A simple but general expression for the longitudinal Kerr coefficient is derived for a general multilayer structure containing a single magnetic film. The expression is given in terms of well-known optical parameters of the system such as the ' Potential Transmittance ' of the magnetic film. A number of special cases are considered and the expression is then used to establish the details of design of systems with much larger Kerr coefficients than previously predicted.
IntroductionIn the theory of magneto-optical effects in multilayer structures of dielectric and magnetic thin films developed by Smith [1] the range of applicability of the solutions is sometimes obscured by the approximations which are made at various stages in the calculations to facilitate the algebraic manipulations. Moreover, the solutions are not always expressed in terms of parameters which are familiar to workers in the field of multilayer thin films applied to optical filters. It is shown in the following account that both of these difficulties can be avoided by the introduction of the concept ' Potential Transmittance' first discussed by Berning and Turner [2] in connection with so-called ' Induced Transmission' filters. In this way a perfectly general but simple expression for the modulus of the longitudinal Kerr coefficient can be obtained in terms of easily recognizable optical properties of the general system. Moreover, the expressions appropriate to special cases such as those of a thick or thin magnetic film or of various types of mirror substrates can be readily deduced from the general expression.The details of design of multilayer structures for optimizing the longitudinal Kerr coefficient, and hence the signal-to-noise ratio associated with the effect, will be discussed by reference to the general expression and to the type of system proposed earlier by one of the authors [3]. It will be shown that enhancement of the Kerr coefficient much greater than previously predicted is possible if the systems are designed to maintain their desired properties over as wide a range of angles of incidence as possible. The key to the solution of this particular problem is the fact that the systems required for the enhancement of the Kerr coefficient are almost identical with those of ' Induced Transmission' filters; and details of the design for such filters to operate satisfactorily over a wide range of angles of incidence has recently been established [4] both experimentally and theoretically.