Optimized Nonreciprocal Rib Waveguides for Integrated Magneto-optic Isolators

Garnet films of composition (Lu,Bi)3(Fe,Ga,Al)5O12 and (Tm,Bi)3(Fe,Ga)5O12 are grown by liquid-phase epitaxy on [111]-oriented substrates of gadolinium gallium garnet. Ferrimagnetic films with positive or negative Faraday-rotation as well as paramagnetic films with negligible Faraday-rotation are produced by variations of the rare earth ion substitutions. The temperature dependence of Faraday-rotation is fitted with a molecular field model. Optical rib waveguides in single and double layer garnet films with different Faraday-rotations are realized. The nonreciprocal phase shift of the TM0-Mode is studied both theoretically and experimentally at a wavelength of 1.3 μm. Results show that the maximum nonreciprocal effect at room temperature of double layer films with opposite Faraday-rotation is 1.6 times as large as that of comparable single layer waveguides. But, because of the large temperature dependence of the Faraday-rotation of the positive rotating films, these waveguides show a large temperature dependence of the nonreciprocal phase shift. This problem can be avoided if the positive rotating layer is replaced by a paramagnetic layer. Agreement between calculations and measurements is excellent. INTRODUCTION Magneto-optic isolators play an important role in optical communication technique. They are used to protect the semiconductor lasers from reflected light. At present only bulk isolators are available. To realize cheap integrated optical isolators, magnetic garnet films can be used. They combine low absorption with high Faraday-rotation in the near infrared. The Faraday-rotation, which is the basis of the nonreciprocal effects, can be enhanced by bismuth substitution. Various kinds of optical isolators have been proposed [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. Some promising concepts of integrated optical isolators and circulators rely on the nonreciprocal phase shift of TM modes [11, 12], which is the difference ∆β = βfw − βbw between the forward and backward propagation constants βfw and βbw of TM modes, respectively. The device length of such isolators is inversely proportional to this effect so that an enhancement is desirable. For this purpose double layer garnet films with opposite Faraday-rotation are suitable [13]. In this paper it is shown, how the temperature dependence and the absolute value of ∆β can be optimized by choosing a proper geometry of the waveguides. NONRECIPROCAL RIB WAVEGUIDES The following analysis is performed for the basic rib geometry sketched in Fig. 1. Mode propagation is assumed along the z axis and the magnetization M is adjusted in the film plane transversely to the propagation direction. Neglecting optical damping, the dielectric tensor of the magneto-optic films can be written as