Abstract

Whispering Gallery Mode resonators made from optically nonlinear crystals have small mode volume and extremely high quality factor which makes them ideal for various nonlinear conversion process at low power, ultimately at single photon level.

Highlights

  • The ordinary and extraordinary thermorefractive coefficients in birefringent materials can significantly differ. This allows for the differential tuning of the TE and transverse magnetic filed (TM) whispering gallery modes (WGMs) spectra, a capability very important for some sensor applications [211, 212]10 and for achieving the phase matching in various nonlinear optics applications [213]

  • Analysis of nonlinear optical processes dynamics in phasematched WGM resonators has been reported for the second harmonic generation (SHG) [107, 213, 256, 317, 335] and optical parametric oscillator (OPO) [213, 253,254,255,256, 336], as well as for the sum-frequency generation (SFG) [320, 321, 337, 338] and difference-frequency generation (DFG) [339]

  • Generation of optical frequency sum [320] and difference [368] have been demonstrated. Some of these experiments [108, 110, 112, 158, 228, 255, 257, 318,319,320, 357, 360, 361, 366, 367] have been relying on the natural phase matching whereas Quasi-phase matching (QPM) with periodical domain inversion was harnessed in others [107, 157, 326, 363,364,365]

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Summary

The role of nonlinearity in optical science

Light does not interact with light in everyday life. This interaction can only be induced by means of nonlinear physical systems and is only observable with strong enough electromagnetic fields. Methods involving optical fibers [1], plasmons [2], hollow-core photonic crystal fibers [3], as well as metameterials [4,5,6] allow reducing the light power requirement This reduction is still insufficient for many applications where it is desirable to achieve a strong nonlinear response with faint light, at a few- or single-photon level. Unlike other types of optical cavities, monolithic ones can be integrated on a chip and multiplexed, which makes them indispensable in creation of chipscale nonlinear optical devices able to generate optical harmonics, produce non-classical states of light, process quantum information and so on These resonators allow reducing the footprint of nonlinear optics experiments and moving them from the lab to industrial applications, and facilitate nonlinear interaction at the single-photon level, representing one of the major goals of optical science nowadays. In the rest of this section, we briefly review the history and distinctive properties of WGM resonators

Discovery of WGM phenomena
Historic investigations of microwave WGM resonators
Historic investigations of optical WGM resonators and their close relatives
What is special about WGM resonators
Mode structure and dispersion equation
Geometrical dispersion and effective index approximation
Tuning the resonator spectrum
Thermal
Mechanical stress and deformation
Electro-optical
Other methods of WGM spectrum engineering
Mode crossing
Second-order nonlinear processes
Electro-optical phenomena and applications of WGMRs
Vp cos wmw t
Natural phase matching and selection rules for secondorder processes
Crystal symmetry based and ‘cyclic’ QPM
Exotic phase matching in WGM resonators
Dynamics of the second-order processes in triply resonant systems
Experimental observations of the second-order processes
Third-order nonlinear processes
Interaction Hamiltonian and phase matching
Hyper-parametric oscillation
Cascaded hyper-parametric oscillation as frequency comb generation
Mode-locked Kerr-comb generation
Forced frequency combs
Frequency dependent absorption in mode locking
THG and up-conversion via FWM
Raman and Brillouin scattering
General prerequisites for efficient quantum optics processes
Second-order processes above threshold: squeezing
Second-order processes below threshold: photon pairs generation
Third-order processes for generation of non-classical light
Direct coupling of WGM light with quantum systems
Quantum Zeno effect
Summary and conclusion
Applications and phenomena not covered in this review
Anticipated development of the field
Findings
Fabrication challenges and scalability quest

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