Unified Optical Scanning Technology

Chapter 4.9 - Scanner Devices and Techniques: Electrooptic (Gradient) Scanners

4.9 ELECTROOPTIC (GRADIENT) SCANNERS

A general form of low-inertia scanner is the gradient deflector [Bei2,Bei6], capable of extremely rapid beam deflection and flyback. Utilizing a controllable gradient of index of refraction across the beam, a propagating wavefront undergoes increasing retardation transverse to the beam. The rays, as the orthogonal trajectories of the wavefronts, bend in the direction of the shorter wavelength. Referring to Figure 4.27a, the small bend angle Θ through such a deflection cell is expressed as

Fig. 4.27 Equivalent gradient deflectors. [a] Basic deflector cell having continuous optical index gradient, grad n(y). Ray 1 propagates through a higher index (effecting a greater retardation) than ray 2, rotating the wave about an effective z-line pivot located at the approximate center of the cell. [b] Analogous prismatic cell, in which na > np such that ray 1 is retarded more than ray 2, tipping the wave through the deflected angle. The deflected angles are enlarged slightly by the index change at the output. From [Βei8].

where n is the number of wavelengths per unit axial length ℓ, y is the transverse distance and k is a cell system constant. This relationship may be generalized to the gradient deflector equation with vector notation [Bei6]

in which

For the electrooptic material form, in which the wavefront traverses a gradient of index of refraction over the differential distance dℓ, the differential in deflection angle within the material becomes

where n is the index of retraction, no is its average value, and grad n is the rate of change of n in the direction of deflection. It is noteworthy that n now represents the index of refraction, whereas above, n represented the wavelength density. The full scan angle may now be expressed for the condition of the light waves traversing index change Δn over the beam aperture D in a cell of length L, to develop the typically small deflection angle

where nf is the refractive index of the final medium (forming, per Fig. 4-27, the refractive angular change of the beam as it leaves the cell). Utilizing our basic Equation 3-5, the corresponding resolution in elements per scan for a given Δn is now shown independent of D as

The Δn, determined by the material and its applied field, is given by

where no,e is the (ordinary, extraordinary) index of refraction, rij is the electrooptic coefficient, and Ez= V/Z is the electric field in the z-direction, perpendicular to the x- and y-directions.

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