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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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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
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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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• 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
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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 :