Comment on Light Beam Deflectors John G. Skinner Bell Telephone Laboratories, Inc., Murray Hill, New Jersey. Received 28 August 1964. With reference to the letter "Light Beam Deflection Using the Kerr Effect in Single Crystal Prisms of BaTiO 3 " by W. Haas, R. Johannes, and P. Cholet in the August issue of this journal [3, 988 (1964)], the author wishes to make the following comment. When using an electrooptic element, such as a prism, to produce a deflection of a light beam the important requirement is not maximum deflection, for a given change in the refractive index, but rather the maximum number of resolvable spots. The induced angular deflection of the system always can be increased by passive elements, such as a telescope, but the number of resolvable spots is determined solely by the active element. The dimensions of a spot, that is formed from the transmitted beam, is determined by the divergence of the beam due to the diffraction effect at the limiting aperture of the prism. If we assume that the emerging beam is rectangular in cross section with a width A and a wavelength λ, then the half-angle divergence of the beam due to the diffraction effect is dФ = λ/A. Using the Rayleigh criterion of resolution then two spots are just resolved when the angular displacement of the beam dε equals dФ, i.e., when the minimum intensity of one spot falls on the maximum of the adjacent spot. Therefore, the number of resolvable spots N equals dε/dФ = dε-A/λ. In order to obtain the maximum number of resolvable spots it is necessary to maximize the product of the induced deflection dε and the beam width A. In the extreme case of the incident beam just grazing the prism face, the value of dε is a maximum but the emergent beam width approaches a minimum such that the value of N is a minimum (whether it is the minimum or not depends on the prism angle and the refractive index of the material). In the case of an isosceles-shaped prism it is a simple matter to show that N is a maximum when the beam traverses the prism symmetrically, i.e., when the passive deflection of the prism is a minimum, and that its value is given by N = b(dn)/X, where b is the base length of the prism and (dn) is the induced change in refractive index. 1504 APPLIED OPTICS / Vol. 3, No. 12 / December 1964

Comment on Light Beam Deflectors

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Page 1: Comment on Light Beam Deflectors

Comment on Light Beam Deflectors John G. Skinner

Bell Telephone Laboratories, Inc., Murray Hill, New Jersey. Received 28 August 1964.

With reference to the letter "Light Beam Deflection Using the Kerr Effect in Single Crystal Prisms of BaTiO3" by W. Haas, R. Johannes, and P. Cholet in the August issue of this journal [3, 988 (1964)], the author wishes to make the following comment. When using an electrooptic element, such as a prism, to produce a deflection of a light beam the important requirement is not maximum deflection, for a given change in the refractive index, but rather the maximum number of resolvable spots. The induced angular deflection of the system always can be increased by passive elements, such as a telescope, but the number of resolvable spots is determined solely by the active element.

The dimensions of a spot, that is formed from the transmitted beam, is determined by the divergence of the beam due to the diffraction effect a t the limiting aperture of the prism. If we assume that the emerging beam is rectangular in cross section with a width A and a wavelength λ, then the half-angle divergence of the beam due to the diffraction effect is dФ = λ / A . Using the Rayleigh criterion of resolution then two spots are just resolved when the angular displacement of the beam dε equals dФ, i.e., when the minimum intensity of one spot falls on the maximum of the adjacent spot. Therefore, the number of resolvable spots N equals dε/dФ = dε-A/λ. In order to obtain the maximum number of resolvable spots it is necessary to maximize the product of the induced deflection dε and the beam width A. In the extreme case of the incident beam just grazing the prism face, the value of dε is a maximum but the emergent beam width approaches a minimum such that the value of N is a minimum (whether it is the minimum or not depends on the prism angle and the refractive index of the material). In the case of an isosceles-shaped prism it is a simple matter to show that N is a maximum when the beam traverses the prism symmetrically, i.e., when the passive deflection of the prism is a minimum, and that its value is given by N = b(dn)/X, where b is the base length of the prism and (dn) is the induced change in refractive index.

1504 APPLIED OPTICS / Vol. 3, No. 12 / December 1964