L. Pilozzi

Radiative topological states in resonant photonic crystals.

We present a theory of topological edge states in one-dimensional resonant photonic crystals with a compound unit cell. Contrary to the conventional electronic topological states, the modes under consideration are radiative; i.e., they decay in time due to the light escape through the structure boundaries. We demonstrate that the edge states survive despite their radiative decay and can be detected both in time- and frequency-dependent light reflection.

Resonant Fibonacci quantum well structures in one dimension

We propose a resonant one-dimensional quasicrystal, namely, a multiple quantum well (MQW) structure satisfying the Fibonacci-chain rule with the golden ratio between the long and short interwell distances. The resonant Bragg condition is generalized from the periodic to Fibonacci MQWs. A dispersion equation for exciton polaritons is derived in the two-wave approximation; the effective allowed and forbidden bands are found. The reflection spectra from the proposed structures are calculated as a function of the well number and detuning from the Bragg condition.

Topological lasing in resonant photonic structures

The use of virtually lossless topologically isolated edge states may lead to a novel class of thresholdless lasers operating without inversion. One needs however to understand if topological states may be coupled to external radiation, and act as active cavities. We study a two-level topological insulator and show that self-induced transparency pulses can directly excite edge states. We simulate laser emission by a suitable designed topological cavity, and show that it can emit tunable radiation. For a configuration of sites following the off-diagonal Aubry-André-Harper model[1, 2], we solve the Maxwell-Bloch equations in the time domain and provide a first principle confirmation of topological lasers. Our results open the road to a new class of light emitters with topological protection for applications ranging from low-cost energetically-effective integrated lasers sources, also including silicon photonics, to strong coupling devices for studying ultrafast quantum processes with engineered vacuum.

Polariton-polariton scattering in microcavities: A microscopic theory

We apply the fermion commutation technique for composite bosons to polariton-polariton scattering in semiconductor planar microcavities. Derivations are presented in a simple and physically transparent fashion. A procedure of orthogonolization of the initial and final two-exciton state wave functions is used to calculate the effective scattering-matrix elements and the scattering rates. We show how the bosonic stimulation of the scattering appears in this full fermionic approach whose equivalence to the bosonization method is thus demonstrated in the regime of low exciton density. We find an additional contribution to polariton-polariton scattering due to the exciton oscillator strength saturation, which we analyze as well. We present a theory of the polariton-polariton scattering with opposite spin orientations and show that this scattering process takes place mainly via dark excitonic states. Analytical estimations of the effective scattering amplitudes are given.

Topological cascade laser for frequency comb generation in PI-symmetric structures

The cascade of resonant PT-symmetric topological structures is shown to emit laser light with a frequency comb spectrum. We consider optically active topological lattices supporting edge modes at regularly spaced frequencies. When the amplified resonances in the PT-broken regime match the edge modes of the topological gratings, we predict the emission of discrete laser lines. A proper design enables the engineering of the spectral features for specific applications. Topological protection makes the system very well suited for a novel generation of compact frequency comb emitters for spectroscopy, metrology, and quantum information.

Giant reflection band and anomalous negative transmission in a resonant dielectric grating slab: application to a planar cavity

The fundamental optical effects that are at basis of giant reflection band and anomalous negative transmission in a self-sustained rectangular dielectric grating slab in P polarization and for incidence angle not very far from the Brewsters angle of the equivalent slab, are investigated. Notice, that the self sustained dielectric grating slab is the simplest system that, due to the Bragg diffraction, can show both the former optical effects. A systematic study of its optical response is performed by an analytical exact solution of the Maxwell equations for a general incidence geometry. At variance of the well known broad reflection bands in high contrast dielectric grating slab in the sub-wavelength regime, obtained by the destructive interference between the travelling fundamental wave and the first diffracted wave (a generalization of the so called second kind Woods anomalies), the giant reflection band is a subtle effect due to the interplay, as well as among the travelling fundamental wave and the first quasi-guided diffracted one, also among the higher in-plane wave- vector components of the evanescent/divergent waves. To better describe this effect we will compare the optical response of the self-sustained high contrast dielectric grating slab with a system composed by an equivalent homogeneous slab with a thin rectangular high contrast dielectric grating engraved in one of the two surfaces, usually taken as a prototype for the second kind Woods anomalies generation. Finally, the electromagnetic field confinement in a patterned planar cavity, where the mirrors are two self-sustained rectangular dielectric grating slabs, is briefly discussed.

Fundamental collapse of the exciton-exciton effective scattering

(1) Istituto dei Sistemi Complessi, CNR, C.P. 10, Monterotondo Stazione, Roma I-00016 and(2) Institut des NanoSciences de Paris, CNRS, Universit´e Pierre et Marie Curie, 140 rue de Lourmel, 75015 Paris(Dated: August 11, 2010)The exciton-exciton effective scattering which rules the time evolution of two excitons is studiedas a function of initial momentum difference, scattering angle and electron-to-hole mass ratio. Weshow that this effective scattering can collapse for energy-conserving configurations provided thatthe difference between the two initial exciton momenta is larger than a threshold value. Sizeablescatterings then exist in the forward direction only. We even find that, for an electron-to-hole massratio close to 1/2, the exciton-exciton effective scattering stays close to zero in all directions whenthe difference between the initial exciton momenta has a very specific value. This unexpected butquite remarkable collapse comes from tricky compensation between direct and exchange Coulombprocesses which originates from the fundamental undistinguishability of the exciton fermionic com-ponents.

Exciton-polariton and local-field effects in rectangular gratings

Abstract Exciton-polariton of a quantum well embedded in a semiconducting slab with a rectangular dielectric grating lithographed on the surface is studied as a prototype of a system showing spatial dispersion and Bragg periodicity. Model calculations of the optical response point out dramatic distortion in absorbance peak of the exciton. This feature is produced by exciton induced interaction among two or more traveling electromagnetic modes, when some of these become strongly localized (stationary or guided waves) in the sample. Local field effects in the optical response are also computed and briefly discussed.

Machine learning inverse problem for topological photonics

Topology opens many new horizons for photonics, from integrated optics to lasers. The complexity of large-scale devices asks for an effective solution of the inverse problem: how best to engineer the topology for a specific application? We introduce a machine-learning approach applicable in general to numerous topological problems. As a toy model, we train a neural network with the Aubry–Andre–Harper band structure model and then adopt the network for solving the inverse problem. Our application is able to identify the parameters of a complex topological insulator in order to obtain protected edge states at target frequencies. One challenging aspect is handling the multivalued branches of the direct problem and discarding unphysical solutions. We overcome this problem by adopting a self-consistent method to only select physically relevant solutions. We demonstrate our technique in a realistic design and by resorting to the widely available open-source TensorFlow library.Topological photonics is a growing field with applications spanning from integrated optics to lasers. This study presents a machine learning method to solve the inverse problem that may help finding optimized solutions to engineer the topology for each specific application

Topologically protected frequency combs in PT-symmetric structures

By combining gain and loss with topological order in PT-symmetric chains we achieve amplified protected modes with a spectrum of regurarly spaced frequencies whose offset and line spacing can be tuned through the structure parameters.