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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. 056621-7, May 31 2005.

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  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. 056621-7, May 31 2005

  2. Micro-cavities Basic Principles A CCW folded back upon itself in a fashion that preserves symmetry 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. At rest Rotating w |W0Q| w (km ; W0) Dw w (-km ; W0) w0 w (km ; W0 = 0 ) k -km km W0Q Solution • Procedure: • Tight binding theory • Non self-adjoint formulation (Galerkin) • Results: • Dispersion: 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 :

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