

For a given sample’s position z and for continuous excitation (CW) the intensity of the excitation beam is

       

2 2 2

2 exp 2 ) , ( a r a P t r W

• 

This function has axial symmetry. It is convenient to solve the Laplace equation in cylindrical coordinates. where Po is the total light power

Thermal diffusivity equation –Laplace Equation We write the Laplace equation considering axial symmetry D thermal diffusivity coefficient  absorption coefficient

p

C

heat capacity  density

         

p

C t r W T D t T ) , (

2

In cylindrical coordinates with axial symmetry

2 2 2

1 z r r r r               

We will also neglect the dependence on z (thin lens approximation)

The solution of this equation was first

• btained by Whinnery in 1973 (add ref

here)

        d d t r G t W C t r T

t p

    



 0 0

) , , , ( ) , ( ) , (

 

              ) ( 4 exp ) ( 2 ) ( 2 / ) , , (

2 2

      t D r t D t D r I t r G

• Io is the modified Bessel function of

zeroth order

Using the table integral

   

2 2 2 2 2

2 4 / exp exp ) ( p p b d p b Io     





   

We obtain

  4 /

• P

T 

and  is the thermal conductivity coefficient where

 

   d a r T t r T

c

t t

• 

  



 ) / 2 1 /( 1 1 2 2 /

2 exp ) / 1 ( ) , ( D a tc 4 /

2



• 20
• 10

10 20 0.000 0.001 0.002 0.003 0.004 t=0.1 s t=1 s t=10 s t=100 s

Temperature change (

• K)

r/re

For water using a 30 mW of 532 nm light

Field of Temperatures generated by the absorption of a beam of light

Refraction index depends on temperature                          

2 2 2

• T

T n T T n n ) T ( n

For most of the solvents first order is enough. For example for ethanol

T C 10 4 3 . 1 ) T ( n

1

• 4

    

 

Thermal lens works as a phase plate (thin lens approximation)

E 

)) r ( i exp( E    

) r ( 

r 

) ( 2 ) ( r T T n L r

p

          

The solid samples the thermoelastic effects add an additional term

) ( 2 ) ( r T n T n L r

T p

                  

Where T is the linear thermo-elastic coefficient

CW excitaion

 





     

1 )) ( / 2 1 /( 1

) ) ( 2 exp( 1 ) , , (

z t t

• c

d g z m t z g   

The phase difference with respect to the center of the beam is

) ( / ) ( ) (

2 2

z a z a z m

p



  



p e

• dT

dn L P   2  

where

 



) t , z , ( n ) t , z , r ( n 2 ) t , z , r (

p

    

Using the results obtained for the temperature Mode matching coefficient

D Aperture Sample Focusing lens

Single beam photothermal lens (PTL) experiment

Pump-probe experiment (m>1)

Probe focusing lens Beamsplitter sample Aperture Detector Pump filter Pump focusing lens

ap z, ab d zop zob

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.

Probe beam

L2 B S A D F L1

ae

Pump beam

z d

Pump-probe optimized mode-mismatched experiment (m>>1)

We define the PTL signal as

) , , ( ) , , ( ) , , ( ) , ( t z W t z W z t W t z S

p p p

  



   

b p p

rdr r t z E t z W

2 2

, , , ( ) , , ( 

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 2

) , , , ( ) , , , ( ) , , , ( ) , ( t z E t z E t z E t z S

p p p

  

Plane of the sample Detection plane We suppose r, r’ << (d-z)

R 

r 

' r 

d-z=d’ x y y’ x’ j j’

We calculate the probe amplitude at the far field using the Fresnel approximation

Using a Fresnel diffraction approximation we obtain*





      )) , ( ) 1 ( exp( ) , , , ( dg t g i g iV t z Ep

 





     

1 )) ( / 2 1 /( 1

) ) ( 2 exp( 1 ) , , (

z t t

• c

d g z m t z g   

d z z z z z V

• p

p

• p
• p

p

/ ] 1 ) / [( /

2 

 

zop is the Rayleigh range of the probe field, zp is the probe beam waist position, d is the detector position

* 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*

 

 

            

 c c

• t

t V m m V t mVt t z S / 2 2 1 2 1 / 4 tan ) , (

2 2 2 1

) ( / ) ( ) (

2 2

z a z a z m

p



  



p e

• dT

dn l P    

D z a z tc 4 / ) ( ) (

2



* Marcano A, Loper C, Melikechi N (2002) Pump probe mode mismatched Z- scan, J OptSoc Am B 19: 119-124.

• 2
• 1

1 2

• 0,004

0,000 0,004

TL signal

1 s 0.01 s 0.001 s

Sample position (cm)

The TL signals were calculated using the following parameters: o=0.01, p=632 nm, e=532 nm, zop=0.1 cm, ze=0.1 cm, d=200 cm, D=0.891 10-3 cm2/s and different time values as indicated.

m=1

• 20
• 10

10 20 0,0000 0,0015 0,0030 0.01 s 0.1 s 1 s TL signal Sample position (cm)

The TL signals were calculated using the following parameters: o=0.01, p=632 nm, e=532 nm, zp=100 cm, ze=0.1 cm, L=200 cm, ae=0 and D=0.891 10-3 cm2/s and different time values as indicated

Optimized mode mis-match experiment

Mode-mismatched scheme

Probe transmission through the aperture

5 10 20 40 T(z,t) To Photocurrent (nA) Time (s)

Transmitted through the aperture probe light (632 nm) using 250 mW of 532 nm excitation beam of light . The sample is a 2-mm column of water

Experimental PTL signal PTL signal calculated using the data of previous slide. The solid line is the theoretical fitting of the data.

• T

T t T t z S   ) ( ) , (

(a) (b)

Time (sec) TL signal (arb. units)

0.0 0.5 1.0

• 5000

5000 0.0 0.5 1.0

• 0.5

0.0 0.5

PTL signal as a function of time from the distilled water sample (a) and BK7

• ptical 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.

• 10
• 5

5 10 0.0 1.0x10

• 7

(a) (b)

Sample position (cm)

• 10

10

• 0.0010
• 0.0005

0.0000

Z-scan signal for the distilled water sample (a) and the BK7 optical glass slab (b).

Marcano A. , C. Loper and N. Melikechi, Appl. Phys. Lett., 78, 3415-3417 (2001).

• 10

10

• 0.0006
• 0.0004
• 0.0002

0.0000

PTL signal

4 Hz 7 Hz

Sample position (cm)

PTL signal from water for two different chopping frequencies : 4 y 7 Hz.

2 4 0.0 0.2 0.4 0.6

T=0 T=15 cm-1

PTL Signal Time (s)

T=8.6 cm-1

a b

2 4 0.0 0.4 0.8 1.2

T=15 cm

• 1

Normalized PTL Signal Time (s)

T=0

PTL signal is nearly scattering free

    

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 532 nm CW light from the DPSS Nd-YAG laser,b- Normalized PTL signal for T=0 (black) and T=15 cm-1 (light grey) over the stationary values showing the different signal-to- noise ratios.

2 4 6 8 10 1E-4 1E-3 0.01 0.1 1 Turbidity (cm

• 1)

PTL signal Transmittance

PTL signal as a function of turbidity The solid line is the model prediction. The dependence of transmittance is also plotted for comparison

0.0 0.5 1.0

• 0.6
• 0.3

0.0 0.3 0.6 Time (s)

Pump PTL signal Meat 2 mm

PTL Signal

1 10 0.01 0.1 PTL Signal Turbidity (cm

• 1)

Whole milk in water

The signal can be detected in highly turbid samples

Marcano A., Isaac Basaldua, Aaron Villette, Raymond Edziah, Jinjie Liu, Omar Ziane, and Noureddine Melikechi, “Photothermal lens spectrometry measurements in highly turbid media”, Appl. Spectros. 67 (9), 1013-1018, 2013 (DOI: 10.1366/12-06970).

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 thermo- elastic equation for the surface deformations and the heat conduction equation.

 

p

C t r I T D T t ) , (

2

    

 

T u u

T

            ) 1 ( 2 ) 2 1 (

2

 

where  is the Poisson ratio, T is the thermo-elastic

) , , (   t z T

Boundary conditions

 

  z zz z rz

 

Normal stress components

 

 

) , , ( ) , , ( 2 t u t r u

z z p

    

Initial condition

) , , (  z r T

The phase difference will be

u(z,r,t)

z r Sample

Pump beam

Scheme of the PTM experiment

• 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.92(13), 131903/3 (2008). DOI: 10.1063/1.2905261.
• F. Sato, L. C. Malacarne, P. R. B. Pedreira, M. P. Belancon, R. S. Mendes, M.
• L. Baesso, N. G. Astrath and J. Shen, “Time-resolved thermal mirror method:

A theoretical study”, J. Appl. Phys.104(5), 053520/9 (2008). DOI: 10.1063/1.2975997.

• L. C. Malacarne, N. G. C. Astrath, G. V.B.Lukasievicz, E. K. Lenzi, M. S.

Baesso and S. Bialkowski, “Time-resolved thermal lens and thermal mirror spectroscopy with sample-fluid heat coupling: A complete model for material characterization’, Appl. Spectros.65(1), 99-104 (2011). DOI: 10.1366/10-06096.

• V. S. Zanuto, L. S. Herculano, M. S. Baesso, G.V.B. Lukazievicz, C. Jacinto,
• L. C. Malacarne and N.G.C. Astrath, “Thermal mirror spectrometry: an

experimental investigation of optical glasses”, Opt. Mat.35(5), 1129–1133 (2013).DOI: 10.1016/j.optmat.2013.01.003.

• N. G. C. Astrath, L. C. Malacarne, V. S. Zanuto, M. P. Belancon, R. S.

Mendes, M. L. Baesso and C. Jacinto, “Finite size effect on the surface deformation thermal mirror method”, J. Opt. Soc. Am. B28(7), 1735-1739 (2011). DOI:10.1364/JOSAB.28.001735.

References for PTM theory

 

  

   d gm J t f t g

• )

, ( 8 / exp ) , (

2

   





 

                           2 2 4 exp 2 2 ) , (

2

            Erf Erfc f

where

c

t t /   a r g / 

;

Erf(x) is the error function and Erfc(x) is the complementary error function.

For opaque materials

• A. Marcano, G. Gwanmesia, M. King and D. Caballero, Opt. Eng., 53(12), 127101

(2014). DOI:10.1117/1.OE.53.12.127101.

1 p T

• )

)( 1 ( P



       

 is thermal quantum yield  is the thermal conductivity P is the pump power

D a tc 4

2



PTM time build-up





      )) , ( ) 1 ( exp( ) , ( dg t g i g iV t Ep

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

2 2 2

) , ( ) , ( ) , ( ) ( t E t E t E t S

p p p PTM

  

2000 4000 0.0 0.5 1.0 Normalized PTM Signal Time (t/tc)

=-0.1, zp=100 =-0.1, zp=2000 2000 4000 0.0 0.1 0.2 0.3

=-0.1, zp=100

PTM Signal Time (t/tc)

=-0.1, zp=2000

PTM signal for different probe beam Rayleigh ranges

0.0 0.5 1.0 0.0 0.5 1.0 PTM stationary value



PTM signal as a function of PTM phase amplitude

Ref Pump laser Probe laser S Ampl. Osc. SG b DL FL B1 B2 M1 M2 M3 D A

PTM mode-mismatch set-up

500 1000 1500 0.0 0.5 1.0 Normalized PTM Signal Time (in tc units) Glass filter 532 nm, 15 mW tc=1.6 10

• 3 s.

Smax=0.56

1000 2000 3000 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Normalized PTM t/tc Glassy carbon 445 nm, 146 mW, 3 Hz tc=60 10

• 6 s

Sstationary=0.235

500 1000 1500 2000 0.0 0.5 1.0 Ni, 532 nm, 50 mW tc=1.2 10

• 5 s

Sstationary=0.091 Normalized PTM Signal Time (in tc units)

PTM signal from Ni and glassy carbon samples using 532 nm and 445 nm diode lasers

0.1 1 10 100 1 10 100 1000

Sn Pt Ti Cu Ni Quartz

tc (ms) D (10

• 6 m

2s

• 1)

• 0.99712
• Adj. R-Square

• 0.98565

Dy2TiO5 Glass

Values of tc versus D

0.01 0.1 1 10 100 0.01 0.1 1 10

Dy2Ti2O7 Dy2TiO5 Sn Ni Cu Quartz Ti Glassy Carbon

Se/P (W

• 1)

o/P (W

• 1)

Glass

Stationary value versus PTM phase

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.