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Compensation of Thermally Induced Birefringence in Active Medium Made of Polycrystalline Ceramics. Mikhail A. Kagan. Pennsylvania State University, University Park, PA, USA. Efim A. Khazanov. Institute of Applied Physics , Nizhny Novgorod, Russia. Introduction - PowerPoint PPT Presentation
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1Institute of Applied Physics, Russia [email protected]
Compensation of Thermally Induced Birefringence in Active Medium Made of Polycrystalline Ceramics.
Efim A. KhazanovEfim A. KhazanovInstitute of Applied Physics, Nizhny Novgorod, Russia
Mikhail A. KaganMikhail A. KaganPennsylvania State University,
University Park, PA, USA
2Institute of Applied Physics, Russia [email protected]
Outline.
Introduction
Polycrystalline ceramics vs glass and a single crystal
Thermally induced birefringence in polycrystalline ceramics
Ceramics description
Depolarization in single crystal and polycrystalline ceramics
Birefringence compensation in polycrystalline ceramics
Conclusion
3Institute of Applied Physics, Russia [email protected]
Introduction. Structure of polycrystalline ceramics.
4Institute of Applied Physics, Russia [email protected]
Polycrystalline ceramics vs glass and single crystal. Properties.
Single crystalNd:YAG
CeramicsNd:YAG
GlassNd
Grain size, m 100…30
at. % Nd 1 1…10 1…8
Thermoconductivity,W/Кm
12 11…9 0.5
lifetime, c 230 230…70 600…250
optical quality good so so perfect
max diameter, cm 2 100 100
price expensive very cheapin future
cheap
5Institute of Applied Physics, Russia [email protected]
Depolarization in single crystal and ceramics.Thermo-induced birefringence.
angle of declination of eigen polarizations r,phases delay between eigen polarizations r,Lg
Grain Jones matrix Ag=Ag(r,ggg, Lg
r
e2
e1
xy
z k
y x
c, z
x
z
x, a
y, b
x
y
z, c
x
y
x
y
z
r
crystal/grain orientation Euler angles (
6Institute of Applied Physics, Russia [email protected]
Jones matrix of whole element (k realization)
A(r,,kA1(r,111,L1A2(r,222,L2AN(r,NNN,LN
Local depolarization (r,,k)=ч Eout(r,,k) /Ein(r,)ч
Average (over realizations) local depolarization <(r,)>
Integrated depolarization: k
and its deviation : <> and
Depolarization in single crystal and ceramics.Local and integrated.
…..1 2 3 4 ….. N
Ein(r,) Eout(r,)
7Institute of Applied Physics, Russia [email protected]
Mathematical statement of the problem. Assumptions.
1. The number of grains, NN within a beam’s path is fixedfixed.
2. The orientationorientation of crystallographic axes in a certain grain does not does not dependdepend on vicinal grainsvicinal grains.
3. The distribution function ff(LLgg for a single grain is uniformuniform with respect to the angular partangular part and the gaussiangaussian with respect to LLgg
8Institute of Applied Physics, Russia [email protected]
Ceramics description.Jones matrixes Quaternion formalism.
10
010
* σUUMedia without absorption is described by a unitary matrix U,
1032
3210
ii
iiU =00+11+22+33
where k, 02+1
2+22+3
2=1, j – Pauli matrixes
That could be presented as
0 1, 1 I, 2 J, 3 K
Quaternion U=0+1I+2J+3K
I2=J2=K2= -1; IJ=-JI=K, JK=-KJ=I, KI=-IK=J
Transition to Quaternions
9Institute of Applied Physics, Russia [email protected]
Ceramics description.Quaternion properties.
(U1U2…
UN)*=UN
*…U2
*U1* conjugation
cos+Isin=exp(I) Euler formula
Iexp(J) = exp(- J)I(takes place for every imaginary unit)
(takes place for two different imaginary units)
Optical element Jones matrix Quaternion
Linear phase plate (,0)
)2exp(0
0)2exp()(
i
iP )2exp(I
Rotator by angle
)cos()sin(
)sin()cos()(
R )exp( J
Linear phase plate (,) Q(,)=R-1()P()R() exp(J)exp(I/2)exp(-J)
Jones matrixes and quaternions for several typical optical elements
- angle of declination, - phases delay between eigen polarizations
10Institute of Applied Physics, Russia [email protected]
Ceramics Single crystal 1
2
3
)( length grain mean
)( length grain of deviation g
gLD
)( length grain mean
)( length rod
gL
LN
Difference between depolarization in single crystal and ceramics. List of parameters.
- crystal constant 2.3YAG
p - normalized (unitless) heat power
single crystal orientation
, ,
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Difference between depolarization in single crystal and ceramics. Local depopolarization Г(r,).
Ceramics Single crystal
(r=0)0 (=0,90o)0 (r=0)=0 (=0)=0
High value of deviation of
J. Lu, Appl. Phys. Lett., 78, 2000
S. D. Sims, Applied Optics, 6, 1967Analytical plot
0
1
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Difference between depolarization in single crystal and ceramics. Integrated depopolarization .
Ceramics Single crystal [111]
128
5375
X
Xp
XpN
sin1
4
1)( 3
21 X
ceramics –1=(crystal–1)(16/15)2
0 1 2 3 4 5 6 7 8 9 100
10
20
30
40
Inte
grat
ed
dep
opol
ariz
atio
n, %
ceramics N=[111] single crystal
normalized heat power р
+ N=30
o N=100
р N=300
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Birefringence compensation in active elements. Typical schemes.
900 active
elementactive
element1a
W.Scott, M. De Wit Appl. Phys. Lett. 18, 3, 1973 V.Gelikonov et al. JETF lett., 13, 775, 1987
Faradaymirror
activeelement
l 450
uniaxialcrystal
activeelement
1b
1c
l
activeelement /4 2a /2active
elementactive
element2b
W.A. Clarkson. et al. Opt. Lett., 24, 820, 1999
E.Khazanov et al. JOSA B, 19, 667, 2002
14Institute of Applied Physics, Russia [email protected]
at pN-1 <<1
а(r,)=2c(r,)=b(r,) 0.07p2 N-1
(solid lines)
Compensation of thermally induced birefringence in ceramics. Schemes 1a-c.
900 activeelement
activeelement1a
а(r,)
Faradaymirror
activeelementl
450
1b
b(r,)
uniaxial crystal
activeelement
1c
c(r,)
if l<<30…100m=<Lg>, then b(r,) є 0
0 5 10 150
0.05
0.1
0.15
0.2
0.25
0.3
N=30
N=100
N=300
no compensation
Integrated depolarization
Inte
grat
ed d
epol
ariz
atio
n
Normalized heat power p
•Small scale modulation
•at pN-1 <<1
а(r,)= 2c(r,)= b(r,) (l <Lg>)
Single crystal
а,b,c(r,) є0
Local depolarization
ceramics0
1
p=5
15Institute of Applied Physics, Russia [email protected]
•small scale modulation
•weak dependence of and on N
Compensation of thermally induced birefringence in ceramics. Schemes 2а-b.
/2activeelement
activeelement
2b
l
activeelement
/42a
(l <Lg>)
0 2 4 60
0.05
0.1
0.15
0.2
0.25
0.3
Integrated depolarization
Inte
grat
ed d
epol
ariz
atio
n
normalized heat power p
Local depolarization
ceramics
1
0
single crystal
1
0
p=5
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Conclusion. Main results.
Analytical expressions for mean depolarization < Г(r,) > and <> without compensation and with compensation by means of all known techniques
Output polarization depends on a dimensionless heat release power р, and parameter N , ratio of the rod length to mean grain length <Lg>
Depolarization < Г(r,) > and <> for ceramics rod are close to Г and for a single crystal [111], BUT:
Both polarized and depolarized radiation always have small-scale
modulation with a characteristic size of about < Lg >. Birefringence compensation by means of all known techniques is worse for ceramics than for a single crystal. Additional depolarization is
proportional to the quantity p2N-1.An increase in N is expedient from the viewpoint of both diminution of depth of the modulation and birefringence compensation.
17Institute of Applied Physics, Russia [email protected]
AknowlegementsAknowlegements
Special thanks to prof. J.Collinsprof. J.Collins and prof. N.Samarthprof. N.Samarthof Pennsylvania State University.
The work of M.Kagan was supported by the Dunkan Fellowship of Physics Department of PennState University.
