Physics and applications of photonic crystals

doi:10.1016/j.photonics.2004.08.001

Photonics and Nanostructures - Fundamentals and Applications

Volume 2, Issue 2, October 2004, Pages 87-95

https://doi.org/10.1016/j.photonics.2004.08.001 Get rights and content

Abstract

In this article, we investigate how the photonic band gaps and the variety of band dispersions of photonic crystals can be utilized for various applications and how they further give rise to completely novel optical phenomena. The enhancement of spontaneous emission through coupled cavity waveguides in a one-dimensional silicon nitride photonic microcrystal is investigated. We then present the highly directive radiation from sources embedded in two-dimensional photonic crystals. The manifestation of novel and intriguing optical properties of photonic crystals are exemplified experimentally by the negative refraction and the focusing of electromagnetic waves through a photonic crystal slab with subwavelength resolution.

Introduction

It is amazing that a simple analogy between an electron in a semiconductor crystal (periodic arrangement of atomic potentials) and a photon in a periodically modulated dielectric medium can reveal so enormously rich and novel electromagnetic (EM) phenomena [1], [2]. Photonic crystals (PCs), as we call them now, are periodic dielectric, or metallic structures, which possess a variety of band dispersions, and band gaps, where the propagation is prohibited for certain ranges of wavelengths. Using different materials (i.e., different dielectric constants) and by adjusting geometrical parameters, the propagation of light can be modified virtually in any way in a controllable manner. Furthermore, the scale invariant nature of the governing Maxwell's equations enables the study of electromagnetic phenomena in the first place, without being held back by structural complexities. A similar advantage is also present from a dimensionality point of view; that is, the lack of confinement in spatial directions in 2D or 1D PC structures does not hinder the investigation of certain EM phenomena. Having said this, keeping the structural uniformity while scaling the PCs down to optical wavelengths is still a challenging problem, especially in three-dimensions (3D). Numerous fabrication techniques are investigated in the last decade, such as alternating layer deposition and etching process for 3D PCs [3], and electron lithography in combination with dry etching for 2D AlGaAs PCs [4]. The investigation of PCs was quickly spread over a wide range of photonics applications in the last decade, gearing towards micro- and nanoscale to be used in telecommunication and optical wavelengths [5], [6], [7], [8], [9].

In this paper, we aim to provide a brief review of certain physical properties and applications of PCs. The paper is organized as follows: First, we consider the optical properties of coupled micro-cavity waveguide (CMCW) structures in 1D PCs and the enhancement of the spontaneous emission. Next, we discuss how a 2D PC can be utilized to obtain a highly directive radiation from embedded sources. The last section is devoted to the experimental demonstration and simulation of a completely novel optical phenomenon, namely the negative refraction, and subwavelength focusing through a 2D PC slab.

Section snippets

Coupled cavity waveguides in 1D photonic microcrystals and the enhancement of spontaneous emission

Many optical applications demand the ability to control the spontaneous emission for inhibition or enhancement. Fermi's Golden Rule states that the spontaneous emission rate is directly proportional to the photon density of modes, $Γ_{s} \sim ρ (ω) \sim v_{g}^{- 1}$ . By introducing a defect into a PC structure, a highly localized mode inside the photonic band gap appears, where the density of photon modes can be altered locally [10], [11], analogous to the impurity states in a semiconductor band gap [12]. The

Highly directive radiation from photonic crystals hosting embedded sources

In this section, we present an experimental and theoretical study of the angular distribution of the radiation emitted from a source embedded in a 2D PC. The spatial confinement of the radiation emitted by sources is highly desirable for certain antenna applications. Several studies are reported, which employ PCs for the confinement of the radiation as a cover to the source [22], [23], [24], or the source being embedded inside the PC [25], [26]. By adjusting the geometrical parameters of the PC

Negative refraction and point focusing using a photonic crystal superlens

The previous two sections can be considered as examples of the improvement of existing optical processes by utilizing the optical properties of PCs. However, there is more that the PCs can provide. In this section, we consider some examples of the novel optical phenomena that have become accessible by the PCs.

In 1960, Veselago [28] proposed and investigated the electrodynamics in a medium possessing negative index of refraction. Almost four decades after its introduction, the realization idea

Conclusions

In this article we presented certain optical properties of PC structures. The improvement of existing optical applications by PCs is exemplified by the enhancement of spontaneous emission through a PC-based coupled micro-cavity waveguide, and by the exceptionally directive radiation from an omnidirectional source embedded in a PC. We then discussed a novel and unusual optical phenomenon observed in PCs, namely the negative refraction. This phenomenon may lead to optical applications such as

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Increased density of states at the band edge of photonic crystals exhibited to show interesting properties such as band edge lasing [11–13], enhanced photoluminescence in a microcavity [3], defect mode lasing [14–16]. The modification of spontaneous emission features from a 1D PC near the photonic band edge has been observed in periodic AlAs/AlGaAs structures with a GaAs emitting layer [17], in liquid-crystal Bragg structures [13], and in Bragg structures based on amorphous nitrides and silicon oxide [18]. If we focalize our attention on Er3+ doped systems, the spontaneous emission from erbium ions was modified by the behavior of the density of states at the lower photonic band edge in Photonic Band Gap (PBG) structures consisting of alternating a-Si:H/a-SiOx:H layers [19].
All Er³⁺ doped dielectric 1-D Photonic Band Gap Structure was fabricated by rf-sputtering technique. The structure was constituted by of twenty pairs of SiO_2/TiO₂ alternated layers doped with Er³⁺ ions. The scanning electron microscopy was used to check the morphology of the structure. Transmission measurements put in evidence the stop band in the range 1500 nm–1950 nm. The photoluminescence measurements were obtained by optically exciting the sample and detecting the emitted light in the 1.5 μm region at different detection angles. Luminescence spectra and luminescence decay curves put in evidence that the presence of the stop band modify the emission features of the Er³⁺ ions.
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This PBG is similar to the electronic band gap in crystalline semiconductors and this is due to the analogy of the propagation of photons and electrons respectively in the photonic structure and the semiconductors which are governed by Shrödinger and Maxwell equations [5]. Photonic crystal have been from 1987 the subject of intensive research because their attractivity in many applications which require special localisation of light such as waveguides, multiplexers… [6] and can initiate new research field, as plasma [7,8] and superconductor photonic crystals [9], metamaterial devices. The introduction of defect in a photonic crystal breaks the periodicity for the dielectric constant and allows the appearance of a transmission band in the PBG.
Hybrid inorganic/organic one dimensional photonic crystal based on alternating layers of Si/HMDSO is elaborated. The inorganic silicon is deposited by radiofrequency magnetron sputtering and the organic HMDSO is deposited by PECVD technique. As the Si refractive index is n = 3.4, and the refractive index of HMDSO layer depend on the deposition conditions, to get a photonic crystal with high and low refractive index presenting a good contrast, we have varied the radiofrequency power of PECVD process to obtain HMDSO layer with low refractive index (n = 1.45). Photonic band gap of this hybrid structure is obtained from the transmission and reflection spectra and appears after 9 alternative layers of Si/HMDSO. The introduction of defects in our photonic crystal leads to the emergence of localized modes within the photonic band gap. Our results are interpreted by using a theoretical model based on transfer matrix.
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Two dimensional photonic crystal slabs with elliptical holes exposed to the normal incident laser light are proposed and designed as a tunable broadband polarization rotator. The photonic crystal electric field mode due to the eccentricity and orientation of the holes will provide a mean to exchange power between two orthogonal polarization states. Around guided resonance wavelengths of photonic crystals with 45° oriented elliptical holes, 20% polarization mode conversion is achieved. By tuning of the difference of the two radii of the elliptical holes we are able to span a bandwidth of 130 nm and 70 nm around wavelengths of 1445 nm and 1650 nm. The unique properties of these devices such as ease of engineering and simplified light coupling scheme will make them a promising polarization mode converter in high speed polarization-multiplexed optical transmission systems.
Experimental evidence of the photonic band gap in hybrid one-dimensional photonic crystal based on a mixture of (HMDSO, O<inf>2</inf>)
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This periodicity varies on one, two or three dimensions (1D, 2D, 3D) [2] and can induce a photonic band gap where photon propagation is prohibited and it is defined as a frequency region characterized by zero density of the electromagnetic states [3,4]. These structures, also called photonic band gap materials [5], are attractive in many applications which require spacial localization of light [2,6]. The propagation of photons in the PCs is similar to the propagation of electrons in crystalline semiconductors, and a photonic band gap created in PCs similar to the electronic band gap in crystalline semiconductors [7,8].
Hybrid One-dimensional photonic crystal coated from a mixture of an organic compound (HMDSO) and oxygen (O₂) is elaborated by PECVD technique. The originality of the method consists in obtaining layers of different permittivity with the same gas mixture, but with different flow. The change in flow is optimized to obtain organic/inorganic layers of good quality with high and low refractive index of 2.1 and 1.4 corresponding respectively to HMDSO and SiO₂ materials as assigned by IR measurement. Evidence of the photonic band gap is obtained by measuring the transmissions and reflections spectra which show that it appears only after 13 periods with a width of 325 nm corresponding to energy 3.8 eV. We have also introduced a defect in this photonic structure by changing the thickness of central layer, and observed the presence of a frequency mode corresponding to this defect. Our results are interpreted by using a theoretical model based on transfer matrix wich well reproduced the experimental data.
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In this study, we analyze the tunability of complete photonic band gap of square and triangular photonic crystal slabs composed of square and hexagonal air holes in anisotropic tellurium background with SiO₂ as cladding material. The non-circular holes are infiltrated with liquid crystal. Using the supercell method based on plane wave expansion, we study the variation of complete band gap by changing the optical axis orientation of liquid crystal. Our numerical results show that noticeable tunability of complete photonic band gap can be obtained in both square and triangular structures with non-circular holes.
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Geometrical, electronic and nonlinear optical (NLO) properties of several alkali metal doped boron nitride nanocages (MB₁₂N₁₁ and MB₁₁N₁₂) are explored theoretically. NLO (Non Linear Optical) properties are obtained through first hyperpolarizability, and rationalized on the basis of dipole moment change during excitation to crucial transition state, and band gap. It is revealed that first hyperpolarizability (β₀) is increased to a larger extent (1.3 × 10⁴ au for KB₁₂N₁₁) in doped boron nitride nanocages as compared to pure B₁₂N₁₂ (0 au). MB₁₂N₁₁ nanocages show an increasing trend of β₀ and β_vec with increase in atomic number of alkali metal, in contrast, MB₁₁N₁₂ nanocages show unmonotonic dependency. Further, HOMO-LUMO gap is lowered significantly since a new level is introduced near Fermi level in all doped structures. All the doped structures show n-type semiconductor properties due to diffuse excess electrons in the system which give rise to new HOMO. The present idea offers potential application of these nanocages in new kind of electronic devices and is helpful in designing novel high-performance NLO materials.

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Physics and applications of photonic crystals

Abstract

Introduction

Section snippets

Coupled cavity waveguides in 1D photonic microcrystals and the enhancement of spontaneous emission

Highly directive radiation from photonic crystals hosting embedded sources

Negative refraction and point focusing using a photonic crystal superlens

Conclusions

Photonic Crystals: Molding the Flow of Light

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