Theory of four-wave mixing for bound and leaky modes

Allayarov, Izzatjon; Schmidt, Markus A.; Weiß, Thomas

doi:10.1103/physreva.101.043806

Cited by 9 publications

(3 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [13,84,102,106,113,114], this form of reversing the external bias is called 'reciprocal conjugation' and denoted by a superscript R, because the considered systems are composed of purely reciprocal materials.…”

Section: Pole Expansion Of the Green's Dyadicmentioning

confidence: 99%

See 1 more Smart Citation

Resonant states and their role in nanophotonics

Both¹,

Weiß

2021

Semicond. Sci. Technol.

Self Cite

View full text Add to dashboard Cite

Resonant phenomena have been extensively used in micro- and nanophotonics. Mathematically, these phenomena originate in a discrete set of basis functions known as resonant states or quasi-normal modes. Therefore, it is extremely beneficial to develop theoretical approaches that use these resonant states as a physically meaningful basis in order to describe the light–matter interaction in micro- and nanoresonators. However, the question of how to normalize resonant states correctly for such an expansion initially hampered many theoretical attempts. Only recently, this problem of normalization has been solved via different approaches, providing a completely rigorous basis for not only explaining but also quantifying a large variety of resonant phenomena. This review article provides an overview of the related activities in the field and typical applications. We compare the different approaches with a focus on formulations via the Mittag-Leffler expansion of the Green’s dyadic on the complex frequency plane and an analytic normalization scheme for the resonant states. Specifically, we discuss the pole expansion of the near and far field and outline related theoretical tools such as the resonant-state expansion and first-order perturbation theories. These approaches allow for efficiently describing light–matter interaction between local emitters and resonators, scattering of light at nanoparticles, and resonantly-enhanced optical sensing. Moreover, the resulting equations provide insight into the underlying physical mechanisms, which can be used to tailor the light–matter interaction and to predict new phenomena such as the recently observed complex-valued mode volumes. Since the Mittag-Leffler theorem is valid beyond the continuation of physical quantities to the complex frequency plane, an introduction to alternative modal approaches, namely those based on permittivity eigenmodes and propagating modes, is included here as well. While the link of these approaches to resonant phenomena is less obvious, they can be advantageous in some cases. Finally, we show that modal theories can be even applied in nonlinear optics. Hence, the theory of resonant states provides a general theoretical framework in micro- and nanophotonics.

show abstract

Section: Pole Expansion Of the Green's Dyadicmentioning

confidence: 99%

“…The nonlinear gain results in optical pulses that are spectrally broader and more compressed temporally than expected from the simpler theory of bound modes. In addition to the Kerr nonlinearity, it is also possible to describe four-wave mixing of bound and leaky modes [114,202].…”

Section: Application In Nonlinear Opticsmentioning

confidence: 99%

Resonant states and their role in nanophotonics

Both¹,

Weiß

2021

Semicond. Sci. Technol.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Originally proposed for purely dielectric shapes (slabs, microspheres, microcavities [20]) with nondispersive dielectric permittivity, the method was then generalized to dispersive open systems [31], photonic crystal slabs, and periodic arrays of nanoantennas at normal [32] and oblique incidence [33], and open systems containing magnetic, chiral, or bi-anisotropic materials [34]. In addition, the method has been extended to waveguide geometries such as dielectric slab waveguides [35,36] and optical fibers [37], with a possibility to account for nonuniformities [38] and nonlinearities [39,40].…”

Section: Introductionmentioning

confidence: 99%

Influence of disorder on a Bragg microcavity

et al. 2020

Self Cite

View full text Add to dashboard Cite

Using the resonant-state expansion for leaky optical modes of a planar Bragg microcavity, we investigate the influence of disorder on its fundamental cavity mode. We model the disorder by randomly varying the thickness of the Bragg-pair slabs (composing the mirrors) and the cavity, and calculate the resonant energy and linewidth of each disordered microcavity exactly, comparing the results with the resonant-state expansion for a large basis set and within its first and second orders of perturbation theory. We show that random shifts of interfaces cause a growth of the inhomogeneous broadening of the fundamental mode that is proportional to the magnitude of disorder. Simultaneously, the quality factor of the microcavity decreases inversely proportional to the square of the magnitude of disorder. We also find that first-order perturbation theory works very accurately up to a reasonably large disorder magnitude, especially for calculating the resonance energy, which allows us to derive qualitatively the scaling of the microcavity properties with disorder strength.

show abstract