Recent advancements in computational inverse design have begun to reshape the landscape of structures and techniques available to nanophotonics. Here, we outline a cross section of key developments at the intersection of these two fields: moving from a recap of foundational results to motivation of emerging applications in nonlinear, topological, near-field and on-chip optics.The development of devices in nanophotonics has historically relied on intuition-based approaches, the impetus for which develops from knowledge of some a priori known physical effect. The specific features of such devices are then typically calculated and matched to suitable applications by tuning small sets of characteristic parameters. This approach has had a long track record of success, giving rise to a rich and widely exploited library of templates that includes multilayer thin films 1 , Fabry-Perot 2 and microring resonators 3 , silicon waveguides 4,5 , photonic crystals 6 , plasmonic nanostructures 7 , and nanobeam cavities 8 , top of Fig. 1. Combining the principles of index guiding and bandgap engineering, along with material resonances, this collection of designs enables remarkable manipulation of light over bands of frequencies spanning from the ultra-violet to the mid infrared: group velocity can be slowed by more than two orders of magnitude 9 , light confined to volumes thousands of times smaller than its free-space wavelength 10 , and resonances made to persist in micron sized areas for tens of millions of cycles 11 .Yet, as the scope of nanophotonics broadens to include large bandwidth or multi-frequency applications, nonlinear phenomena, and dense integration, continuing with this prototypical approach poses a challenge of increasing complexity. For instance, consider the design of a wavelength-scale structure for enhancing nonlinear interactions 12 , discussed below. Even in the simplest case, several interdependent characteristics must be simultaneously optimized, among which are large quality factors at each individual wavelength and nonlinear overlaps, which must be controlled in as small a volume as possible. In such a situation, the templates of the aforementioned standard library offer no clear or best way to proceed; there is no definite reason to expect that an optimal design can be found in any of the traditional templates, or that such a design necessarily exists. Moreover, the performance of a given nonlinear device is likely to be highly dependent on the particular characteristics of the problem, and as greater demands are placed on functionality it becomes increasingly doubtful that any one class of structures will have the broad applicability of past devices. This lack of evident strategies for broadband applications also brings to attention the space of structures included in the standard photonic library. Predominately, traditional designs are repetitive mixtures and combinations of highly symmetric shapes described by a small collection of parameters. Since intuition-based optimization is then carried out ...

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Interactions induced by electromagnetic fluctuations, such as van der Waals and Casimir forces, are of universal nature present at any length scale between any types of systems with finite dimensions. Such interactions are important not only for the fundamental science of materials behavior, but also for the design and improvement of micro-and nano-structured devices. In the past decade, many new materials have become available, which has stimulated the need of understanding their dispersive interactions. The field of van der Waals and Casimir forces has experienced an impetus in terms of developing novel theoretical and computational methods to provide new insights in related phenomena. The understanding of such forces has far reaching consequences as it bridges concepts in materials, atomic and molecular physics, condensed matter physics, high energy physics, chemistry and biology. In this review, we summarize major breakthroughs and emphasize the common origin of van der Waals and Casimir interactions. We examine progress related to novel ab initio modeling approaches and their application in various systems, interactions in materials with Dirac-like spectra, force manipulations through nontrivial boundary conditions, and applications of van der Waals forces in organic and biological matter. The outlook of the review is to give the scientific community a materials perspective of van der Waals and Casimir phenomena and stimulate the development of experimental techniques and applications.

We derive general conditions for 100% frequency conversion in any doubly resonant nonlinear cavity, for both second-and third-harmonic generation via χ (2) and χ (3) nonlinearities. We find that conversion efficiency is optimized for a certain "critical" power depending on the cavity parameters, and assuming reasonable parameters we predict 100% conversion using milliwatts of power or less. These results follow from a semi-analytical coupled-mode theory framework which is generalized from previous work to include both χ (2) and χ (3) media as well as inhomogeneous (fully vectorial) cavities, analyzed in the high-efficiency limit where down-conversion processes lead to a maximum efficiency at the critical power, and which is verified by direct finite-difference time-domain (FDTD) simulations of the nonlinear Maxwell equations. Explicit formulas for the nonlinear coupling coefficients are derived in terms of the linear cavity eigenmodes, which can be used to design and evaluate cavities in arbitrary geometries.

Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (pixelization). We show that accuracy can be significantly improved by using a subpixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory and compare it with other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.

We formulate and exploit a computational inverse-design method based on topology optimization to demonstrate photonic crystal structures supporting complex spectral degeneracies. In particular, we discover photonic crystals exhibiting third-order Dirac points formed by the accidental degeneracy of monopolar, dipolar, and quadrupolar modes. We show that, under suitable conditions, these modes can coalesce and form a third-order exceptional point, leading to strong modifications in the spontaneous emission (SE) of emitters, related to the local density of states. We find that SE can be enhanced by a factor of 8 in passive structures, with larger enhancements ∼ ffiffiffiffiffi n 3 p possible at exceptional points of higher order n. [3,4], and as precursors to nontrivial topological effects [5][6][7]. Recent work also showed that Dirac-point degeneracies can give rise to rings of exceptional points [8]. An exceptional point (EP) is a singularity in a non-Hermitian system where two or more eigenvectors and their corresponding complex eigenvalues coalesce, leading to a nondiagonalizable, defective Hamiltonian [9,10]. EPs have been studied in various physical contexts, most notably lasers and atomic as well as molecular systems [11,12]. In recent decades, interest in EPs has been reignited in connection with non-Hermitian parity-time symmetric systems [13], especially optical media involving carefully designed gain and loss profiles [14][15][16][17][18][19][20], where they can lead to intriguing phenomena such as excess noise [21,22], chiral modes [23], directional transport [24,25], and anomalous lasing behavior [26][27][28]. Also recently, it became possible to directly observe EPs in photonic crystals (PhCs) [8] and optoelectronic microcavities [29]. Thus far, however, the main focus of these works has been the effect of second-order exceptional points (EP2s) realized through photonic radiations, where only two modes coalesce; apart from a few mathematical analyses [30][31][32] or works focused on acoustic systems [33], there has been little or no investigation into the design and consequences of EPs of higher order (where more than two modes collapse).In this Letter, we formulate and exploit a powerful inverse-design method, based on topology optimization (TO), to develop complex photonic crystals supporting Dirac points formed out of the accidental degeneracy [34] of modes belonging to different symmetry representations. We show that such higher-order Dirac points can be exploited to create third-order exceptional points (EP3s) along with complex contours of EP2s. Furthermore, we consider possible enhancements and spectral modifications in the spontaneous emission (SE) rate of emitters, showing that the local density of states (LDOS) at an EP3 (14) can be enhanced eightfold (in passive systems) and can exhibit a cubic Lorentzian spectrum under special conditions. More generally, we find enhancement factors ∼ ffiffiffiffiffi n 3 p with increasing EP order n. Although the area of photonic inverse design is not new ...

We give an example of a geometry in which two metallic objects in vacuum experience a repulsive Casimir force. The geometry consists of an elongated metal particle centered above a metal plate with a hole. We prove that this geometry has a repulsive regime using a symmetry argument and confirm it with numerical calculations for both perfect and realistic metals. The system does not support stable levitation, as the particle is unstable to displacements away from the symmetry axis.

Abstract:We present a general theory of spontaneous emission at exceptional points (EPs)-exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light-matter interaction described by the local density of states (e.g., absorption, thermal emission, and nonlinear frequency conversion). Whereas traditional spontaneous-emission theories imply infinite enhancement factors at EPs, we derive finite bounds on the enhancement, proving maximum enhancement of 4 in passive systems with second-order EPs and significantly larger enhancements (exceeding 400×) in gain-aided and higher-order EP systems. In contrast to non-degenerate resonances, which are typically associated with Lorentzian emission curves in systems with low losses, EPs are associated with non-Lorentzian lineshapes, leading to enhancements that scale nonlinearly with the resonance quality factor. Our theory can be applied to dispersive media, with proper normalization of the resonant modes. References and links1. E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681--681 (1946). (CRC Press, 1995, vol. X). 3. S. V. Gaponenko, Introduction to Nanophotonics (Cambridge University, 2010 H. Yokoyama and K. Ujihara, Spontaneous Emission and Laser Oscillation in Microcavities