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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

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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

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**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):

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**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

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

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