Local density of optical states in the band gap of a finite one-dimensional photonic crystal

Yeganegi, Elahe; Lagendijk, Ad; Mosk, Allard; Vos, Willem L.

doi:10.1103/physrevb.89.045123

Cited by 36 publications

(22 citation statements)

References 56 publications

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“…2 of the main text, we calculate the Floquet spectrum of a semi-infinite strip of width N y = 8 unit cells (N x = 1 with twisted boundary conditions). Due to the finite size, the Bloch wave spectrum is discrete; we interpolate this finite level spacing using Lorentzians of width 1/N [29]. The local density of states on the edge is obtained by integrating over the waveguide closest to the edge (one of the two sublattices).…”

Section: Continuum Modelmentioning

confidence: 99%

Edge Solitons in Nonlinear-Photonic Topological Insulators

2016

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We show theoretically that a photonic topological insulator can support edge solitons that are strongly self-localized and propagate unidirectionally along the lattice edge. The photonic topological insulator consists of a Floquet lattice of coupled helical waveguides, in a medium with local Kerr nonlinearity. The soliton behavior is strongly affected by the topological phase of the linear lattice. The topologically nontrivial phase gives a continuous family of solitons, while the topologically trivial phase gives an embedded soliton that occurs at a single power, and arises from a self-induced local nonlinear shift in the inter-site coupling. The solitons can be used for nonlinear switching and logical operations, functionalities that have not yet been explored in topological photonics. We demonstrate using solitons to perform selective filtering via propagation through a narrow channel, and using soliton collisions for optical switching.PACS numbers: 42.65. Jx, 42.65.Tg, 42.65.Sf, 42.82.Et Topologically nontrivial photonic bands, analogous to electronic topological insulators, have now been realized and studied in a variety of photonic structures [1][2][3][4][5][6][7][8][9][10]. These "photonic topological insulators" (PTIs) feature edge states that are topologically protected against certain classes of disorder, and have interesting potential applications as robust waveguides and delay lines. Thus far, PTIs have mostly been studied in the linear limit, in which existing concepts of band topology can be directly applied to the electromagnetic wave equations, such as by mapping the propagation equations for a linear photonic lattice to the linear Schrödinger equation [6]. Even recent studies of PTIs arising in optically nonlinear systems, such as exciton-polaritons in quantum wells, have focused on topological edge states that are linear perturbations around a steady-state nonlinear background [11][12][13]. There have been only a handful of investigations into the non-perturbative nonlinear dynamics that could arise in PTIs [14][15][16][17][18]. Notably, Lumer et al. discovered a localized stationary soliton lying in the bulk of a two-dimensional (2D) PTI, which can be interpreted as a point region of a different topological phase that is "selfinduced" by topological edge states circulating around it [14]. Ablowitz et al. have found evidence for moving edge solitons in weakly nonlinear 2D PTIs, though this was done by taking broad envelope superpositions of existing topological edge states, and reducing the system to a 1D nonlinear Schrödinger equation [15]. In 1D lattices, nonlinear dynamics of boundary states and self-induced topological transitions have also been studied [16,17]. This paper describes a class of moving lattice edge solitons that arise in experimentally feasible 2D PTIs with Kerr nonlinearity. Unlike in Ref. [15], the solitons are derived ab initio, without using broad envelope approximations, in a realistic photonic lattice; furthermore, they can arise whether the underlying lattice is top...

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Section: Continuum Modelmentioning

confidence: 99%

Edge Solitons in Nonlinear-Photonic Topological Insulators

2016

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“…In the mathematical literature [43], it is known as the Hamiltonian's spectral measure associated with the state |ψ d . If |ψ d is an atomic orbital state or some other spatially localized wave function, f(E) can also be identified with the local DOS [52][53][54].…”

Section: B the Measurement Spectral Density Of Statesmentioning

confidence: 99%

Spectral dimension controlling the decay of the quantum first-detection probability

2018

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We consider a quantum system that is initially localized at xin and that is repeatedly projectively probed with a fixed period τ at position x d . We ask for the probability that the system is detected in x d for the very first time, Fn, where n is the number of detection attempts. We relate the asymptotic decay and oscillations of Fn with the system's energy spectrum, which is assumed to be absolutely continuous. In particular Fn is determined by the Hamiltonian's measurement spectral density of states (MSDOS) f(E) that is closely related to the density of energy states (DOS). We find that Fn decays like a power law whose exponent is determined by the power law exponent dS of f(E) around its singularities E * . Our findings are analogous to the classical first passage theory of random walks. In contrast to the classical case, the decay of Fn is accompanied by oscillations with frequencies that are determined by the singularities E * . This gives rise to critical detection periods τc at which the oscillations disappear. In the ordinary case dS can be identified with the spectral dimension found in the DOS. Furthermore, the singularities E * are the van Hove singularities of the DOS in this case. We find that the asymptotic statistics of Fn depend crucially on the initial and detection state and can be wildly different for out-of-the-ordinary states, which is in sharp contrast to the classical theory. The properties of the first detection probabilities can alternatively be derived from the transition amplitudes. All our results are confirmed by numerical simulations of the tight-binding model, and of a free particle in continuous space both with a normal and with an anomalous dispersion relation. We provide explicit asymptotic formulae for the first detection probability in these models.

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“…In this work, we use the MIT Photonic bands [53] software package. While the ideal crystal assumption is not accurate for Bragg structures with only a small number of layers [56,57], the structures of main interest in this work have 10 active layers or more. Additionally, the eigenmode approach is relevant in a future perspective, as it permits calculation of an angularly resolved LDOS [58], which is important for our future work on the modified directionality of upconversion (UC) emission in a Bragg structure.…”

Section: Local Density Of Optical Statesmentioning

confidence: 99%

Enhanced upconversion in one-dimensional photonic crystals: a simulation-based assessment within realistic material and fabrication constraints

Hofmann¹,

Eriksen²,

Fischer³

et al. 2018

Opt. Express

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This paper presents a simulation-based assessment of the potential for improving the upconversion efficiency of β-NaYF:Er by embedding the upconverter in a one-dimensional photonic crystal. The considered family of structures consists of alternating quarter-wave layers of the upconverter material and a spacer material with a higher refractive index. The two photonic effects of the structures, a modified local energy density and a modified local density of optical states, are considered within a rate-equation-modeling framework, which describes the internal dynamics of the upconversion process. Optimal designs are identified, while taking into account production tolerances via Monte Carlo simulations. To determine the maximum upconversion efficiency across all realistically attainable structures, the refractive index of the spacer material is varied within the range of existing materials. Assuming a production tolerance of σ = 1 nm, the optimized structures enable more than 300-fold upconversion photoluminescence enhancements under one sun and upconversion quantum yields exceeding 15% under 30 suns concentration.

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Local density of optical states in the band gap of a finite one-dimensional photonic crystal

Cited by 36 publications

References 56 publications

Edge Solitons in Nonlinear-Photonic Topological Insulators

Edge Solitons in Nonlinear-Photonic Topological Insulators

Spectral dimension controlling the decay of the quantum first-detection probability

Enhanced upconversion in one-dimensional photonic crystals: a simulation-based assessment within realistic material and fabrication constraints

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