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. 056621-7, May 31 2005

Basic Principles

Stationary Rotating at angular velocity

A CCW folded back upon itself in a fashion that preserves symmetry

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:

Micro-cavities

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

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):

• Procedure:

– Tight binding theory

– Non self-adjoint formulation (Galerkin)

• Results:

– Dispersion:

Solution

Q

mm

Q|

m ; )

m ; )

m ; )

At rest Rotating

Depends on system design

The Gyro application

• Measure beats between Co-Rot and Counter-Rot modes:

• Rough estimate:

• For Gyro operating at optical frequency and CCW with :