Photon Bloch Oscillations in Porous Silicon Optical Superlattices

Agarwal, Vivechana; Río, J. A. del; Malpuech, Guillaume; Zamfirescu, M.; Kavokin, A. V.; Coquillat, Dominique; Scalbert, D.; Vladimirova, Maria; Gil, Bernard

doi:10.1103/physrevlett.92.097401

Cited by 145 publications

(94 citation statements)

References 29 publications

(37 reference statements)

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“…The chosen values of refractive indices are easily achievable, for instance, in porous silicon structures. 12 Designing the right substructure, we have slightly detuned the thicknesses of layers from those given by the Bragg condition ͑9͒ in order to tune r , that allowed bringing the OTS closer to the center of the stop bands of both substructures. Figure 1͑b͒ shows by a flash the energy of the OTS in our model structure.…”

Section: ͑4͒mentioning

confidence: 99%

Lossless interface modes at the boundary between two periodic dielectric structures

2005

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Tamm states of light are lossless interface modes decaying exponentially in the surrounding media. We show that they can be formed at the boundary between two periodical dielectric structures, one having a period close to the wavelength of light and another one having a period close to the double of the wavelength. The order of layers at the interface has a crucial effect on the Tamm states. The in-plane dispersion of these states is parabolic with effective masses slightly different for TE and TM polarizations, both of the order of 10 −5 of the free electron mass. DOI: 10.1103/PhysRevB.72.233102 PACS number͑s͒: 78.68.ϩm, 42.70.Qs, 41.20.Jb, 42.25.Lc Surface waves are a specific type of waves that are confined at the boundary between two different media. They are used in subwavelength microscopy, molecular chemistry, cancer research, etc. [1][2][3] The most popular kind of surface wave is a plasmon formed at the boundary of metallic and dielectric media. Recently, the possibility to organize lossless surface waves at the interface between two dielectric media has been discussed. Artigas and Torner 4 have proposed to use specially designed two-dimensional photonic crystals for observation of the so-called Dyakonov modes 5 localized at the surface of the crystal. The photonic structure plays the role of a uniaxial dielectric medium having controllable refractive indices for ordinary and extraordinary light modes.In this Brief Report we propose another type of lossless interface modes, which we call optical Tamm states ͑OTSs͒ by analogy with well-known Tamm states for electrons at crystal boundaries. 6 Contrary to waveguided surface modes 7 and to Dyakonov modes, Tamm states remain localized for any value of the in-plane wave vector ͑including the zero wave-vector͒. OTSs are formed inside the "light cone" limited by a k = / c condition, where k is the wave vector of light and is its frequency. Contrary to electronic Tamm states, optical Tamm states cannot be formed at the surface, but only at the interface between two photonic structures having overlapping band gaps. We propose a simple planar multilayer structure allowing for observation of the OTSs. Ten years ago, one of us developed a theory of Tamm states for electrons confined at the boundary of two semiconductor superlattices. 8 Now we have extended the method of Ref. 8 to describe OTSs. We show that they can be formed at the interface between two periodic dielectric structures having different periods. The OTS lies in the optical stop bands of both parts of the structure. Its in-plane dispersion is parabolic with an effective mass of the order of 10 −5 of a free electron mass. The splitting between TE and TM polarized Tamm states increases quadratically with the in-plane wave vector. We propose realistic multilayer structures based on the porous silicon allowing for observation of the OTSs.Let us consider the interface between two periodical dielectric structures composed by the pairs of layers of thicknesses a r , b r and refractive indices n a , n b on...

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Section: ͑4͒mentioning

confidence: 99%

Lossless interface modes at the boundary between two periodic dielectric structures

2005

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“…The existence of BO has been demonstrated in plenty of systems described by a wave equation. For instance, BO has been reported in ultracold atoms, 6,7 Bose-Einstein condensates, 8 light waves in photonic crystals, [9][10][11] and more recently in sound waves in phononic crystals, [12][13][14][15] proposing alternative ways to mimic the effects of the periodic potentials under external fields.…”

Section: Introductionmentioning

confidence: 99%

Experimental and theoretical demonstration of acoustic Bloch oscillations in porous silicon structures

Lazcano

Arriaga

Aliev

2014

Journal of Applied Physics

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We report the theoretical calculations and the experimental demonstration of acoustic Bloch oscillations and Wannier-Stark ladders in linear tilted multilayer structures based on porous silicon. The considered structures consist of layers with constant porosity alternated by layers with a linear gradient in the parameter g ¼ 1=v 2L along the growth direction in order to tilt the acoustic band gap. The purpose of this gradient is to mimic the tilted electronic miniband structure of a superlattice semiconductor under an external electric field. In this way, acoustic Wannier-Stark ladders of equidistant modes are formed and they were experimentally confirmed in the transmission spectrum around 1.2 GHz. Their frequency separation defines the period of the acoustic Bloch oscillations. We fabricated three different structures with the same thicknesses but different values in the g parameter to observe the effect on the period of the Bloch oscillations. We measured the acoustic transmission spectra in the frequency domain, and by using the Fourier transform, we obtained the transmission in the time domain. The transmission spectra of the fabricated samples show acoustic Bloch oscillations with periods of 27, 24, and 19 ns. The experimental results are in good agreement with the transfer matrix calculations. The observed phenomenon is the acoustic counterpart of the well known electronic Bloch oscillations. V C 2014 AIP Publishing LLC.

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“…The WSL in solid state were finally observed decades later using superlattices [15]. They have recently been found in optics as well [3,4]. As will be shown, by modifying appropriately the small rods in a systematic way one can obtain an elastic analog of WSL [11].…”

Section: Destroying the Symmetrymentioning

confidence: 95%

“…Among them, mechanical [1], microwave [2], optical [3,4,5,6], and elastic systems [7] have been studied along these lines. This approach is sometimes, jokingly speaking, referred to as megascopic physics.…”

Section: Introductionmentioning

confidence: 99%

Building and destroying symmetry in 1-D elastic systems

Flores¹,

Monsiváis²,

Mora³

et al. 2010

AIP Conference Proceedings

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Abstract. Locally periodic rods, which show approximate invariance with respect to translations, are constructed by joining N unit cells. The spectrum then shows a band spectrum. We then break the local periodicity by including one or more defects in the system. When the defects follow a certain definite prescription, an analog of the Wannier-Stark ladders is gotten; when the defects are random, an elastic rod showing Anderson localization is obtained. In all cases experimental values match the theoretical predictions.

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Photon Bloch Oscillations in Porous Silicon Optical Superlattices

Cited by 145 publications

References 29 publications

Lossless interface modes at the boundary between two periodic dielectric structures

Lossless interface modes at the boundary between two periodic dielectric structures

Experimental and theoretical demonstration of acoustic Bloch oscillations in porous silicon structures

Building and destroying symmetry in 1-D elastic systems

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