Analysis of Side-band Inequivalence.

Frequency shifts of red- and blue-scattered (Stokes/anti-Stokes) side-bands in quantum optomechanics are shown to be counter-intuitively inequal, resulting in an unexpected symmetry breaking. This difference is referred to as Side-band Inequivalenve (SI), which normally leans towards red, and being a nonlinear effect it depends on optical power or intracavity photon number. Also there exists a maximum attainable SI at an optimal operation point.

Solution of Cross-Kerr Interaction Combined with Parametric Amplification.

We present a full operator approach to treatment of the cross-Kerr interaction combined with parametric amplification. It is shown that this problem can be exactly integrated using the method of higher-order operators. While the initial basis is infinite-dimensional, an orthogonal transformation can reduce the problem exactly into a six-dimensional basis which can be integrated conveniently.

Higher-Order Interactions in Quantum Optomechanics: Analysis of Quadratic Terms.

This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second order operators which constitute an exactly closed commutators. We consider both types of standard position-field and the recently predicted non-standard momentum-field quadratic interactions, which is significant when the ratio of mechanical frequency to optical frequency is not negligible.

Method of Higher-order Operators for Quantum Optomechanics.

We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises from nonlinear higher-order processes leading to inequal detunings.

Excitonic Emission of Monolayer Semiconductors Near-Field Coupled to High-Q Microresonators.

We present quantum yield measurements of single layer WSe (1L-WSe) integrated with high-Q ( Q > 10) optical microdisk cavities, using an efficient (η > 90%) near-field coupling scheme based on a tapered optical fiber. Coupling of the excitonic emission is achieved by placing 1L-WSe in the evanescent cavity field. This preserves the microresonator high intrinsic quality factor ( Q > 10) below the bandgap of 1L-WSe.

Geometrical approach in physical understanding of the Goos-Haenchen shift in one- and two-dimensional periodic structures.

The Goos-Haenchen shift of a totally reflected beam at the planar interface of two dielectric media, as if the incident beam is reflected from beneath the interface between the incident and transmitted media, has been geometrically associated with the penetration of the incident photons in the less-dense forbidden transmission region. This geometrical approach is here generalized to analytically calculate the Goos-Haenchen shift in one- and two-dimensional periodic structures. Several numerical examples are presented, and the obtained results are successfully tested against the well-known Artman's formula.

Approximate analysis and design of rectangular-lattice photonic crystals.

We present a theoretical analysis of wave propagation in rectangular- and square-lattice photonic crystals by approximating the arbitrary refractive-index function with a staircase profile. This profile has a number of tunable parameters that allow one to fit the band structures of the staircase and the desired structure over a large frequency range. The staircase profile is such that its corresponding two-dimensional wave equation decomposes into two one-dimensional equations by means of a constant decoupling parameter.