High rejection bandpass optical filters based on sub-wavelength metal patch arrays

J. Le Perchec; R. Espiau de Lamaestre; M. Brun; N. Rochat; O. Gravrand; G. Badano; J. Hazart; S. Nicoletti

doi:10.1364/OE.19.015720

1. Introduction

Metals based filters have been extensively considered for filtering applications from the microwave regime to the visible spectral range. Transmission optical filters may be achieved by well designed multi-layered stacks [1] or Fabry-Perot cavities [2, 3]. The latter provide a tunable quality factor, high transmission levels, but at the cost of the adjustment of the working wavelength by the thickness or index profile of the system. This precludes their convenient technological integration in imaging systems for color reconstruction or hyperspectral imaging. On the other hand, transmission of electromagnetic waves may occur through thin metal planes presenting periodic patterns and called Frequency Selective Surfaces [4]. For periods below the wavelength, those surfaces are referred to as capacitive or inductive grids, with respectively lowpass or highpass behavior [5, 6], but can also serves as bandpass filters [7, 8]. Periodic sub-wavelength metallic structures like hole arrays [9, 10] or crosshaped ones [11, 12] and slit gratings [13–15] have been studied and offer a higher compacity suitable for integration within imaging systems [16, 17]. Moreover, their resonant transmission properties can be tuned by sizing their diffracting features. For example, arrangement based on cavity plasmon modes in stacked metal lattices [18–20] or free-standing gratings [21] showed interesting responses, albeit their technological fabrication remains rather tricky compared to the state-of-the art multilayered filters. Those structures often fail in obtaining well behaved spectral lineshapes, especially regarding rejection out of the resonant transmission and angular sensitivity. A recurrent issue for the use of metallic filters in applications is therefore the need for a combination of a fine spectral bandwidth (i.e. lower than a tenth of the wavelength to transmit), high transmission (> 50%), high rejection of light out of the pass-band (> 10dB) and, if possible, insensitivity to light polarization and incident angle. In this paper, we focus us on an electromagnetic structure merging photonic modes and surface wave ones in a suitable manner. Dielectric loading of periodic metal arrays has been know for a long time in the microwave regime [22, 23]. In particular, a proper design of the dielectric thickness is proved to reduce the change in linewidth and shift of resonant frequency with increasing incidence angle [22]. Fine linewidth, high rejection and transmission peak are therefore predicted and observed. The principle is to use guided-mode resonance effects in dielectric waveguide-metal grating structure. The aim is not only to resonantly couple light in the waveguide, but to exploit strong radiation leak of the latter as a transmission signal. In the optical regime however, the literature is scarce on dielectric loading of periodic metal arrays [24–26]. Moreover, scaling down the structure as the wavelength is decreased to the IR range requires higher technological fabrication process control, over suitable substrate.

In this paper, we numerically and experimentally show how dielectric loading of metal patch arrays help addressing the following combination of filtering properties, in the optical range: (i) a high transmission of light (at least > 50%) at a given wavelength λ ₀, and that, independently of the polarization and incidence angle; (ii) a narrow pass-band centered on λ ₀ whose mid-height spectral width can be easily tuned (typically of the order of λ ₀/20); and (iii) a very high rejection of light out of the pass-band over a broad spectral range (typically, rejection > 10dB over the minimal interval [3λ ₀/4; 5λ ₀/4]). The studied filter relies on the generic photonic structure shown in Fig. 1 which can meet all the requirements listed above. It consists in a very thin grating of sub-wavelength rectangular metal patches placed directly over a half-wave dielectric layer of high optical index n ₁. The filling factor of the grating mirror is large, to achieve high rejection. We will first describe the design rules and operating principles of those filters based on numerical investigation. A comprehensive understanding of the filter properties will then be provided thanks to restricted modal method calculation of light transmission through the structure. Finally an experimental validation using large scale microelectronics processes on CEA-LETI platform is shown and discussed.

Fig. 1 (a) Elementary structure of the proposed band-pass optical filter, with a design suitable for the mid-infrared range. Here, aluminium thickness is h = 50nm. (b) Theoretical reflectivity and transmission spectra of the system calculated with RCWA (response independent of the incident light polarization), and (c) map of the normalized magnetic field modulus at the resonance λ ₀ = 4.2μm, showing the excitation of a hybrid mode, i.e. a waveguide mode coupled to a harmonic surface wave (see text).

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2. Free standing filter

Figure 1(a) illustrates the canonical example of an aluminium patch array/silicon half-wave layer based filter, immersed in air, and working in the mid-infrared range [3–5]μm. The grating is only 50 nm thick and characterized by its period P = 1.8μm and opening width w = 200nm. Optical simulations, performed with the Rigourous Coupled Wave Analysis (RCWA), predict a resonant and symmetrical transmission peak, centered at λ ₀ = 4.2μm and reaching almost 70% transmission, independently of the incident polarization (fig 1(b)). The Full Width at Half Maximum (FWHM) is less than 200nm (λ ₀/20), whereas light is nearly totally rejected out of the pass-band over the whole range [3 –5]μm, by a factor of 15 to 25dB. The reflectivity spectrum also displayed on figure 1(b) shows that the structure can serve as stop-band reflection filter. The map of the normalized magnetic field modulus (fig. 1(c)) clearly shows the excitation of a hybrid mode corresponding to the coupling between a horizontal diffracted surface wave and the transverse waveguide mode allowed by the half-wave thickness of the Si layer. Indeed H field is either pinned at the metal surface or maximized in the bulk of the Si layer. This hybridized character and the high index of the waveguide makes the filter behavior rather robust for incidence angle θ ± 10° typically, and that for both fundamental TM and TE polarizations, as shown on the dispersion diagrams in figure 2(a).

Fig. 2 (a) Calculated dispersion diagrams of the resonance mode leading to the high transmission peak of figure 1, for TE and TM polarizations. Relatively weak sensitivity to the incidence angle θ is observed. (b) Transmission spectra for different air gap w, at fixed period P = 1.8μm. We note a trade-off between the maximum signal we can reach and the quality factor of the resonance. (c) Case of an array of rectangular (non-square) metal patches with a period P ₁ = 1.8μm in one direction, and P = 1.5μm in the other, with w = 200 nm. The filter becomes sensitive to polarization, and can then exhibit a dual-band type behavior.

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The transmission profile (i.e. maximum amplitude T_max, spectral width or Full Width at Half Maximum (FWHM), and central wavelength of the band-pass λ_max) can be adapted by adjusting three major geometrical parameters: the period P, the opening width w of the grating, and the height h ₁ of the high index layer (optical index n ₁). For a given spectral window, the grating period P is the major parameter tuning the central wavelength λ ₀ to transmit. The greater the period, the larger the wavelength. Besides, there is a trade-off between the amplitude of the transmission peak and the FWHM (see Figure 2(b)) which can be tuned with the key parameter w. Reducing w, the lineshape becomes sharp whereas the maximum transmission is lowered, and conversely. The size of the patch L = P – w will be chosen greater than 2P/3 (ie w < P/3), and advantageously close to P for a better quality factor of the resonance. To obtain a well behaved resonance of the transmission, the following relations should also be fulfilled:

λ_{0} / n_{1} < P < 2 λ_{0} / n_{1},

n_{1} > 1.7,

h_{1} \approx λ_{0} / 2 n_{1} .

The grating period must be sufficiently sub-wavelength (zero-order grating) to transmit a single mono-directional beam within the whole spectral range of interest (Eq. 1). No embarrassing diffracted beam other than the specular one is then allowed to propagate in the far-field. The use of a high index n ₁ for the half-wave layer, much larger than that of the external regions (Eq. 1), allows working with small periods P and therefore to overcome such diffraction problems. Rayleigh anomalies may however occur within the waveguide, and are correlated to the transmission peak observed, as we will see later with the modal analysis. An other consequence of preventing diffraction orders from appearing in the exit region (of index n_out) is that it favors light rejection over a broad spectral band: for an interval of interest [3λ ₀/4; 5λ ₀/4], we found the satisfactory criterion n ₁/n_out > 1.7. The height h ₁ of the high index waveguide is set to a half wave thickness, so as to both allow a high rejection and a single transmission peak. Indeed, if the height is lower, the guided mode will experience higher radiative losses, and the rejection will be lower, whereas if the height is higher several guided modes will exist, giving rise to several harmonics of transmission resonance in the spectral range of study (not shown). Finally, an interesting possibility is that we can, on the basis of a same patch array, realize a bi-spectral (dual-band) filter sensitive to the polarization of the incident light. This can be made by using rectangular (non-square) patches with two different periodicities in both orthogonal directions of the metal grating. A modulation of the transmission profile could then be obtained (Fig.2(c)).

3. Theoretical interpretation

The underlying physical principle of this nano-structured filter is detailed below. The resonant transmission is based on the strong coupling between the in-plane guided modes of the half-wave dielectric slab and the diffracted modes (notably leaky surface waves) of the metal grating. The systems builds up an electromagnetic resonator which can trap efficiently the incoming light within the dielectric layer, before light escapes towards the region opposite from the incidence one. In the framework of the so-called restricted modal method, we can find an analytical expression of the transmission in function of the opto-geometrical parameters. It consists in retaining only the fundamental mode for the field existing within metal slits, and in applying surface impedance boundary conditions at the dielectric/metal interfaces. Despite not rigorous, this drove us to highlight interesting trends of the observed electromagnetic behavior of the filter. The reader may refer to several papers [13, 14, 27] describing in detail the mathematical procedure used in this simplified model, and its successful validation by experiments considering moderately sub-wavelength metallic structures in the infrared.

Let us consider the metal grating as a one-dimensional structure, and an incident light with a transverse magnetic polarization. If the magnetic field outside the waveguide is written as a Rayleigh expansion:

H_{y}^{out} (x, z) = \sum_{m = - \infty}^{+ \infty} T_{m} e^{{ikn}_{out} (γ_{m}^{out} x + β_{m}^{out} (z - h_{g})),}

with

β_{m}^{out} = \sqrt{1 - {(γ_{m}^{out})}^{2}}

,

n_{out} γ_{m}^{out} = n_{in} sin θ + m λ / P

, and k = 2π/λ, the total transmission in the output region is:

Tr = ℜ (\sum_{m} \frac{n_{in} β_{m}^{out}}{n_{out} cos θ} | T_{m} |^{2}),

n_in is the optical index of the incidence region. As we use a subwavelength grating period (n_out P < λ) all over our spectral range of interest,

β_{m \neq 0}^{out}

are imaginary and the transmitted waves of high order are evanescent and will not contribute to transmission, which favours light rejection (no undesirable radiation leak channel). However, the diffraction order m = 1 within the half-wave layer is well propagating (

β_{1}^{g} > 0

). Applying the convenient boundary conditions and the one-mode approximation between metal patches [14, 27], we find that:

T_{m} = \frac{(w / P) S_{m} Γ}{(β_{m}^{g} / n_{g}) q_{m} + Z p_{m}},

where

p_{m} = cos X_{m} + i Y_{n} sin (X_{m}),

q_{m} = Y_{n} cos X_{m} + i sin (X_{m}),

and

Z = 1 / \sqrt{ɛ}

is the metal surface impedance (ε is the relative permittivity, and |Z| ≪ 1). The propagation constants

β_{m}^{medium} = \sqrt{1 - {(γ_{m}^{medium})}^{2}}

, and

n_{g} γ_{m}^{g} = n_{in} γ_{m}^{in} = n_{out} γ_{m}^{out}

(conservation of the tangential wave vector for each diffraction order). Here, S_m = sec(kγ_mw/2),

X_{m} = k n_{g} h_{g} β_{m}^{g}

, and the Floquet modal impedance ratios are

Y_{m} = (n_{g} β_{m}^{out}) / (n_{out} β_{m}^{g})

. Γ can be viewed as the transmission coefficient of the (non-resonating) air channels:

Γ = \frac{[(1 - Z) (1 - D_{g}^{+}) + (1 + Z) (1 + D_{g}^{-})] V}{(1 + D_{in}^{-}) (1 + D_{g}^{-}) e^{- ikh} - (1 - D_{in}^{+}) (1 - D_{g}^{+}) e^{ikh}},

where h is the metal thickness, and

D_{g}^{\pm} = (1 \pm Z) \frac{w}{P} \sum_{m = - \infty}^{+ \infty} \frac{p_{m} S_{m}^{2}}{q_{m} (β_{m}^{g} / n_{g}) + Z p_{m}},

D_{in}^{\pm} = (1 \pm Z) \frac{w}{P} \sum_{m = - \infty}^{+ \infty} \frac{S_{m}^{2}}{β_{m}^{in} + Z},

V = \frac{2 S_{0} cos θ}{cos θ + Z} \approx 2.

V is the excitation term for an incident plane wave. In the perfect metal case (Z = 0), we directly get :

Γ = \frac{V}{cos (kh) (D_{in} + D_{g}) + i sin (kh) (1 + D_{in} D_{g})} .

All along the paper, we do not study the regime where Fabry-Perot type resonances may occur within the slits (h ≪ λ/2), although such resonances can be qualitatively described with this model. Finally, transmission at normal incidence reduces to:

Tr = \frac{n_{in}}{n_{out}} {| \frac{(w / P) Γ}{cos (k n_{g} h_{g}) / n_{out} + i sin (k n_{g} h_{g}) / n_{g} + Z p_{0}} |}^{2} .

We see that, independently of the complex amplitude Γ, Tr can be maximized when λ ≈ n_gh_g/2. This is why a half-wave layer is preferentially used. Besides, when the following condition is respected:

q_{m} (β_{m}^{g} / n_{g}) + Z p_{m} \approx 0,

i.e. tan(X_m) = iY_m in the perfect metal case, D^g diverges and leads to a zero for the transmission: this is a Wood-Rayleigh (WR) anomaly occurring in the waveguide medium. Such anomalies usually correspond to surface plasmon-polariton modes between a bulk dielectric and a metal grating. Our resonant transmission peak observed on figure 1 does appear between two such WR conditions (harmonics n = 1 and n = 2 in our example, occuring at λ = 4.7μm and 2.85μm respectively). Similar observations made a long time ago about subwavelength periodic slot arrays sandwitched between two dielectric slabs were explained in terms of the transmission line effect of the dielectric layer on the Floquet modal impedances [22]. In particular, such a system would behave as a tank LC circuit at a transmission maximum [26]. Thus, the resonance peak is associated with a hybrid mode resembling a surface guided wave between two WR anomalies. Although the first order is propagating (

β_{1}^{g} > 0

), RCWA calculation shows that it does not transport real power (energy is stored as reactive one in the resonating waveguide). Finally, the thin metal grating serves both as a coupler and as a selective interface, and the transmission peak obeys some scaling laws, say: λ_max ∝ P + O(w), T_max ∝ w/P, and FWHM ∝ w (at the first order). We see on (12) that Tr would increase proportionally with the aperture w (for a fixed period). In parallel, when a resonant transmission occurs, the denominator of Γ is necessarily limited by a damping term also proportional to w, hence a trade-off. This is well consistent with the numerical observations of figure 2(c).

4. CMOS foundry integrated fabrication on Si substrate

Having clarified the behavior of those filters, we implemented their fabrication on a 200mm inches Si wafer using LETI semi-industrial pilot line. Semiconductors such as silicon are interesting substrates for filtering applications in the infrared region because of their transparency over a wide range from short wave to long wave infrared wavelengths. Moreover, the use of standard IC technology allows mass production while significantly reducing the fabrication costs. Those technology are now finding new markets in photonic devices, as illustrated by this work. However, the above theoretical study has shown the need for a half wave thickness membrane of high index material, i.e. of the order of the micron for operation in the infrared. Instead of using more fragile suspended membranes that require additional technological developments (e.g. use of nitride as a layer for mechanical stress control), we chose a bulky integration on standard 735μm thick Si wafers to provide a mechanically robust holder to the filter (Fig. 3(a)). In order to do so, some adjustments of the conceptual design detailed above have been conducted. Indeed, if the difference between the optical index of the substrate and that of the waveguide layer of the filter and/or the distance separating them is too low, diffraction orders of higher number may alter the rejection. Therefore an intermediate low optical index layer (n ₂, with n ₂ < n ₁/1.7) is inserted between the substrate and the high index dielectric waveguide, a quarter-wavelength thickness being enough to make the filter like optically independent from the substrate. In order to keep the desired optical response unchanged, we inserted in practice an adaptative 680nm thick SiO ₂ layer between the 575nm thick Si waveguide and the bulk Si substrate.

Fig. 3 Pictures of the Si wafer on which a series of infrared filter matrix were fabricated on LETI semi-industrial platform. SEM image of the subwavelength aluminium grating (corners of the metal patches are rounded), and sketch of the multi-layer stack with experimental parameters (filters are separated from the substrate by an adaptative low index quarter-wavelength layer to make the filters like optically isolated).

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For the metal pads, we chose a 90nm thick aluminium layer, because this material is ubiquitous on CMOS foundries, and its losses in the infrared are not detrimental to the transmission performance. 90nm thick aluminium was deposited by PVD on top of the dielectric stack. A thin (10nm) silicon nitride layer was inserted between the aluminium and the silicon layers to avoid any intermixing that would deteriorate the transmission properties, due to increased losses within the metal. As the required thickness of the metal pads is small, sample fabrication can be done by UV lithography and plasma dry etching. An anti-reflection coating has also been deposited on the back-side of the wafer to optimize filter overall transmission measured below. The final wafer comprises a series of filters of area 3 × 3mm ², arranged in matrix (Fig. 3(b)). Layer thicknesses are the same all over the wafer, and filters are differing by lateral dimensions (period and slit width). Scanning Electron Microscope (SEM) pictures examination shows that the metal patches have rounded shapes, due to the resolution limit of the 248nm UV lithography used here, and that their edges have a 20° angle with respect to normal (Fig. 3(c)).

5. Optical characterization

Far-field transmission was measured in the air using the quasi-collimated beam (Δθ ≈ 0.5°) of a Fourier Transform Spectrophotometer Bruker ISS55. Figure 4 shows the experimental transmission spectra of filters resonating in the [3 –5]μm range, illustrating the ability to tune the resonance wavelength throughout the IR range, with transmission levels up to 70%, spectral widths of the order of 200nm and rejections of at least 7dB. Table 1 summarizes the geometrical parameters used, together with the experimental optical performances reached. One sees that by keeping the slit width w constant, of the order of 330nm, and increasing the period P by 50% from 1345nm to 2070nm, the FWHM is kept constant, but the maximum transmission is decreased by 40% since the optimal conditions (1) cannot be conserved for all the wavelengths. However, this is a check of the tunability rules for the transmission peak mentionned in the third part of this paper.

Fig. 4 (a) Experimental FTIR transmission spectra of filters, essentially differing by their period (see Table 1 for detailed dimensions of each one and corresponding optical properties). Period is increasing with the spectral position of the transmission maximum. (b) same experimental data, but in log scale, illustrating the large rejection experimentally achieved with those filters.

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Table 1. Table summarizing the main geometrical and optical characteristics of the filters whose transmission spectra are shown in the figure 4.

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Since the dielectric loading of the filters was optimized for a 4μm wavelength operation, we will focus now on the fine structure of its transmission lineshape (Fig 5). As expected, we observe a single narrow resonant transmission peak (FWHM ≈ 150nm, quality factor Q = 27) centered in the [3 –5]μm range, and a rejection level reaching the 15 – 20dB range. The line-shape is however slightly different from the transmission lineshape of the filters theoretically calculated. Those small discrepancies actually give us useful information about the technological robustness of the optical performances. We have identified the deviations of the real filter (Fig 3 and 5) from the ideal one (Fig 1). There is first a shoulder on the large wavelength side of the transmission peak. As the FTIR measurement is done in a non-polarized mode, this originates from a slight difference in the periodicity of the patch array in the x and y directions, as measured by SEM (1.735 vs 1.745μm).

Fig. 5 (a) Comparison of the experimental FTIR transmission spectrum of a filter centered at 4μm with that obtained by FDTD simulation for the actual structure (see text for details). (b) Same data in log scale illustrating the rejection performance.

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A numerical calculation of the transmission is plotted in figure 5, together with the experimental data. The calculation was done using FDTD (Lumerical) by implementing the real structure of the filter. The optical index of the latter material was taken according to the Palik data for monocrystalline silicon, as silicon nitride layer is deposited at high temperature (625°C) on top of the deposited silicon waveguide layer. Such an assumption was checked by the good agreement of experimental and theoretical transmission of the multilayer stack without aluminum coating (not shown). Thicknesses of the various layers (t_SiO ₂ = 680nm, t_Si = 575nm, t_Si ₃ _N ₄ = 11nm, t_Al = 90nm) were measured by SEM on a Focus Ion Beam (FIB) cross section of the stack. The curvature radius of the Al patch corners was measured to be 200nm on the upper side of the aluminum layer. As already mentioned, the etching of the Al layer induced a 20° slope for the vertical sidewalls, and was also taken into account in the layout of the calculation. The width of the slit w = 280nm at the upper level of the Al patch was measured by SEM. Due to the slope of the patch edges, the slit is narrower at the level of the high index waveguide layer. The only adjustable parameter was the period P of the grating: it was nominally set to 1.71μm, measured at 1.74μm by SEM, and taken at 1.68μm to fit the position of the experimental transmission curve. This 3.5% total discrepancy remains within the uncertainty of both technology and metrology used here. Given those parameters, the numerical simulation nicely fits the experimental data (Fig 5). Additional numerical simulations, shown in Fig 6, puts light on the respective influence of 1) the sloppy edges and 2) rounded shape of the patch corners. This figure compares the transmission lineshape of two different filters, one is the numerical model of the fabricated filter described above, and the second one is having sloppy edges (20°) but no rounded corners. One sees that the kink on the short wavelength side (3.8μm) of the transmission peak disappears in the second case. On the other hand, Fig 6(b) compares the transmission lineshape of three different filters, the first one is still the numerical model of the fabricated filter described above and the others have rounded corners but no sloppy edges with either w = 280nm or w = 216nm, respectively. The latter number corresponds to the slit width at the bottom level of the Al layer in sloppy filter. In both cases there is a transmission kink on the low wavelength side, as we kept the rounded shape of the patch corners. More interestingly, the transmission of the w = 216nm filter is closer to the transmission of the reference filter than the one of the w = 280nm filter. This observation illustrates the fact that a critical region for the transmission properties is the metal slit aperture in contact with the high index dielectric waveguide. This is no surprise given the field map in Fig 1 showing enhanced field in the dielectric waveguide region.

Fig. 6 (a) Effect of round shape of the patch corners on the transmission lineshape. (b) Effect of the slope of the patch edges on the transmission lineshape.

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At last, we experimentally checked the angular insensitivity of those filters. A plot of the transmission peak in function of the wavelength and the incidence angle is shown in Fig 7 in both light polarizations for the filter described above. Experiment was carried out using a converging beam (5° half angle). Transmission is well insensitive to incidence angle up to 15°. Above that angle the transmission peak position is more blue shifted in TM polarization than in TE polarization (more robust configuration). Those observations are in full agreement with the calculated behavior shown in Fig.2 for the case of the free standing filter. The kink observed at normal incidence on the short wavelength side of the transmission peak (analysed in Fig 6) is also visible under the form of a minimum transmission line, barely influenced by the incidence angle. Therefore, this feature most probably originates from a localized mode taking birth in the rounded corner region of the filters. Conversely, the splitting of the TE transmission with increased angles, evidenced in Fig 2, is not that visible in the Fig 7 due to the convergence of the incident beam.

Fig. 7 Measured transmission of the filter discussed in Figures 5 and 6, as function of the wavelength, incidence angle and polarization (TE: left, TM: right).

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6. Conclusion

We have theoretically and experimentally studied a resonant bandpass filter based on a very thin subwavelength metal patch array coupled to a high index dielectric waveguide. Transmission properties can be tuned by playing on the lateral dimensions of the grating to reach high and narrow transmission peaks, very good rejection of light out of the passband, and high angular insensitivity. To that respect, they are an interesting alternative to some purely dielectric structures [28, 29]. Moreover, those filters are mechanically robust and easy to fabricate on industrial facilities. Use of technological processes compatible with widespread microelectronic environment opens the perspective of low cost, integrated fabrication of those filters, whose potential use in imaging and sensing applications are numerous. For example, the kind of filters fabricated in this work is particularly suitable for the optical sensing of CO ₂ (which is absorbing around λ = 4.2μm). For imaging applications (infrared photo-detectors, uncooled bolometers, Si based CMOS visible sensor), those filters can be fabricated apart and subsequently packaged with imaging matrix by e.g. waferlevel packaging techniques. One can also straightforwardly integrate those filters within the imaging matrix, by replacing the Si substrate of our demonstration above by the suitable absorbing semiconductor (usually having a high optical index). By varying the periodicity, one can precisely adjust the transmission wavelength and obtain different infrared ”colors” within a restricted detection window. As a result, such a configuration would be particularly suited for hyper-spectral imaging.

Acknowledgments

We acknowledge the financial support of the OSEO HOMES project, and the ANR through Carnot funding. Samples were fabricated on the Leti CMOS foundry and we are particularly grateful to the assistance of E. Vermande and P. Brianceau.

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P(nm)	w(nm)	λ_max (μm)	T_max (%)	FWHM(nm)
1345	345	3.41	74	170
1470	325	3.6	72	170
1590	340	3.76	64	160
1735	335	3.97	60	160
1860	330	4.16	54	170
2070	300	4.51	44	200

High rejection bandpass optical filters based on sub-wavelength metal patch arrays

Abstract

1. Introduction

2. Free standing filter

3. Theoretical interpretation

4. CMOS foundry integrated fabrication on Si substrate

5. Optical characterization

6. Conclusion

Acknowledgments

References and links

Cited By

Figures (7)

Tables (1)

Equations (15)

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