Chapter XII Propagation of Optical Beams in Fibers

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Presentation transcript:

Chapter XII Propagation of Optical Beams in Fibers Lecture 20 Chapter XII Propagation of Optical Beams in Fibers Highlights Optical guide modes in fibers Step-index Circular Waveguide  HE modes and EH modes Linearly Polarized Modes  LP modes Optical Pulse Propagation and Pulse Spreading  Compensation methods Attenuation in Silica Fibers Several kinds of Fibers

§12.1 Wave Equations in Cylindrical Coordinates Geometric Optics Analysis (For multimode analysis) Propagation Ray in Fibers TE and TM modes Critical angle of confined mode HE and EH modes Numerical Aperture (NA) The ability to receive optical beam  the bigger the better, however enlarges mode dispersion

§12.1 Wave Equations in Cylindrical Coordinates Electromagnetic Theory Analysis (For singlemode analysis) Cylindrical coordinate system For z component

§12.1 Wave Equations in Cylindrical Coordinates Bessel function’s asymptotic features can be found in textbook. arguments < 1 corresponding to the inner core case arguments > 1 corresponding to the cladding layer case Once Ez, Hz are determined, can then be obtained from Maxwell curl equations.

§12.2 The Step-Index Circular Waveguide Wave Components Recall for confined mode propagation Cladding (r>a) region (evanescent) Core (r<a) region (finite at the center) The other component in different region can then be obtained

§12.2 The Step-Index Circular Waveguide Boundary condition requires be continous at r=a

§12.2 The Step-Index Circular Waveguide Once the eigenvalues have been found, we can solve for the ratios of B/A, C/A and D/A that determined six field components of the mode corresponding to each propagation constant. (see textbook for detail)

§12.2 The Step-Index Circular Waveguide Mode Characteristics and Cutoff Conditions Slab waveguide modes TE and TM Circular waveguide modes EH and HE

§12.2 The Step-Index Circular Waveguide EH modes HE modes Recall

§12.2 The Step-Index Circular Waveguide TEom and TMom modes TE0m mode TM0m mode

§12.2 The Step-Index Circular Waveguide Graphic solutions Cutoff condition Normalized frequency

§12.2 The Step-Index Circular Waveguide Graphic solutions No longer TE or TM but the EH or HE modes For EH modes Cutoff condition

§12.2 The Step-Index Circular Waveguide For HE modes No cutoff for HE11 Cutoff condition Fundamental mode

§12.2 The Step-Index Circular Waveguide Normalized propagation constant as a function of V Near cutoff the modes are poorly confined; far above cutoff, the mode is tightly confined to the core. Again, HE11 is the fundamental mode can propagate in any wavelength.