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ULTRASHORT LASER PULSE
PROPAGATION IN HIGHLY
SCATTERING MEDIA
A.P. Popov
2
What is the task?
• Pulse structure
• Output pulse duration τ(ti)
• Photon scattering multiplicity
• Absorption, scattering, transmission
• Change of medium parameters
• Effect of stranger particles on skin properties
3
Modelled setup
3
2
4
1
5
3
8
6
7
1 – Cr: forsterite laser, 2 – attenuator, 3 – “blind” mirrors,
4 – beam splitter, 5 –power meter, 6 – vessel with scattering
medium, 7 – streak-camera, 8 – CCD-camera
4
Scheme of the modelled experiment
Incident laser beam
Detector
Scattering
particle
Absorbing particle
Detector
5
Forward detected photons vs registration time
100
L = 0 .1 m m
Rel. num ber of photons, %
L = 0 .2 m m
L = 0 .4 m m
10
g = 0 .9 8
пЃ­ = 85 m m
-1
s
пЃ­ = 0 .6 m m
1
-1
a
*
l = 0 .4 3 m m
0 ,1
0
1
2
3
4
5
6
7
R e g is tra tio n tim e , p s
8
9
10
6
Forward detected photons vs registration time
4
L = 0 .6 m m
Rel. num ber of photons, %
L = 0 .8 m m
L = 1 .0 m m
3
g = 0 .9 8
пЃ­ = 85 m m
-1
s
2
пЃ­ = 0 .6 m m
-1
a
*
l = 0 .4 3 m m
1
0
0
1
2
3
4
5
6
R e g is tra tio n tim e , p s
7
8
9
10
7
Behavior of scattered and unscattered parts of radiation at
various sample thickness
1
U n s c a tte re d p a rt T c
Transm ission, rel. units
S c a tte re d p a rt T s
B e e r's la w
0 ,1
0 ,0 1
1 E -3
g = 0 .9
пЃ­
1 E -4
пЃ­
s
a
= 10 m m
-1
= 0 .0 1 m m
-1
n = 1 .3 7
1 E -5
0
100 200
300 400 500 600 700
T h ic k n e s s , пЃ­ m
800 900 1000
8
12
Forward detected photons vs their scattering
multiplicity
Rel. num ber of photons, %
10
L = 0 .1 m m
L = 0 .2 m m
8
L = 0 .4 m m
g = 0 .9 8
6
пЃ­ = 85 m m
-1
s
пЃ­ = 0 .6 m m
4
a
2
0
0
10
20
30
40
N u m b e r o f s c a tte rin g a c ts
50
60
-1
9
Forward detected photons vs their scattering
multiplicity
L = 0 .6 m m
0 ,8
Rel. num ber of photons, %
L = 0 .8 m m
L = 1 .0 m m
0 ,6
g = 0 .9 8
пЃ­ = 85 m m
-1
s
0 ,4
пЃ­ = 0 .6 m m
-1
a
0 ,2
0 ,0
0
50
100
150
200
250
N u m b e r o f s c a tte rin g a c ts
300
350
10
M axim um of scattering m ultiplicity
Maximum of scattering multiplicity vs medium thickness
100
g = 0 .9 8
80
пЃ­ = 85 m m
-1
s
пЃ­ = 0 .6 m m
-1
a
60
Y = A + B * X
A= -1 ,6 1 0 9 6 + /-0 ,7 3 5 9 4
40
B = 9 5 ,6 9 8 6 3 + /-1 ,2 1 2 6 2 m m
20
0
0 ,0
0 ,2
0 ,4
0 ,6
0 ,8
M e d iu m th ic k n e s s , m m
1 ,0
-1
11
Radiation scattering within medium
Rel. num ber of scattering, %
30
пЃ­ = 95 m m
-1
пЃ­ = 75 m m
-1
s
25
s
20
g = 0 .9 5
пЃ­ = 1 mm
15
-1
a
L = 1 mm
10
5
0
0 ,0
0 ,2
0 ,4
0 ,6
D e p th , m m
0 ,8
1 ,0
12
Forward detected photons vs registration time
пЃ­ = 0 .1 m m
-1
пЃ­ = 0 .4 m m
-1
пЃ­ = 0 .8 m m
-1
a
0 ,0 8
Rel. num ber of photons, %
a
a
0 ,0 6
g = 0 .8 5
пЃ­ = 35 m m
-1
s
0 ,0 4
L = 1 mm
0 ,0 2
0 ,0 0
0
10
20
30
R e g is tra tio n tim e , p s
40
50
13
Forward detected photons vs registration time
350
t i = 1 p s - 2 0 tim e s
t i = 5 p s - 4 tim e s
300
t i = 1 0 p s - 2 tim e s
Num ber of photons
250
g = 0 .7 6
пЃ­
200
пЃ­
150
s
Г = 20 m m
-1
= 0 .0 7 6 m m
n = 1 .3 9
100
50
0
0
10
20
30
R e g is tra tio n tim e , p s
40
50
-1
14
Forward detected photons vs registration time
t = 0 .1 p s - 1 0 0 tim e s
i
300
t = 1 .0 p s - 1 0 tim e s
i
t = 5 .0 p s - 2 tim e s
i
Num ber of photons
250
t = 1 0 .0 p s - n o
i
200
g << 1
150
пЃ­ = 35 m m
-1
s
пЃ­ = 0 .6 m m
100
-1
a
L = 1 mm
50
0
0
5
10
15
20
25
30
35
R e g is tra tio n tim e , p s
40
45
50
15
Determination of optical
parameters of skin
3
2
1
4
6
5
1 – incident beam, 2, 3 – integrating spheres,
dealing with reflectance and transmission respectively,
4, 5 – photodetectors, 6 – sample
16
Skin structure
Stratum corneum
Epidermis
Dermis - 1
Dermis - 2
Dermis
Dermis - 3
Subcutaneous fat
17
Parameters of epidermis with substances
Skin type
Ојa,
mm-1
Ојs,
mm-1
g
Diffuse
reflectance R,
%
Transmission
T, %
Absorption
A, %
Skin
0.15
20
0.8
20.4
75.2
4.4
Skin +
0.25С…Fluo
1.00
20
0.8
14.3
64.1
21.6
Skin +
1С…TiO2
Skin +
2С…TiO2
Skin +
0.25С…Fluo
+ 1С…TiO2
0.15
30
0.8
26.5
68.7
4.8
0.15
40
0.8
31.2
63.6
5.2
1.00
30
0.8
18.6
57.1
24.3
Skin +
0.25С…Fluo
+ 2С…TiO2
1.00
40
0.8
22.3
51.7
26.0
18
Ratio of radiation components for epidermis with various
substances
D if. re fle c ta n c e
100
90
T ra n s m is s io n
80
A b s o rp tio n
Intensity, %
70
60
50
40
30
20
10
0
1
2
3
S k in typ e
4
19
Stratum corneum with particles of TiO2
Incident
radiation
Layer with
TiO2
Rest of stratum
corneum
Transmitted
radiation
20
Absorption in different parts of stratum corneum
0 ,7
R el. num ber of photons, %
0 ,6
0 ,5
W h o le s tra tu m c o rn e u m
0 ,4
R e s t s tra tu m c o rn e u m
la ye r w ith p a rtic le s o f T iO 2
0 ,3
0 ,2
0 ,1
0 ,0
0
1
2
3
4
5
T h ic k n e s s , пЃ­ m
6
7
8
21
Pulses of various durations passed through stratum
corneum with scattering substance (TiO2)
2 ,0
Rel. num ber of photons, %
1 ,8
t i = 0 .0 1 p s
1 ,6
t i = 0 .0 5 p s
1 ,4
t i = 0 .1 0 p s
g = 0 .8
1 ,2
1 ,0
0 ,8
пЃ­
1
пЃ­
2
пЃ­
0 ,6
s
s
a
= 150 m m
= 100 m m
= 0 .1 m m
-1
-1
-1
n = 1 .5
0 ,4
0 ,2
0 ,0
0 ,0 8
0 ,1 0
0 ,1 2
0 ,1 4
0 ,1 6
0 ,1 8
R e g is tra tio n tim e , p s
0 ,2 0
0 ,2 2
0 ,2 4
22
Summary
• Ballistic, snake- and diffusion components
registration
• Scattering multiplicity, time detection of pulse
maximum depends linear on Ојs, L
• Decreasing of μa makes detected pulses longer and
increase their amplitude
• There exists maximum of scattered and absorbed
radiation under the medium surface
23
Summary
• Multiple scattering makes short pulses longer
• Scattering substance injection causes absorption
and reflectance increase in upper skin layers,
transmission decrease
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