Syllabus
INTEGRATED OPTICS & FIBER OPTICS
(F365, 2/0 Zk) Štefan Višňovský.
Waves in bounded regions. Wave equation in non uniform media: plane wave solutions. Optical systems with constant index of refraction along a special axis. Boundary conditions at interfaces. Fresnel equations. Phase shift for TE and TM waves at total reflection, longitudinal and transverse propagation constants.
Waveguide with ideally conducting walls, propagation characteristics. TE and TM modes in rectangular waveguides. TEM waves. Resonance cavities.
Ray model for an optical planar waveguide. Rectangular profile of the index of refraction. Radiation, substrate and guided modes. Characteristic equation of a planar waveguide and its graphical solutions. Cut-off conditions. Normalized waveguide characteristics. Goos-Haenchen shift. Effective waveguide thickness. Planar dielectric waveguides of general permittivity profile. Parabolic profile (analogy with the quantum harmonic oscillator). 1/cosh permittivity profile.
Wave propagation in anisotropic planar dielectric structures. Eigen values of the propagation constant and associated eigen modes. Periodic waveguides.
Maxwell equations in symmetric planar dielectric waveguide. Even and odd TE and TM modes. Field profiles. Relations between field amplitudes and transmitted power.
Maxwell equations in general planar waveguide with step index profile. Characteristic equations for TE and TM modes. Field profiles. Analogy with a nonsymmetrical rectangular quantum well.
Couplers for dielectic waveguides. Prism coupler. Diffraction grating coupler. Wedge coupler. Rule of maximum index of refraction.
Cylindrical dielectric waveguide with rectangular index profile (optical fiber). Transformation of Maxwell equations into cylindrical coordinates. Vector Helmholtz wave equation in cylindrical coordinates. Fields characterized in terms of cylindrical functions. TE and TM modes. Fundamental mode. Mode nomenclature. Conditions for monomode transmission.
Monomode cylindrical waveguide with a generalized permittivity profile. Weak guidance approximation. Cartesian field components as a function of cylindrical coordinates. Analytic expressions for permittivity profiles. Limiting cases: step profile and Gaussian profile. Fundamental mode parameters deduced from variation approach. Poynting vector as a function of radial profile. Condition for maximum power concentration at the fiber axis. Extension to fibers with elliptic profiles.
Annotation
Transmission of large volumes of information at optical frequencies. Propagation of electromagnetic wave in the media confined in one or two dimensions.
Ray optics approach to optical waveguides. Transfer of ideas from microwave theory and quantum mechanics.
Preparation of thin film optical devices. Integrated optics.
Electromagnetic theory of dielectric waveguides. Waveguiding in planar and cylindrical structures. Optical fibers with step-like and graded permittivity profiles. Conditions for single mode operation..
Coupling of free space waves into the waveguide. Thin film electro-optic, acousto-optic and magneto-optic modulators.