1. All-Optical Gyroscope Based on Sagnac Effect in Photonic Crystal Coupled Cavity Waveguides and Slow Light Structures
Work published in:
B.Z. Steinberg, ‘’Rotating photonic crystals: a medium for compact optical gyroscopes”,
Phys. Rev. E, vol 71, pp , May

2. Basic Principles
A CCW folded back upon itself in a fashion that preserves symmetry
Micro-cavities
Stationary
Rotating at angular velocity
C - wise and counter C - wise propag are identical.
“Conventional” self-adjoint formulation.
Dispersion is the same as that of a regular CCW except for additional requirement of periodicity:
Co-Rotation and Counter - Rotation propag DIFFER.
E-D in accelerating systems; non self-adjoint
Dispersion differ for Co-R and Counter-R:
Two different directions

3. Formulation E-D in the rotating system frame of reference:
We have the same form of Maxwell’s equations:
But constitutive relations differ:
The resulting wave equation is (first order in velocity):

4. Solution Procedure: Results: Tight binding theory
Non self-adjoint formulation (Galerkin)
Results:
Dispersion:
W0 Q w k km
-km
|W0 Q| Dw
w (-km ; W0 ) w0
w (km ; W0 )
w (km ; W0 = 0 )
At rest
Rotating
Depends on system design

5. The Gyro application
Measure beats between Co-Rot and Counter-Rot modes:
Rough estimate:
For Gyro operating at optical frequency and CCW with :