Abstract
Transducer conversion losses as well as acoustic and optic attenuation in solidstate acoustooptic light deflectors are responsible for temperature and stress fields which lead to deformation, index fields and changes in acoustic wavelength. For users, these effects result in beam deflection, lensing, aberration and a deterioration in efficiency. The known Maréchal criterion and a new criterion noted by the author set a limit of about one quarter wavelength to optic and acoustic wave aberrations. Maximum deflection efficiencies and light powers are determined as functions of the geometry, thermal boundary conditions, material constants and operating modes. A new thermal figure of meritM th 1 equalizes the differences of the acoustooptic figures of meritM 2. To corroborate the theoretical results, performance limits for typical operating modes have been measured. Some new deflector designs are proposed and experimentally verified on the basis of the theoretical results.
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Abbreviations
- θ:
-
deflection angle
- λ:
-
light wavelength in matter
- λ0 :
-
light wavelength in vacuum
- ϑ:
-
ultrasound velocity
- f, Δf :
-
acoustic frequency, bandwidth
- αv :
-
temperature coefficient of acoustic velocity
- b, s, d, L, H :
-
dimensions of acoustooptic deflector (Fig. 1b)
- a :
-
light beam aperture
- N :
-
resolution of deflector
- ~w :
-
optical wavefront distortion
- Δw :
-
rms-value ofw
- n, n i :
-
refractive index, principal refractive indices
- u AI :
-
deformation of optical window
- E :
-
elastic constant
- σij :
-
stress tensor
- αw, σij :
-
thermal expansion coefficient(s)
- T :
-
temperature rise relative to ambient temperature
- πij :
-
piezooptical coefficients
- A, D :
-
thermal material constants defined by (8)
- w * :
-
acoustic wavefront distortion
- k ϑ :
-
thermal diffusitivity constant
- K :
-
thermal conductivity
- W :
-
heat power density generated within deflector
- WW}:
-
time-averaged value ofW
- r, r′ :
-
position vectors
- G :
-
Green's function
- δ:
-
delta function
- τ:
-
volume
- ν:
-
coordinate normal to surface
- i, j, q :
-
integer indices
- αD :
-
acoustic attenuation coefficient
- P ac :
-
acoustic power
- P 0 :
-
acoustic power radiated from transducer
- P w :
-
power loss within deflector
- φ:
-
Airy stress function
- F :
-
area
- T′,σ′ xx :
-
normalized values ofT andσ xx
- M 2 :
-
acoustooptic figure of merit
- M th 1,M th 2 :
-
thermal figures of merit
- M tot :
-
total figure of merit:M tot=M 2·M th 1
- ε:
-
percentage of dissipated acoustic power
- ηB :
-
deflection efficiency (Bragg condition fulfilled)
- K i :
-
principal thermal conductivities
- ϱ,p ij :
-
photoclastic constant(s)
- ϱ:
-
mass density
- c δ :
-
specific heat
References
H.Eschler:Die Begrenzung der Leistungsfähigkeit akustooptischer Lichtablenker durch thermische Effekte. Doctoral Thesis, Technische Universität München (July 1975)
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Ref. 5 p. 18
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Ref. 5 p. 92
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Extract from the doctoral thesis of the Dipl.-Ing. Hans Eschler entitled „Die Begrenzung der Leistungsfähigkeit akustooptischer Lichtablenker durch thermische Effekte” and approved by „Fachbereich Elektrotechnik der Technischen Universität München” in July 1975.
Presently with the Zentrallaboratorium für Nachrichtentechnik, Siemens AG.