Ring Resonator Gyroscope: System Level Analysis and Parameter Optimization
Publication Type:Conference Proceedings
Source:Canadian Semiconductor Science and Technology Conference, Vancouver, B.C., Canada., p.MPA1 (2011)
Keywords:optical gyroscope; resolution; critical coupling; optimum coupling; optimum detuning
Introduction: Although several theoretical studies regarding the use of micro-ring
resonators for gyroscopic applications have been carried out, to the best of our
knowledge there has not yet been a thorough study of the interdependence of the
propagation loss, α, resonator length, L, coupling coefficients, κ a and κ b , and off-
resonance detuning, φ, necessary to achieve a truly optimized sensitivity for either the
through or the drop port of a double-bus racetrack resonator optical gyroscope (RROG).
Optimized parameter values for some particular cases have been depicted in references
such as , but this being a particular single-bus waveguide case, with the restriction of a
small length-propagation loss product, Lα, it precludes the proper application of such
optimized parameters for the case of a gyroscope, where relatively large length values
are desirable to enhance the Sagnac effect. Based on our modeling, we propose solid-
state, RROGs with optical paths in the millimeter range, to be fabricated in Si 3 N 4 by
currently existing CMOS-compatible techniques, with sensitivities comparable to those of
MEMS-based gyroscopes, as shown in Figure 1.
Methods: The feasibility of using double-bus-waveguide ring resonators as RROGs,
based on the Sagnac effect, is assessed. The veracity of the general assumption that
critical coupling (CC) offers the best sensitivities is also investigated. We do this by using
analytical and numerical modelling of the spectral responses, noise levels and angular
rate sensitivities for both the through or the drop port of the RROG system depicted in
Figure 2, with and without CC restrictions, for three different values for α. These three
values are consistent with two low-loss Si 3 N 4 (α 1 =0.06  and α 2 =0.12 dB/cm ) and
one silicon-on-insulator (α 3 =3 dB/cm ) waveguide fabrication technologies.
Results: Analytical and numerical optimizations of the values of κ a and κ b , φ, and L have
been carried out. As shown in Figure 3a, the sensitivity depends not only on L (more
accurately, the enclosed area) of the resonator, which enhances the Sagnac effect, but it
is also affected by φ, κ a , and κ b . For each propagation loss, there is an L value beyond
which the sensitivity is severely deteriorated. Such a critical length L c increases for
decreasing propagation loss α. The absolute minimum angular rates for shot-noise-
limited RROGs with α= 0.06 dB/cm are 0.46 and 4.4 mdeg/s, for the through and the
drop port, for which L cT = 2.7 m and L cD =1.6 m, respectively.
Discussion: For low propagation losses, the L c values are impractical if the ring
resonators are to be built with no spirals or waveguide crossings in one single wafer.
Therefore, we restricted L to values within the range of 50 to 250 mm, which do not yield
the absolute achievable minima for the smallest α, but are able to compete with
commercial gyroscopes of similar lengthscales. For instance, L= 50 mm exhibits
sensitivities of 7.4 and 29.5 mdeg/s for the through and the drop port, respectively. As
shown in Figure 1, these values are equal or better than those of MEMS gyroscopes.
Conclusion: Our derivations suggest that the RROG prototypes would have sensitivity
levels and dimensions comparable to those of commercial MEMS gyroscopes, but would
have no moving parts and thus have longer lifetimes. The propagation loss is the main
factor that hinders the resolution. Based on our analysis, we conclude that in
contradiction to the general assumption regarding CC, undercoupled rings show the best
sensitivities for both the through and the drop ports. For all propagation losses, through-
port sensing is better than drop-port sensing by as much as one order of magnitude.
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