Related papers: Minimum Dielectric-Resonator Mode Volumes
We study long-lived resonances (lowest-loss modes) in hexagonally shaped dielectric resonators in order to gain insight into the physics of a class of microcrystal lasers. Numerical results on resonance positions and lifetimes, near-field…
We report on measurements and modeling of the mode structure of tunable Fabry-P\'erot optical microcavities with imperfect mirrors. We find that non-spherical mirror shape and finite mirror size lead to loss, mode deformation, and shifted…
Lasing at telecommunication wavelengths from annular resonators employing radial Bragg reflectors is demonstrated at room temperature under pulsed optical pumping. Sub milliwatt pump threshold levels are observed for resonators with 0.5-1.5…
Efficient micro-resonators simultaneously require a large quality factor $Q$ and a small volume $V$. However, the former is ultimately limited by bending losses, the unavoidable radiation of energy of a wave upon changing direction of…
In this survey article we will consider universal lower bounds on the volume of a Riemannian manifold, given in terms of the volume of lower dimensional objects (primarily the lengths of geodesics). By `universal' we mean without curvature…
Graded-index optical elements are capable of shaping light precisely and in very specific ways. While classical freeform optics uses only a two-dimensional domain such as the surface of a lens, recent technological advances in laser…
Identification and subsequent manipulation of resonant modes typically relies on comparison with calculations which require precise knowledge of material parameters and dimensions. For millimetre-sized resonators that support…
We introduce a new technique for reducing the dimension of the ambient space of low-degree polynomials in the Gaussian space while preserving their relative correlation structure, analogous to the Johnson-Lindenstrauss lemma. As…
Field localization, characterized by mode volume, is central to optics, photonics, and all light-matter interactions. Smaller mode volumes amplify the electric field per photon, enhancing spontaneous emission, strengthening nonlinear…
We describe the design of optimized multilayer dielectric coatings for precision laser interferometry. By setting up an appropriate cost function and then using a global optimizer to find a minimum in the parameter space, we were able to…
We prove several discrete Gagliardo-Nirenberg-Sobolev and Poincar\'e-Sobolev inequalities for some approximations with arbitrary boundary values on finite volume meshes. The keypoint of our approach is to use the continuous embedding of the…
Having simultaneously a high quality factor (i.e. a narrow resonant band) and a shorter interaction time between the resonating system and the external sources (i.e. a wide resonant band) is a desirable characteristic for mechanical…
The mode volume is a very important figure of merits, which transversally arouse the physics and applications of electromagnetic cavities. Its modern definition was not obtained simply, and I try to briefly summarize the evolution of ideas.…
A proof of the resonant property of linear periodically loaded antennas with subwavelength elements is obtained by applying a Lagrangian formalism. A Lagrangian is developed by modeling the antenna with lumped inductance and capacitance…
Engineered micro- and nanomechanical resonators with ultra-low dissipation constitute the ideal systems for applications ranging from high-precision sensing such as magnetic resonance force microscopy, to quantum transduction between…
Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…
Inverse design algorithms are the basis for realizing high-performance, freeform nanophotonic devices. Current methods to enforce geometric constraints, such as practical fabrication constraints, are heuristic and not robust. In this work,…
In this paper, we prove upper bounds for the volume spectrum of a Riemannian manifold that depend only on the volume, dimension and a conformal invariant.
A recently developed technique for the system--and--bath quantization of open optical cavities is applied to three resonator geometries: A one dimensional dielectric, a Fabry--Perot resonator, and a dielectric disk. The system--and--bath…
The goal of this paper is to present a lower bound for the Mahler volume of at least 4-dimensional symmetric convex bodies. We define a computable dimension dependent constant through a 2-dimensional variational (max-min) procedure and…