1. 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

2. §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

3. §12.1 Wave Equations in Cylindrical Coordinates
Electromagnetic Theory Analysis
(For singlemode analysis)
Cylindrical coordinate system
For z component

4. §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.

5. §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

6. §12.2 The Step-Index Circular Waveguide
Boundary condition requires
be continous at r=a

7. §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)

8. §12.2 The Step-Index Circular Waveguide
Mode Characteristics and Cutoff Conditions
Slab waveguide modes
TE and TM
Circular waveguide modes
EH and HE

9. §12.2 The Step-Index Circular Waveguide
EH modes
HE modes
Recall

10. §12.2 The Step-Index Circular Waveguide
TEom and TMom modes
TE0m mode
TM0m mode

11. §12.2 The Step-Index Circular Waveguide
Graphic solutions
Cutoff condition
Normalized frequency

12. §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

13. §12.2 The Step-Index Circular Waveguide
For HE modes
No cutoff for HE11
Cutoff condition
Fundamental mode

14. §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.