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The performance of infrared (IR) dual-band detector can be substantially improved by simultaneously increasing IR absorptions for both sensor bands. Currently available methods only provide absorption enhancement for single spectral band, but not for the dual-band. The Fabry-Perot (FP) cavity generates a series of resonances in multispectral bands. With this flexibility, we introduced a novel type of dual-band detector structure containing a multilayer FP cavity with two absorbing layers and a subwavelength-period grating mirror, which is capable of simultaneously enhancing the middle wave infrared (MWIR) and the long wave infrared (LWIR) detection. Compared with the bare-absorption-layer detector (common dual-band detector), the optimized FP cavity can provide about 13 times and 17 times absorption enhancement in LWIR and MWIR bands respectively.
©2011 Optical Society of America
1. Introduction
Infrared (IR) dual-band detectors [1]can support simultaneous detection of signals in the two IR transmitting windows, i.e., the middle wave infrared (MWIR, 3 to 5μm) and long wave infrared (LWIR, 8 to 12μm) windows. Compared with the traditional single-band IR detector, the dual-band ones may have better image contrast, longer detecting distance, and higher spatial resolution for target discrimination, benefiting from the increased target information obtained from the two windows [2]. Dual-band detection in the MWIR and LWIR atmospheric windows is a highly desirable technology in a number of applications such as environmental monitoring, missile warning and guidance, night vision, target detection and tracking, etc [3]. However, the complicated lens of the traditional dual-band systems usually have ten or more surfaces and use a selection of high to low refractive index lens materials, making the IR signal on the detector much weaker [4] and thus resulting in a relatively low responsivity and detectivity.
Optimized resonators with enhanced optical field in their cavities can be used to achieve strong enhancement of optical absorption. Conventional resonators utilizing dielectric photonic crystals (PCs) [5,6], deep-etched plasmonic PCs [7], and Fabry-Perot (FP) cavities with distributed Bragg reflectors (DBRs) [8] have been employed to improve the performance of IR detectors. In order to obtain the cavities of PCs, detectors equipped with PCs will have some part of active material etched off and this sacrifice may eventually affect the absorption enhancement factor. FP cavities with DBRs, usually consists of alternate quarter wave optical thickness dielectric layers with low and high refractive index. To achieve enough reflectance (>80%), a very thick DBR (stack number >15) has to be fabricated. In addition, these previously reported resonators are all designed for the single band. Resonators which provide simultaneous enhancements of the radiation absorptions for the IR dual-bands are still lacking.
In this paper, a MWIR&LWIR dual-band detector equipped with FP resonator with metallic subwavelength grating is proposed. With the designed FP resonator, multispectral resonant standing waves are established inside the cavity. By placing the MWIR and LWIR active layer each at the location where their corresponding standing wave antinodes are located, the absorption can then be enhanced by a factor of 17 and 13 times in the MWIR and LWIR bands, respectively, compared to the dual-band detectors without FP resonator. With the absorption enhancements and spectral selectivity provided by the FP resonator, the proposed dual-band detector may be used to detect combustible, toxic or environmental harmful gases [9], such as CH4, CO, C2H6 (MWIR absorptions), and SF6, SO2F2 (LWIR absorptions).
2. Resonance modes in the F-P cavity
The F-P cavity was first proposed in 1899 by Fabry and Perot [10]. The cavity consists of two optically thin metal films which are separated by a dielectric slab (shown in Fig. 1 .). When the FP cavity is designed for dual-band absorption, its two characteristic features, i.e., the multiple resonances and the standing-wave field distribution, are utilized.
Fig. 1 Schematic of the F-P multiple interference. The F-P cavity has a cavity length of l, two identical metal films of thickness of t. and a dielectric slab with refractive index n sandwiched between the two metal films.
Under normal incidence, i.e., i = 0, the FP resonant wavelength is determined as
where λN is the wavelength of the Nth resonance, n is the refractive index, and l is the thickness of the medium separating the two metal films. From the Eq. (1), we know that when the optical distance between the two reflecting faces nl equals an integer number of half wavelengths, the given FP cavity can then support a series of individual resonant wavelengths which may cover multiple spectral bands.Suppose a wave with its electric field vector parallel to the y axis being normally incident upon the FP cavity. Then between the two metal films, a standing-wave field is established by the interference of the oppositely propagating waves. Since the electric field experiences a π phase change on reflection [11], the downward and upward propagating waves have the form
where ω = 2πc/λ, k = 2π/λ and is the unit vector directed along the y axis. Then the synthesis wave inside the cavity iswith . With highly reflective metal films, ΔE can be quite small and the standing wave dominates inside the cavity. As can be seen from the Eq. (3), the amplitude of the standing wave is z-dependent. The antinodes (amplitude maxima) occur whenFrom Eqs. (1) and (4), we can predict the number of antinodes and their corresponding positions inside the cavity for resonances of different orders. For example, for the fundamental (N = 1), second-order (N = 2) and third-order (N = 3) F-P resonance modes, the standing-wave fields have one, two, and there antinodes, respectively, which are located at z = l/2 (for N = 1), z = l/4, 3l/4 (for N = 2) and z = l/6, l/2, 5l/6 (for N = 3).Let’s consider an FP cavity consisting of two silver films with t = 20nm and separated by an air slab with l = 400nm. The cavity is illuminated by a normally incident wave with its electric field vector parallel to the y axis. The transmittance spectrum of the FP cavity and the standing-wave field distributions (of Ey) for the fundamental, second-order and third-order resonances are calculated by using the rigorous theory, as shown in Fig. 2 . It is seen that the number of antinodes and their positions agree well with our predictions. Furthermore, although the fundamental mode at λ1 = 877nm and the third-order mode at λ3 = 285nm belong to different spectral bands, their field distributions both have an antinode at the center of the cavity (as seen form Figs. 2(b) and 2(d)). This implies that the dual-band absorption may be enhanced simultaneously, if we place the lossy dielectric material at the center of the F-P cavity.
Fig. 2 Numerically calculated (a) spectral transmittance of the FP cavity and the Ey field distribution of the (b) fundamental, (c) second-order and (d) third-order resonance modes.
3. F-P cavity designed for the IR dual-band absorption enhancement
The design of any FP cavity relies on the use of a pair of highly reflective elements which are substantially separated so as to generate multiple resonances. In the visible, this can be achieved by just using the two thin metal films (as seen from Fig. 1). However, unlike visible region, a pair of metal films seems unsuitable to be used in the LWIR spectral region, because they may bring higher absorption losses within the conducting layers at these wavelengths [12]. One way of reducing the absorption loss is to replace the top metal film with the 1D or more generally the 2D (for unpolarized radiation) subwavelength metallic grating. On condition that the period of the grating is much smaller than the incident wavelengths, the metallic grating can provide a high IR reflectance without incurring the absorption loss afflicting the traditional FP cavity design.
In order to achieve simultaneous absorption enhancement in both the MWIR and LWIR bands, the designed FP cavity must generate resonances that fall into these two spectral bands. Additionally, since the MWIR and LWIR active layers are usually separated inside the infrared dual-band detector [13], the antinodes of the two resonances should appear accordingly with these active layers, facilitating the simultaneous absorption. The proposed FP resonator with metallic subwavelength grating is schematically presented in Fig. 3(a) . The two absorption layers are placed separately in the cavity so that one would absorb primarily LWIR radiation and the other MWIR. Suppose that the incident LWIR and MWIR intensities are I_{LW} and I_{MW}, so that the total intensity is
The purpose of the dual-band detector is to measure I_{LW} and I_{MW}, or at least the ratio I_{LW}/ I_{MW}. We then have detector 1and detector 2, which are nominally the LWIR and MWIR absorption layer, respectively. These detectors give measurable signals S_1 and S_2. The absorption pies from Fig. 5 (discussed later) indicate that detectors 1 and 2 measure both LWIR and MWIR intensities. The fractions are readily obtained from the pies: if we denote them by F_{1LW}, F_{1MW}, F_{2LW}, and F_{2MW}, the signals are As long as there is a clear difference between the fractions F, so that the determinant of the matrix defined by Eqs. (6) and (7) is nonzero, which means that the two unknowns I_{LW} and I_{MW} can be solved respectively.Fig. 3 (a) Schematic of the designed F-P cavity and (b) its spectral response under normal incidence
Fig. 5 Absorption pie for (a) LWIR resonant wavelength (λ1 = 9.9μm) and (b) MWIR resonant wavelength (λ4 = 3.77μm).
Used as the top reflective element, a shallow etched (~100nm) Au grating is designed on the top metal layer of the detector. This design does not introduce any etching damage to the detector material and can be used with any detector system. A Si based dual-band detector [14] with the IR responses caused by band to band transitions is employed in the design. The top Au grating should have a period smaller than the incident wavelength, i.e., d = 2μm, such that the unwanted nonzero diffraction orders are excluded. Since the period of grating is chosen smaller than the incident wavelength, the grating layer can then considered as a dielectric layer [15] with its refractive index or reflectance tuned by the filling factor f. For the MWIR&LWIR bands, the average reflectance of Au grating is 54.36%, 83.48%, and 95.59% with f = 0.1, 0.3, 0.5, respectively. By choosing f to be 0.3, which means less metal is filled on the top of the cavity, the grating can then provide enough reflectance (>80%) without much radiation absorbed in the grating layer. Between the Au grating and Au film, IR transparent material GaAs layer and lossy Si layer are stacked alternatively. The thickness of each layer is optimized numerically so as to generate both MWIR and LWIR resonance modes in the cavity. The position of each layer is also carefully arranged so that the antinodes of the MWIR and LWIR resonance fields must precisely access to their corresponding absorption layers. For the optimized FP cavity with t1 = t7 = 0.1μm, t2 = 0.35μm, t3 = 0.45μm, t4 = 0.1μm, t5 = 0.25μm, and t6 = 0.2μm, its spectral response under normal incidence is calculated by using the Fourier Mode Method (FMM) [16]. As can be seen from Fig. 3(b), the designed FP resonator generates altogether five resonances at λ1 = 9.9μm, λ2 = 5.4μm, λ3 = 4.78μm, λ4 = 3.77μm and λ5 = 3.16μm within the wavelength range of 3~12μm. The fundamental resonance falls into the LWIR region, while the third-order, fourth-order and fifth-order resonances appear in the MWIR region.
In an FP cavity, in general, the positions of antinodes of an odd-order resonance differ from those of an even-order resonance (demonstrated in Fig. 2). Accordingly, the LWIR absorption layer is placed where the antinodes of the fundamental resonance (at λ1 = 9.9μm) would appear, while the MWIR absorption layer is placed with respect to the fourth-order resonance (at λ4 = 3.77μm). To determine the field distribution of the resonant mode, FMM is applied again. First, the fields in the grating and cavity (homogeneous) regions are described by expansions as a Fourier series according to the periodicity of the grating profile and Rayleigh expansions, respectively. Then the Helmholtz equation is expanded according to the Fourier series representation, leading to a set of coupled differential equations. The fields are finally determined by solving the these equations. The calculated field distributions of the fundamental mode and the fourth-order mode inside the FP cavity are shown in Figs. 4(a) and 4(b), respectively. For the fundamental resonance, there is only one antinode appearing in the FP cavity and the majority of the field is confined in the LWIR absorption layer. For the fourth-order resonance, more than one antinodes exist in the FP cavity and among them, the one with the maximum amplitude is located in the area where the MWIR absorption layer is placed. Hence, with the antinodes of the LWIR and MWIR resonance fields being confined in their corresponding absorption layers, the dual-band absorption can be enhanced simultaneously.
Fig. 4 The field distribution of (a) the fundamental resonance with λ1 = 9.9μm and the fourth resonance with λ4 = 3.77μm inside the FP cavity. The white color pillars stand for metallic ridges and the dotted grey lines mark the areas where LWIR or MWIR absorption layer is placed.
The absorption in different layers (shown in Fig. 5) and the absorption enhancement factor for the dual-band are calculated. At normal incidence, the LWIR and MWIR absorption layers take 46.69% and 48.34% of the total absorption at resonance wavelength λ1 = 9.9μm and λ4 = 3.77μm, respectively. Compared with the bare absorption layer (without Au grating and Au film), the designed FP resonator provides an absorption enhancement factor of 13 and 17 times for the LWIR and MWIR bands, respectively.
4. Fabrication considerations
As presented in Fig. 3(a), the GaAs and Si layers are stacked alternatively inside the FP cavity. Therefore, it is needed to grow semiconductor layers one after another from the bottom to top. However, since gold film is not lattice matched to GaAs, GaAs layer cannot be directly grown on the gold surface [17]. So we may first choose a substrate material that is lattice matched to GaAs and then remove the substrate after epitaxy. Thus, the Au film (bottom reflector) can be deposited at the bottom of the structure. This process sounds quite challenging but not impossible. Another possible way is to find an alternative to the Au film. Semiconductor film stack (which of course should be lattice matched to GaAs) consisting of alternate high and low refractive index materials can serve as achromatic highly reflective element, which can replace the Au film. Then we can grow GaAs directly on the semiconductor stack without removing the substrate. Of course high reflectance requires a large number of films in the stack with accurate thickness control, which can be realized by the modern coating technology.
Compared with the growth of semiconductor materials, the fabrication of the subwavelength grating is much easier. Since the resonance is mainly determined by the optical length in the FP cavity and the subwavelength metallic grating serves more as a reflecting element, the tolerances of the grating parameters are therefore not so tight. The grating is designed with the depth tolerance better than 10nm, and the period tolerance better than 5nm. Within these tolerances, the relative resonance shift will be controlled below 1%.
5. Conclusion
In this paper, we have demonstrated a design of FP resonator with a subwavelength metallic grating serving as the reflecting element. The multiple resonances and their corresponding resonant fields in the FP cavity were analyzed numerically. With the optimized FP cavity, the absorption can be enhanced by a factor of 17 and 13 times in the MWIR and LWIR bands, respectively. Apart from absorption enhancement, the designed FP resonator also provides spectral selectivity for the dual-band detector, which can be used for the gas detection in the future.
Acknowledgement
This work was supported by the Academy of Finland (Project No. 129155 and Project No. 128420) and the National Basic Research Program of China under Grant No 2007CB935303.
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