Angular-rate sensing by mode splitting in a Whispering-gallery-mode optical microresonator

Yang, Zhaohua; Huo, Jiayan; Han, Xiaowei

doi:10.1016/j.measurement.2018.01.017

Cited by 6 publications

(7 citation statements)

References 15 publications

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“…c is the speed of light in vacuum, neff is the effective refracting. The rate equations of the coupled fiber-microresonator system in the presence of a particle with allowance for rotation can be expressed as [18]:dnormaldt[aCWaCCW]=[−(i(ωc+g+Δωu)+keff2)−(ig+Γ2)−(ig+Γ2)−(i(ωc+g−Δωu)+keff2)][aCWaCCW]−[Kc0]aCWin…”

Section: Principle and Theoretical Modelmentioning

confidence: 99%

“…

is the speed of light in vacuum,

is the effective refracting. The rate equations of the coupled fiber-microresonator system in the presence of a particle with allowance for rotation can be expressed as [ 18 ]:

Here

and

are the amplitudes of CW and CCW,

is defined as the effective damping rate of the system.

, where

is the intrinsic damping rate,

is the microresonator-taper coupling rate,

is the additional damping rate owing to scattering loss,

is the coupling coefficient of the light scattered in the resonator.…”

Section: Principle and Theoretical Modelmentioning

confidence: 99%

“…The imaginary part of the eigenvalue obtained by the state-space method represents the resonant frequency. By transforming the system matrix (2) into a diagonal matrix, the resonant frequencies of SM and ASM can be derived as:

After simplification using

, where

represents the value of static splitting, it is straightforward that the amount of splitting can be calculated from

using Equations (3) and (4) as

Additional damping owing to scattering loss can be ignored when the resonator is in the absorption-limited regime and the relationship between the splitting value [ 18 ] and the angular rate can be found as

also written as

.…”

Section: Principle and Theoretical Modelmentioning

confidence: 99%

“…While the degeneracy resonance will be split into two non-degenerate standing-wave modes (the symmetric mode (SM) and asymmetric mode (ASM)) if the symmetric resonator experiences any perturbation in the field distributions, such as structure defects, scattering around the cavity or rotation, namely, mode splitting [ 13 , 14 , 15 ]. Because of the successful demonstration in theory and experiments of nanoparticle detection by the above mode splitting, a new scheme for sensing has been developed [ 16 , 17 , 18 , 19 ].…”

Section: Introductionmentioning

confidence: 99%

“…Rotation of a resonator can also redistribute the internal modes in the frequency domain and give rise to mode splitting [ 18 ]. By detecting the frequency difference between the SM and ASM in the angular rate sensing based on mode splitting, good noise suppression is offered because of the same cavity environment experienced by the two modes.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Kerr Noise in Angular-Rate Sensing Based on Mode Splitting in a Whispering-Gallery-Mode Microresonator

Yang

Sun

2019

Micromachines

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Whispering-gallery-mode (WGM) microresonators have shown their potential in high-precision gyroscopes because of their small volume and high-quality factors. However, Kerr noise can always be the limit of accuracy. Angular-rate sensing based on mode splitting treats backscattering as a measured signal, which can induce mode splitting, while it is considered as a main source of noise in conventional resonator optical gyroscopes. Meanwhile, mode splitting also provides superior noise suppression owing to its self-reference scheme. Kerr noise in this scheme has not been defined and solved yet. Here, the mechanism of the Kerr noise in the measurement is analyzed and the mathematical expressions are derived, indicating the relationship between the Kerr noise and the output of the system. The influence caused by Kerr noise on the output is simulated and discussed. Simulations show that the deviation of the splitting caused by Kerr noise is 1.913 × 10−5 Hz at an angular rate of 5 × 106 °/s and the corresponding deviation of the angular rate is 9.26 × 10−9 °/s. It has been proven that angular-rate sensing based on mode splitting offers good suppression of Kerr noise.

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Section: Principle and Theoretical Modelmentioning

confidence: 99%

“…

is the speed of light in vacuum,

is the effective refracting. The rate equations of the coupled fiber-microresonator system in the presence of a particle with allowance for rotation can be expressed as [ 18 ]:

Here

and

are the amplitudes of CW and CCW,

is defined as the effective damping rate of the system.

, where

is the intrinsic damping rate,

is the microresonator-taper coupling rate,

is the additional damping rate owing to scattering loss,

is the coupling coefficient of the light scattered in the resonator.…”

Section: Principle and Theoretical Modelmentioning

confidence: 99%

After simplification using

, where

represents the value of static splitting, it is straightforward that the amount of splitting can be calculated from

using Equations (3) and (4) as

also written as

.…”

Section: Principle and Theoretical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analysis of Kerr Noise in Angular-Rate Sensing Based on Mode Splitting in a Whispering-Gallery-Mode Microresonator

Yang

Sun

2019

Micromachines

Self Cite

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Backscattering in nonlinear microring resonators via a Gaussian treatment of coupled cavity modes

McCutcheon

2021

APL Photonics

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Systems of coupled cavity modes have the potential to provide bright quantum optical states of light in a highly versatile manner. Microring resonators, for instance, are highly scalable candidates for photon sources. Thanks to CMOS fabrication techniques for their small footprint and the relative ease of coupling many such microrings together. However, surface roughness of the waveguides and defects in the coupler geometry routinely induce splitting of the cavity modes due to backscattering and backcoupling. The parasitic back-propagating mode in a microring leads to hybridization of the modes, altering the linear and nonlinear properties of a system of coupled cavity modes and ultimately constraining the fidelity of quantum light sources that can be produced. In this paper, we derive a comprehensive general model for Gaussian nonlinear processes in systems of coupled cavity modes based on an effective field Hamiltonian and a dispersive input–output model. The resulting dynamics of the equations of motion are evaluated in a Gaussian process formalism via symplectic transformations on the optical modes. We then use this framework to numerically model and explore the problem of backscattering in microring resonators in physically relevant parameter regimes, involving the splitting of various resonances, and we calculate the consequent impurity and heralding efficiency of various heralded photon schemes. We provide a perturbative explanation of the observations and assess the correspondence between spontaneous and stimulated processes in these systems.

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Large-range and high-sensitivity displacement sensing based on a SNAP microresonator by multimode encoding technique

Dong

Zeng

Wang

et al. 2023

Meas. Sci. Technol.

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Probe-type micro-displacement sensors with a large range and high sensitivity have important applications in both aerospace and nano-lithography. However, the state-of-the-art measurement range achieved using conventional methods such as CCD imaging and fiber grating demodulation is limited to only tens of micrometers. In this study, we propose and demonstrate a displacement sensing mechanism with a large range and high sensitivity for measuring linear displacements. The mechanism is based on a multimode encoding technique implemented on a Surface Nanoscale Axial Photonics (SNAP) microcavity platform. By tracking the transmittance variations of multiple axial modes and employing encoding techniques, we can determine the rough absolute position as well as the axial mode with the highest sensitivity in each region. Moreover, the selected mode for each region is exploited to accurately measure the micro-displacement with a large range and high accuracy. As a proof-of-principle experiment, the results indicate a large sensing range about 346 μm and a high sensitivity ranging up to 0.013/μm. Assuming that the transmittance can be resolved by 0.1%, the resolution of the measurement is about 0.1 μm.

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Angular-rate sensing by mode splitting in a Whispering-gallery-mode optical microresonator

Cited by 6 publications

References 15 publications

Analysis of Kerr Noise in Angular-Rate Sensing Based on Mode Splitting in a Whispering-Gallery-Mode Microresonator

Analysis of Kerr Noise in Angular-Rate Sensing Based on Mode Splitting in a Whispering-Gallery-Mode Microresonator

Backscattering in nonlinear microring resonators via a Gaussian treatment of coupled cavity modes

Large-range and high-sensitivity displacement sensing based on a SNAP microresonator by multimode encoding technique

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