Author Affiliations
1School of Optical Science and Engineering, University of New Mexico, Albuquerque, New Mexico 87106, USA2Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA3Center for High Technology Materials, University of New Mexico, Albuquerque, New Mexico 87106, USA4NASA Marshall Space Flight Center, Space Systems Department, Huntsville, Alabama 35812, USAshow less
Fig. 1. Sketches of bidirectional ML gyro configurations (left) and their corresponding beat-note responses (right). The
× corresponds to a pulse crossing that does not introduce phase coupling.
G is the gain, and
Δϕ=Δ/τrt is the differential round-trip phase shift. Note that the time unit in Eq. (
1) has been normalized to
τrt. (a) Linear (i.e., no dead band) response. (b) When a scattering interface is placed at the crossing point, a square-root (i.e., dead band) response is observed (data from Ref. [
21]).
Fig. 2. Polar plots of the imaginary versus real part of the beat field near (left) and far (right) from the EP (dead band). Near the EP the beat note stems from amplitude modulation, while far from the EP it is caused by pure phase modulation.
Fig. 3. Beat-signal spectrum from a numerical solution of Eq. (1) (top), and experimentally measured beat-note signal (bottom) showing the clustering of frequency harmonics near the dead band (left) and their absence for larger Δ (right).
Fig. 4. Beat-signal spectrum from a numerical solution of Eq. (1) showing the clustering of harmonics near the EP (dead band).
Fig. 5. Gyro beat-note response curve changes with
κ˜ and
s. All large circles are beat frequencies numerically solved from Eq. (
1) with
κ˜=0.05 and
s=0 (blue),
s=0.03 (orange),
s=0.05 (yellow), and
s=0.06 (purple). The green circles are with
κ˜=0 and
s=0.05. The red-dashed curves correspond to the eigenvalue beat frequency
2Δω determined from Eq. (
5). When saturable gain is included, the green circles shift to the positions of the cyan crosses because the COG (rather than the most prevalent peak) of the spectrum must be used. An example of data matching the
κ˜=0 case can be found in Ref. [
21].
Fig. 6. Numerical solution (blue circles) to Eq. (1) and analytic prediction (red dashes) of Eq. (6) showing an EP at Δ=0 for κ˜=0.05 with a saturable gain in one resonator, α^1=0.051, αL=0, β=1, γ=0, and a constant loss in the other, α2=−|κ˜|=−0.05. Inset: because the gain difference depends on Δ, it only cancels the coupling exactly at Δ=0. The time dependence of the fields in polar coordinates is shown in Visualization 1 for Δ=0.01.