Journal of Physical Studies 17(2), Article 2401 [4 pages] (2013) DOI: https://doi.org/10.30970/jps.17.2401 QUANTUM MECHANICAL ANALOGY OF LIGHT PROPAGATION IN PLANAR WAVEGUIDES H. P. Laba1, V. M. Tkachuk2 1Department of Telecomunications, Lviv Polytechnic National University 12, S. Bandery St., Lviv, UA--79013, Ukraine, 2Department for Theoretical Physics, Ivan Franko National University of Lviv, 12, Drahomanov St., Lviv, UA--79005, Ukraine, e-mail: tkachuk@ktf.franko.lviv.ua

We establish an exact analogue of equations describing the propagation of TE and TM modes in planar waveguide with an arbitrary continuous dependence of refractive index on coordinates with stationary Schr$\ddot{\rm o}$dinger equation. The effective potential energies involved in Schr$\ddot{\rm o}$dinger equation for TE and TM modes are different but in the limit of a weak dependence of refractive index on the coordinates they coincide. For comparison of these potential energies in the case of arbitrary dependence of refractive index on cordinates we consider examples which show essential difference between effective potential energies for TE and TM modes.

PACS number(s): 42.79.Gn, 03.65.-w.

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