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A 4×4 matrix formulation of optical reflection from multilayer dielectric and magnetic films has been developed and applied to a structure consisting of a dielectric film on top of a magnetic film all on a mirror substrate. The dielectric thickness d1 is specified by tan (n1β12πd1/λ0) = (1/n1β1) (λ0/2πd), where λ0 is the free-space wavelength, n1 the index of refraction of the dielectric, β1 the cosine of the angle of propagation in the dielectric (measured to the film normal), and d the thickness of the magnetic film (d≃200 Å). The longitudinal Kerr reflection coefficient k⊥ = H∥r/H⊥t, where r and t refer to reflected and transmitted (incident) waves, and ∥ and ⊥ to the states of polarization, is calculated under the assumption that k1«1 to be k⊥ = i2γ0n12 (2πd/λ0) p, where γ0≃1 is the cosine of the angle of light incidence (measured to the film plane), and p is the gyromagnetic constant. In principle for large n1 the upper limit on |k⊥| is determined only by the breakdown of the assumption k⊥«1. For n1≃3, d=200 Å, λ0=1 μ, and p=5×10−2 (Fe at 1 μ), the energy-conversion efficiency w =|k⊥|≃10−4.
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D. O. Smith (1964) studied this question.
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