1、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 o
2、f Fibers,12.1 Wave Equations in Cylindrical Coordinates,Geometric Optics Analysis,TE and TM modes,HE and EH modes,Critical angle of confined mode,Numerical Aperture (NA),Propagation Ray in Fibers,The ability to receive optical beam, the bigger the better, however enlarges mode dispersion,(For multim
3、ode analysis),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,Once Ez, Hz are determined,can then be obtained from,Maxwell curl equations.,Bessel func
4、tions asymptotic features can be found in textbook.,arguments 1 corresponding to the inner core case,arguments 1 corresponding to the cladding layer case,12.2 The Step-Index Circular Waveguide,Recall for confined mode propagation,Cladding (ra) region (evanescent),Core (ra) region (finite at the cent
5、er),The other component in different region can then be obtained,Wave Components,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 de
6、termined six field components of the mode corresponding to each propagation constant. (see textbook for detail),Mode Characteristics and Cutoff Conditions,12.2 The Step-Index Circular Waveguide,Slab waveguide modes,TE and TM,Circular waveguide modes,EH and HE,12.2 The Step-Index Circular Waveguide,E
7、H 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
8、 EH modes,Cutoff condition,12.2 The Step-Index Circular Waveguide,For HE modes,Cutoff condition,No cutoff for HE11,Fundamental mode,12.2 The Step-Index Circular Waveguide,Near cutoff the modes are poorly confined; far above cutoff, the mode is tightly confined to the core.,Normalized propagation constant as a function of V,Again, HE11 is the fundamental mode can propagate in any wavelength.,
