Luis Morales-Inostroza

Observation of Localized States in Lieb Photonic Lattices.

We present the first experimental demonstration of a new type of localized state in the continuum, namely, compacton-like linear states in flat-band lattices. To this end, we employ photonic Lieb lattices, which exhibit three tight-binding bands, with one being perfectly flat. Discrete predictions are confirmed by realistic continuous numerical simulations as well as by direct experiments. Our results could be of great importance for fundamental physics as well as for various applications where light needs to be conducted in a diffractionless and localized manner over long distances.

Transport in Sawtooth photonic lattices.

We investigate, theoretically and experimentally, a photonic realization of a Sawtooth lattice. This special lattice exhibits two spectral bands, with one of them experiencing a complete collapse to a highly degenerate flat band for a special set of inter-site coupling constants. We report the observation of different transport regimes, including strong transport inhibition due to the appearance of the non-diffractive flat band. Moreover, we excite localized Shockley surface states residing in the gap between the two linear bands.

Quantum localized states in photonic flat-band lattices

The localization of light in flat-band lattices has been recently proposed and experimentally demonstrated in several configurations, assuming a classical description of light. Here, we study the problem of light localization in the quantum regime. We focus on quasi one-dimensional and two-dimensional lattices which exhibit a perfect flat-band inside their linear spectrum. Localized quantum states are constructed as eigenstates of the interaction Hamiltonian with a vanishing eigenvalue and a well defined total photon number. These are superpositions of Fock states with probability amplitudes given by positive as well as negative square roots of multinomial coefficients. The classical picture can be recovered by considering poissonian superpositions of localized quantum states with different total photon number. We also study the separability properties of flat band quantum states and apply them to the transmission of information via multi-core fibers, where these states allow for the total passive suppression of photon crosstalk and exhibit robustness against photon losses. At the end, we propose a novel on-chip setup for the experimental preparation of localized quantum states of light for any number of photons.

Simple method to construct flat-band lattices

We develop a simple and general method to construct arbitrary flat-band lattices. We identify the basic ingredients behind zero-dispersion bands and develop a method to construct extended lattices based on a consecutive repetition of a given miniarray. The number of degenerated localized states is defined by the number of connected miniarrays times the number of modes preserving the symmetry at a given connector site. In this way, we create one or more (depending on the lattice geometry) complete degenerated flat bands for quasi-one- and two-dimensional systems. We probe our method by studying several examples and discuss the effect of additional interactions such as anisotropy or nonlinearity. We test our method by studying numerically a ribbon lattice using a continuous description.

Observation of localized ground and excited orbitals in graphene photonic ribbons

We report on the experimental realization of a quasi-one-dimensional photonic graphene ribbon supporting four flat-bands (FBs). We study the dynamics of fundamental and dipolar modes, which are analogous to the s and p orbitals, respectively. In the experiment, both modes (orbitals) are effectively decoupled from each other, implying two sets of six bands, where two of them are completely flat (dispersionless). Using an image generator setup, we excite the s and p FB modes and demonstrate their non-diffracting propagation for the first time. Our results open an exciting route towards photonic emulation of higher orbital dynamics.

Photorefractive writing and probing of anisotropic linear and nonlinear lattices

We study experimentally the writing of one- and two-dimensional photorefractive lattices, focusing on the often overlooked transient regime. Our measurements agree well with theory, in particular concerning the ratio of the drift to diffusion terms. We then study the transverse dynamics of coherent waves propagating in the lattices, in a few novel and simple configurations. For defocusing linear waves with broad transverse spectrum, we remark that both the intensity distributions in real space (?discrete diffraction?) and Fourier space (?Brillouin zone spectroscopy?) reflect the Bragg planes and band structure. For nonlinear waves, we observe modulational instability and discrete solitons formation in time domain. We discuss also the non-ideal effects inherent to the photo-induction technique: anisotropy, residual nonlinearity, diffusive term, non-stationarity.

Erratum: Photorefractive writing and probing of anisotropic linear and nonlinear lattices (2014 J. Opt. 17 025101)

An error was made in the typesetting of the sentence below equation (8) in the published version of this article. This sentence should read: ‘In the right hand side of equation (8), the first term proportional to |E0| is the drift term, and the second, proportional to kB T/e =D/μ (where D is the diffusion coefficient and μ the electron mobility), the diffusive term.’ In addition, a global change was made incorrectly throughout the paper. The word ‘focused’ has been incorrectly changed to the word ‘defocusing’. The occurrences of this error are listed below with the corrected sentences. Line numbers indicate the start of the sentence. Abstract, line 5 should read: For focused linear waves with broad transverse spectrum, we remark that both the intensity distributions in real space (‘discrete diffraction’) and Fourier space (‘Brillouin zone spectroscopy’) reflect the Bragg planes and band structure. Page 3, right-hand column, line 5 from bottom should read: On the other hand, the extraordinary polarized beam is used as a probe beam, which eventually is shapen anisotropically using a cylindrical lens, or focused with regular lenses. Page 5, right-hand column, line 3 should read: The probe beam is a plane wave (first two columns) or a beam with broad transverse spectrum, narrowly focused at the crystal input face (to a waist w0 = 2.0 μm), that expands in the crystal (last two columns). Page 6, figure 4 caption should read as: Figure 4. Intensity of a linear probe beam (and writing beam, in second column) at crystal output in real and Fourier space, for a 1D (upper row), square (middle row) and a diamond lattice (lower row). The probe beam is a plane wave (first two columns) or a narrowly focused wave at the crystal input, which expands in the lattice (last two columns). (a), (e) and (i) real space output for a plane wave input probe with lattice period d = 27 μm (1D lattice) and d = 38.5 μm (2D lattices) (b), (f) and (j) Fourier images of lattice writing beams (four outside points) and the probe which is a point at k = 0. (c), (g) and (k) real space output for a focused probe (discrete diffraction patterns) with d = 7 μm (1D lattice) and d = 10 μm (2D lattices). White lines show the ballistic positions ±yL of vertical Bragg components ±kL. (d), (h) and (l) Fourier images of the focused probe (Brillouin zone spectroscopy), with d = 13.6 μm (1D lattice) and d = 19.2 μm (2D lattices), with vertical Bragg components ±kL shown as white lines. Page 6, left-hand column, line 13 should read: With a focused, expanding linear probe, in real space (figures 4(c), (g) and (k)), we observe the patterns commonly called ‘discrete diffraction’ [24], displaying two outer expanding lobes of high intensity, particularly well seen in the 1D case (figure 4(c)). Page 7, right-hand column, line 18 should read: The Fourier images with focused probe (figures 4(d), (h) and (l)) are generally referred to as ‘BZ spectroscopy’ [23, 26]. Page 9, left-hand column, line 4 from bottom should read: In figure 8, we show the output intensity at times tW = 23, 39, 54 s, when a diamond 2D lattice and a focused probe beam are simultaneously applied, with a ratio of peak input probe intensity to average lattice intensity Ip/IL ∼ 0.5. Page 9, right-hand column, line 29 should read: With focused, expanding wavepackets with a broad transverse spectrum, we analyzed discrete diffraction patterns (at finite Journal of Optics