Omnidirectional photonic bandgaps in porous silicon based mirrors with a Gaussian profile refractive index

Estevez, J. O.; Arriaga, J.; Blas, A. Méndez; Agarwal, Vivechana

doi:10.1063/1.3028073

Cited by 32 publications

(22 citation statements)

References 18 publications

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“…different refractive indexes) and varying thicknesses can be obtained by HF electrochemical etching by modulating the value of the current density during the anodization process [14]. Thus we fix n A = 1.4 and n B = 2.4 in our calculations since they correspond to experimentally accessible porous silicon refractive index values [14,15].…”

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confidence: 99%

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Photonic heterostructures with Lévy-type disorder: Statistics of coherent transmission

2012

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We study the electromagnetic transmission T through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed distribution -Lévy-type distribution. Based on recent predictions made for 1D coherent transport with Lévy-type disorder, we show numerically that for a system of length L (i) the average − ln T ∝ L α for 0 < α < 1, while − ln T ∝ L for 1 ≤ α < 2, α being the exponent of the power-law decay of the layer-thickness probability distribution; and (ii) the transmission distribution P (T ) is independent of the angle of incidence and frequency of the electromagnetic wave, but it is fully determined by the values of α and ln T . Additionally we have found and numerically verified that T ∝ L −α with 0 < α < 1. Random processes characterized by density probabilities with a long tail (Lévy-type processes) have been found and studied in very different phenomena and fields such as biology, economy, and physics. One of the main features of a Lévy-type density distribution p(l) is the slow decay of its tail. More precisely, for large l,with 0 < α < 2. Note that the second moment diverges for all α and if 0 < α < 1 also the first moment diverge. This kind of distributions are also known as α-stable distributions [1]. A window on new optical materials which allow for the experimental study of Lévy flights in an outstanding controllable way was recently opened with the construction of the so-called Lévy glass [2]: titanium dioxide particles are suspended in a matrix made of glass microspheres. The distribution of the microsphere diameters is properly chosen in order that light can travel performing Lévy flights within the microspheres. The diameter distribution is characterized by the exponent α of the power-law decay of its tail; it was found [2] that when 0 < α < 1 the transport is supperdiffusive, while for α = 2 the normal diffusive transport is recovered. This experimental investigation has motivated several theoretical works on the effects of the presence of Lévy-type processes on different transport quantities in one dimension, as well as in higher dimensional systems [3][4][5][6]8].On the other hand, coherent electron transport through one-dimensional (1D) quantum wires with Lévy-type disorder was studied in Ref. [6]. It was found that for the dimensionless conductance, or transmission, T :(i) the average (over different disorder realizations) of the logarithm of the transmission behaves asand (ii) the distribution of transmission P (T ) is fully determined by the exponent α and the ensemble average ln T .We point out that although for 1 ≤ α < 2, the average ln T depends linearly on L, as in the standard Anderson localization problem, it is interesting to remark that the statistical properties of T are not those predicted by the standard scaling approach to localization, in particular by the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation [7]. That is, for 1 ≤ α < 2 the transmission fluctuations are larger than those considered in the DMPK equation. Thus, the standard statist...

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“…For instance, since ω/ω 0 = λ 0 /λ, if λ 0 = 2L a typical experiment in the visible range with λ ∼ 500nm and L ∼ 10µ [14,15] will set the ratio ω/ω 0 to 40. Then, θ can be tuned to specify a desired value of T or ln T .…”

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confidence: 99%

Photonic heterostructures with Lévy-type disorder: Statistics of coherent transmission

2012

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“…2(c). This later system has shown to have a wide omnidirectional reflectance [8]. A collection of results for effective PBG is shown in Fig.…”

Section: Model Systems and Simulation Toolmentioning

confidence: 96%

Optical properties of hybrid periodic/quasiregular dielectric multilayers

Escorcia‐García

Duque

2011

Superlattices and Microstructures

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“…Photonic crystals that are composed of one-dimensional (1D) periodic dielectric materials of continuously varying refraction index with defect modes have recently received much attention [1][2][3][4][5][6][7][8][9]. Gradient-index optical materials have been used to fabricate interference filters [1,2] and environment sensors [10], and potential applications such as broadband laser protection eyewear and spectral beam splitter have also been demonstrated [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…Many applications based on 1D photonic crystals are formed by repeating two or more distinct homogeneous dielectric layers with different refraction indices [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]; however, studies on 1D periodic dielectric structures with smoothly varying refraction index are still valuable, because of advantages such as reduced optical losses and better mechanical properties in contrast to discrete multilayer structures [13,[34][35][36][37]. To enlarge the omnidirectional photonic band gap, porous silicon dielectric mirrors formed by a periodic repetition of a Gaussian profile refractive index have been developed [8,9]. Using the glancing angle deposition technique (GLAD), narrow bandpass filters have been fabricated with an introduction of a phase shift defect into a 1D rugate (a sinusoidal variation of the refraction index) photonic structure [2,3].…”

Section: Introductionmentioning

confidence: 99%

Phase Shift Defect Modes in One-Dimensional Asymmetrical Photonic Structures Consisting of Two Rugate Segments With Different Periodicities

Liu¹,

Lu²

2011

PIER

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Abstract-A theoretical study of optical properties of phase shift defects in one-dimensional asymmetrical photonic structures consisting of two rugate segments with different periodicities at both normal and oblique incidence is presented. Using the propagation matrix method we numerically calculated transmittance spectra, defect wavelengths, energy density distributions, and group velocities for TE and TM waves, respectively. Our study shows that by adjusting the periodicity of one rugate segment, the defect wavelengths can be shifted toward either a shorter wavelength or a longer wavelength. The differences of the energy density distributions of TE and TM waves at different angles of incidence are explained with the help of group velocity. Effects of the change of the period of one rugate segment on the peak energy densities of defect modes and minimum group velocities at different angles of incidence are also investigated.

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Omnidirectional photonic bandgaps in porous silicon based mirrors with a Gaussian profile refractive index

Cited by 32 publications

References 18 publications

Photonic heterostructures with Lévy-type disorder: Statistics of coherent transmission

Photonic heterostructures with Lévy-type disorder: Statistics of coherent transmission

Optical properties of hybrid periodic/quasiregular dielectric multilayers

Phase Shift Defect Modes in One-Dimensional Asymmetrical Photonic Structures Consisting of Two Rugate Segments With Different Periodicities

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