Scholarly article on topic 'Guided resonance in negative index photonic crystals: a new approach'

Guided resonance in negative index photonic crystals: a new approach Academic research paper on "Nano-technology"

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Light: Science & Applications
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Academic research paper on topic "Guided resonance in negative index photonic crystals: a new approach"


Light: Science & Applications (2014)3, e120; doi:10.1038/lsa.2014.1 © 2014 CIOMP. All rights reserved 2047-7538/14


Guided resonance in negative index photonic crystals: a new approach

Silvia Romano1, Stefano Cabrini2, Ivo Rendina1 and Vito Mocella1

The behavior of a negative refraction photonic crystal slab irradiated with out-of-plane incident beam is an unexplored subject. In such an experimental configuration, guided mode resonance appears in the reflection spectrum. We show that, in this case, the light coupled inside the photonic crystal is backpropagating. A relationship with the negative index properties is established using a new approach in which the guided resonance is recovered by modeling the photonic crystal layer with a simple Lorentz resonator using the Fresnel reflection formula.

Light: Science & Applications (2014) 3, e120; doi:10.1038/lsa.2014.1; published online 3 January 2014 Keywords: diffraction gratings; guided mode resonance; negative index; photonic crystals


In 1902, Wood observed the presence of narrow bright and dark bands in the reflectivity spectrum of an optical grating. These bands were dependent on the polarization of the incident light, and because they could not be explained by grating theory, they were classified as anomalies.1 This effect was theoretically explained for the first time by Rayleigh2 and then by Hessel and Oliner3 in 1965, who demonstrated that these anomalies in the reflections from gratings were related to the excitation of surface waves on metallic grating structures. Similar resonant anomalies have been observed in various materials with a periodic patterning applied to a surface that can support excitations, such as plasmon polariton resonance or sharp spectral features in shallow grating waveguide structures.4 In particular, the reflection and transmission of an incident wave on a photonic crystal (PhC) slab can produce sharp resonance in the spectrum when the radiation is coupled with the modes of the structure.5-7 Guided mode resonance has been well studied in the photonic crystal literature. Due to the extremely narrow shape of the resonance when superposed on the background reflection, guided mode resonances can be used to design optical bandpass filters with elevated symmetrical responses and low side-bands8,9 or distributed feedback lasers with a high Q factor.10 Moreover, the confinement of the optical field within the slab can be used to trap11 single particles or to enhance signals from fluorescent elements, thus enabling high-sensitivity sensors.12 In this paper, we reveal novel insight into the reflectivity properties of a negative refraction photonic crystal slab. In particular, by studying a hexagonal airhole lattice in silicon, we highlight that the out-of-plane incoming radiation is negatively refracted in the structure. While the in-plane properties of negative refraction in a photonic crystal slab have been studied over the last years,13-20 this is the first experimental demonstration of negative refraction detected out-of-plane. In particular, we provide imaging of the radiation coupled into a photonic crystal slab

when the resonance occurs. Using an infrared camera, we were able to visualize the interaction between the incident light and backpropagat-ing coupled radiation. In addition, we propose a new theoretical approach to the guided resonance phenomenon, based on the Fresnel formula, which shows very good agreement with the experimental data and which completes the usually adopted phenomeno-logical model21-23 in the context of the Fano resonance approach.


Guided mode resonance arises from resonant coupling between external radiation and the modes of a photonic crystal slab and is manifest as a spike in the reflectivity signal.5,7 The model widely used in the literature for the analysis of guided resonance is derived from phenomenological considerations based on a line shape analysis of the resonance. Indeed, a typical guided-mode reflection spectrum can be considered as an example of the Fano resonance phenomenon, which appears in the optical transmission and reflection spectra of a wide variety of structures, such as metallic or dielectric gratings.21-23 In this case, the spectrum consists of an overlapping between a Lorentz resonance shape and a Fabry-Perot background. However, this simple fit approach cannot provide information about the origin of the coupling process between the external radiation and the photonic crystal structure. In Ref. 24, we experimentally demonstrated that, in the range of negative effective refractive indices, a photonic crystal can be modeled as a Lorentz resonator and can exhibit plasmon-like material beha-vior.25 Therefore, we assume that the PhC slab can be described by a dielectric function given by a simple Lorentz function:

«2 — v2 Z iyv

XCNR-IMM-Unita di Napoli, 80131 Napoli, Italy and 2Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA, USA Correspondence: Dr V Mocella, CNR-IMM-Unita di Napoli, Via P. Castellino 111, 80131 Napoli, Italy


Received 4 June 2013; revised 19 July 2013; accepted 7 August 2013

Figure 1 Schematic view of the experimental set-up used to couple laser light (tunable diode laser, 1520-1620 nm) into the photonic crystal. The inset shows an AFM image of the photonic crystal sample. Please note that the shape of the holes results from the AFM probe effect. AFM, atomic force microscopy; L, lens; P, polarizer; PD, photodiode.

Illuminated silicon

0.15 mm

0.5 mm

0.5 mm c Illuminated silicon

In resonance Out of resonance

0.15 mm

Illuminated silicon

A A . l»r *. m * *

In resonance Out of resonance

Figure 2 Sketches of the IR camera positions (a, d)and infrared images of the illuminated SOI region when resonance occurs (b, e). Comparison between IR images in the resonance condition (1= 1588 nm and 0=65°) and in the out-of-resonance condition (1= 1592 nm and 0=650 acquired in front of the sample (c) and from the lateral side (f). The red circle indicates the spot at which the laser is incident on the sample. IR, infrared; SOI, silicon-on-insulator.

where e is the dielectric constant, v0 is the resonant frequency and y is the damping constant. In this way, the resonator behavior is inherent to the material, and the PhC is described as a homogenous material with e(v) given by Equation (1). In such a case, we can use the usual Fresnel relations to study the features of guided resonance in the reflectivity spectrum. For a three-layer system of dielectric 1/photonic crystal/dielectric 3, the reflectivity R for p-polarized light is given by Raether4

R=\rp \2 =

rp Zrp exp(2ikz2d)

1 + rp rp exp(2ikz2d) with the reflection coefficients given by

rp ej kzi e i kzj i ejkzi z eikzj

and the wave vector components along z axis defined as

kzi —

/ V2 V2

T'V - v

-— sin2 e

The photonic crystal sample is a slab composed of a hexagonal lattice with a thickness of 0.7 mm, as shown in Figure 1. The photonic lattice was obtained using a high-precision nanofabrication process based on high-voltage electron beam lithography and a gas chopping inductively coupled plasma etching process, which alternates an etching step using SF6 and Ar with a passivation step using CHF3 and CH4. Starting with a silicon-on-insulator (SOI) wafer (1.5 mm silicon layer on top of a 1 mm oxide layer), we spin on ZEP 520, a positive electron beam resist, at a thickness of 370 nm. The resist is patterned using a Vistec VB300UHR EWF electron-beam lithography system and is developed with n-amyl acetate. The electron beam-patterned resist is used as a mask to etch the underlying silicon layer, down to the SOI, in an Oxford Plasmalab 100 ICP-RIE with a resist mask. The SF6 chemistry provides the free radicals for isotropic Si etching, while O2 promotes the growth (at cryogenic temperatures) of a passivation film. This passivation film, with a generic temperature-sensitive formula of Si^F^O^, protects the side walls of the etched structures and evaporates after the sample warms to room temperature, leaving behind a clean surface. The etching was performed at —120 °C. The resulting pattern is formed of cylindrical air holes, and the device is characterized by a lattice constant a=472 nm, a hole radius r=0.385a and an area of 1X1 mm2. The ratio r/a=0.385 guarantees the condition of a negative index medium """ v0.14-18,20,25,26 In this case, the photonic crystal behaves as a medium with an effective iso-tropic index neff= — 1 for a wavelength of 1.55 mm. Experimental reflectivity spectra from the photonic crystal sample were obtained using a tunable CW diode laser (Ando AQ4321D) that emits monochromatic light with a maximum variable power of 5 mW and a wavelength varying between 1520 nm and 1620 nm. Because the guided mode resonance is polarization-dependent,5,7 the radiation is linearly polarized and is then focused at the top surface of the sample. The light reflected from the sample is polarized again and is detected by a photodiode (Thorlabs high-speed InGaAs DET410). The incidence angle was varied from 40° to 75°. The experimental set-up is schematized in Figure 1.

occurs. This resonance has only been observed for p-polarization, i.e., with the electric field vector parallel to the incident plane. Although guided resonance has been studied for many years, there have been no experimental reports concerning the propagation of coupled light through the photonic crystal, and there is a gap in research on which modes are excited inside the structure. Whenever coupling occurs, we assume that the radiation propagates through the photonic crystal and can be detected by the out-of-plane scattering from the surface. Figure 2 shows infrared (IR) images of the radiation coupled into the structure under resonance conditions (1=1588 nm and h=65°) acquired from front of the slab and the lateral side. Surprisingly, the radiation propagates for a few millimeters into the photonic crystal. In correspondence to the guided resonance, the light passes through the entire photonic crystal (1X1 mm2), passes through the adjacent SOI planar waveguide (approximately 1 mm in length) and is then scattered at the end of the SOI region due to the irregularities of the surface, illuminating the whole perimeter of the right SOI region, as shown in Figure 2b and 2e. When the wavelength is changed to be slightly out of resonance (1= 1591 nm), the light does not couple with the structure and the SOI perimeter is no longer illuminated (see Figure 2c and 2f for a comparison of the resonance and out-of-resonance conditions). Interestingly, backpropaga-tion of the coupled radiation was observed, which can be related to the negative index behavior of the photonic crystal under consideration. This effect was confirmed by placing an IR camera on the positive refraction side of the device, where no radiation was detected. Rigorous coupled wave approach simulations provided further information regarding this phenomenon. The calculated time-averaged Poynting vector inverts its direction while crossing the photonic crystal

Reflected beam

Incident beam 0

'Guided resonance

Photonic crystal


- 7---7---7~

Photonic crystal surface


S \ \ \ \ \ \


As previously illustrated, a sharp peak appears in the reflection spectrum when coupling between the incident radiation and a guided mode

Figure 3 (a) A sketch of the incident, reflected and guided beams. (b) The calculated time-averaged Poynting vector in a 60x60-nm2 area in the x-zplane, crossing the PhC surface under the resonance conditions. PhC, photonic crystal.

interface within a few tens of we validate our new theoreti mental spectrum with the Fr shows excellent agreement wi in Figure 4a. The fitte< y=-1.5X10n s, £'=12 in tl 0565°. These parameters rem excepting for the resonant fr

S Romano

nanometers, as shown in Figure 3. Fin :al approach by directly fitting the exp isnel formula (2). The calculated fit c th the experimental spectrum, as repo I Lorentz parameters are /=0.0 ie resonance condition, 10=1588 nm ain the same as the incident angle chan

rongly correlated with a resonant effe case, can be modeled with a Lorent estimated the experimental quality fa e order of 103, which is among the hig ned for a PhC slab. In addition, by var iflectivity spectrum, we calculated the b stal.5,7 In Figure 4b, the measured dis face modes as a function of the in-p )nce again, the measured values (squa ith the simulated dispersion curve (tr ous coupled wave approach. These va ulated and measured group velocity of rector, kp. Indeed, from Figure 4b, we

sion characteristics of the su


22 Fan S, Suh W, Joannopoulos JD. Temporal coupled-mode theory for the Fano resonance in optical resonators. J Opt Soc Am A 2003; 20: 569-572.

23 Miroshnichenko A, Flach S, Kivshar YS. Fano resonances in nanoscalestructures. Rev Mod Phys 2010; 82, 2257-2298.

24 Dardano P, Gagliardi M, Rendina I, Cabrini S, Mocella V. Ellipsometric determination of permittivity in a negative index photonic crystal metamaterial. Ligh SciAppl2012; 1: e42. doi:10.1038/lsa.2012.42.

25 De Tommasi E, De Luca AC, Cabrini S, Rendina I, Romano S et al. Plasmon-like surface states in negative refractive index photonic crystals. Appl Phys Lett 2013; 102: 081113.

26 Chatterjee R, Panoiu NC, Liu K, Dios Z, Yu MB etal. Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range. Phys Rev Lett 2008; 100: 187401.

27 Vynck K, Felbacq D, Centeno E, Cabuz AI, Cassagne D et al. All-dielectric rod-type metamaterials at optical frequencies. Phys Rev Lett 2009; 102: 133901.

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