Regular Trends of Acousto-Optic Interaction
in Terahertz Region of Electromagnetic Radiation
P. Nikitin,
V. Voloshinov, V. Gerasimov, B. Knyazev
Lomonosov Moscow State University
Moscow, Russia
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Terahertz region of electromagnetic waves
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Acousto-optic interaction in THz region
Low efficiency of AO interaction
I1
1 2
I0 ∼ λ
High divergence of light and sound beams
∆ϕsound ≈ ∆ϕlight ∼ 3◦
Strong absorption of light in the majority of media
Intencity ∼ exp(−αx)
α ∼ 1 ÷ 10 cm−1
Klein-Cook parameter
Q=
2πλLF 2
nV 2
≈
6·100[µm]·1[cm]·(10[MHz])2
3·(3[km/s])2
≈ 20 1 ⇒ Bragg regime
Grating spacing is comparable to the wavelength of light
λsound ≈ λlight ≈ 140 µm
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Quasi-orthogonal Bragg AO interaction
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Taking into account absorption of light
Wave equation
∂2E
1 ∂ 2 (εE )
∂2E
+
=
∂x 2
∂z 2
c 2 ∂t 2
ε = (n0 + in00 )2
n00 n0
Change of the refractive index due to the sound wave
∆n0 ∼ sin(Kz − Ωt)
Trial solution
E = C0 (x) exp(ik0x x + ik0z z − ω0 t) + C1 (x) exp(ik1x x + ik1z z − ω1 t)
Coupled-wave equations
dC0
α
= − C0 −
dx
2
α
dC1
= − C1 +
dx
2
P. Nikitin, V. Voloshinov, V. Gerasimov, B. Knyazev
q
C1
2
q
C0
2
C0 (0) = 1
C1 (0) = 0
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Taking into account absorption of light
Analytical solution
|C0 (x)|2 = e −αx cos2
0
∆n
2π
q = nk0 0cos
θB = λ cos θB
coupling parameter
qx 2
q
M2 Pa
Ld
|C1 (x)|2 = e −αx sin2
≡
P. Nikitin, V. Voloshinov, V. Gerasimov, B. Knyazev
2A
√
L
00
00
0n
α = n2k
= λ4πn
0 cos θ
cos θB
B
absorption coefficient
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qx 2
Optimal geometry for orthogonal AO interaction
in germanium single-crystal
AO figure of merit
M2 =
2 n6
peff
ρV 3
Sound dir.
[100]
[110]
[111]
(∗)
Type
L
S1,2
L
S1
S2
L
S1,2
n0 = 4.0; n00 = 1.4 · 10−3 (∗)
α = 0.75 cm−1
||
M2 , 10−15 s 3 /kg
151
92
219
7
92
241
31
M2⊥ , 10−15 s 3 /kg
101
92
22
7
92
33
69
E.D.Palik Handbook of Optical Constants of Solids (New York: Academic Press, 1985)
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Experiment
Experimental setup
1 – Free-Electron LASER
2,5 – Polarizer
3 – Attenuator
4 – Mechanical chopper
6 – Diaphragm
7 – Acousto-optic cell
P. Nikitin, V. Voloshinov, V. Gerasimov, B. Knyazev
8 – Detector (Golay cell)
9 – Lock-in amplifier
10 – High-frequency generator
11 – Pulse generator
12 – Chopper control unit
13 – Personal computer
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Experiment
Bragg angle vs sound frequency in Germanium
• I1 = Imax
N I1 = Imax /2
λ = 140µm
∆F = (3.8 ± 0.5) MHz
Number of resolvable elements = ∆F · τ = 7.5
V.B.Voloshinov, P.A.Nikitin, et al. “Deflection of a monochromatic THz beam by acousto-optic
methods”, QUANTUM ELECTRON, 2013, 43 (12), 1139–1142
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Experiment
Efficiency of AO interaction
Medium
Ge
C6 H12
White spirit
CCl4
L, cm
2.0
0.4
0.4
0.4
Lopt , cm
1.3
1.7
0.7
1.4
I1 /I0
(5.0 ± 0.3) · 10−4
(2.7 ± 0.2) · 10−5
(5.0 ± 1.2) · 10−5
0
I1 , I0 - intensity of deflected and transmitted radiation
L - length of piezoelectric transducer
Electric power = 1 W
Klein-Cook parameter
6·140[µm]·2[cm]·(30[MHz])2
≈ 120
4·(5.5[km/s])2
2
Qliquid ≈ 6·140[µm]·0.4[cm]·(4.6[MHz])
≈
1.4·(1.3[km/s])2
QGe ≈
P. Nikitin, V. Voloshinov, V. Gerasimov, B. Knyazev
1 ⇒ Bragg regime
30 1 ⇒ Bragg regime
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Conclusion
Conclusion
1 Review of regular trends of AO interaction in THz region.
2
Development of one-dimensional theory for orthogonal AO
interaction in optically absorbing media. Estimation of the
optimal crystal size.
3
Experimental investigation of AO interaction in THz range:
Ge, C6 H12 , CCl4 and white spirit.
4
The possibility of designing AO deflector capable of deflecting
THz radiation by angles of several tens of degrees was
experimentally confirmed for the first time.
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The End
Thank you for attention!
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