Narrowband midinfrared reflectance filters using guided mode resonance

Abstract

There is a need to develop mid-infrared (IR) spectrometers for applications in which the absorbance of only a few vibrational mode (optical) frequencies needs to be recorded; unfortunately, there are limited alternatives for the same. The key requirement is the development of a means to discretely access a small set of spectral positions from the wideband thermal sources commonly used for spectroscopy. We present here the theory, design, and practical realization of a new class of filters in the mid-infrared (IR) spectral regions based on using guided mode resonances (GMR) for narrowband optical reflection. A simple, periodic surface-relief configuration is chosen to enable both a spectral response and facile fabrication. A theoretical model based on rigorous coupled wave analysis is developed, incorporating anomalous dispersion of filter materials in the mid-IR spectral region. As a proof-of-principle demonstration, a set of four filters for a spectral region around the C-H stretching mode (2600-3000 cm(-1)) are fabricated and responses compared to theory. The reflectance spectra were well-predicted by the developed theory and results were found to be sensitive to the angle of incidence and dispersion characteristics of the material. In summary, the work reported here forms the basis for a rational design of filters that can prove useful for IR absorption spectroscopy.

Figure 1

Geometrical configuration and illustration of light incident at a generalized angle to the GMRF.

Figure 2

A) Parameter regimes for Λ, such that |p| = 1 order (on the left, p = 1 and on the right, p = −1) can correspond to a guided mode for 2600 and 3000 cm⁻¹ for TE polarized EM wave incident at angle θ. The dispersion characteristics are ignored and the refractive indices are approximated to be n^c = 1.0, n^Si₃^N₄ = 2.0 and n^s=1. B) The maximum achievable reflectance of structures with chosen Λ values for a TE polarized EM wave that is normally incident. Depth of the waveguide, d^wg = d^gr and fill fraction, f = 0.5 are arbitrarily chosen for simpler fabrication. The azimuthal angle of incidence is chosen to be ϕ = 0. The dispersion characteristics are ignored and constant real values are chosen for refractive indices as in A).

Figure 3

Sequence of steps involved in fabrication of surface-relieved film on soda lime wafer

Figure 4

Optical setup for spectroscopic measurements of GMRF for A) normal incidence and B) angular incidence

Figure 5

A) Reflection spectra (zero-order diffraction efficiency) of the designed filters. The parameters chosen are: Λ = 2.2, 2.3, 2.4 and 2.5 μm, f = 0.5, d^gr = d^wg = 0.3 μm, n^Si₃^N₄ = 2.0, n^S = 1.48, n^c=1.0. B) E-field distribution in the vicinity of structure with Λ = 2.5 μm at a resonant wavenumber, ν̄= 2659 cm⁻¹ (top) and off-resonance wavenumber, ν̄ = 3400 cm⁻¹. The surface relief of the film to be fabricated is depicted using white lines.

Figure 6

A) Effect on resonances of dispersion characteristics of Si₃N₄ and soda lime, for structure of Λ = 2.3 μm, d^gr = 0.3 μm, and d^wg = 0.3 μm, when a TE-polarized wave is normally incident. B) E-Field amplitude distribution at resonance wavenumber (ν̄ = 2869 cm⁻¹) without considering the dispersion properties of both Si₃N₄ and soda lime. C) E-field amplitude distribution at resonance wavenumber (ν̄ = 2858 cm⁻¹) considering the dispersion properties of Si₃N₄ and soda lime. The surface relief of the film to be fabricated is depicted using white lines. D) Comparison of E-field amplitude distributions shown in (B) and (C) at the interface of grating and waveguide layers.

Figure 7

Spectral variability with changes in incidence angle θ for structure of Λ = 2.3 μm, d^gr = 0.3 μm, and d^wg = 0.3 μm, when a TE-polarized wave is incident with azimuthal angle ϕ = 0°. Only regions around the two resonances observed in Figure 5 are plotted and significant alterations are observed within both regions. Other spectral regions are insignificantly impacted and hence not shown here.

Figure 8

(A) Scanning electron microscopy (SEM) image of one of the fabricated GMRFs, and (B) atomic force microscopy (AFM) images of a 1D GMRF, demonstrating the consistency in depth and the periodicity in surface relief.

Figure 9

A) Structure of the grating layer obtained for the four structures using AFM, (depicted offset from each other here). The AFM results are averaged over 256 scan lines. The structure of the grating layer is used to evaluate Λ and d^gr, the standard deviation of d^gr is ≤ 0.005 μm and the standard deviation in evaluating Λ is ≤0.015 μm. B) The reflectance efficiencies of the four filters with TM-polarized normal incidence, an appropriate d^wg is found with which results predicted by RCWA match those obtained from experiments. C) Structural parameters for the four filters fabricated.

Figure 10

Comparison of experimentally measured and theoretically calculated reflectance spectra of fabricated GMR filters for a TE-polarized incident wave. The structural parameters are obtained from AFM measurements and reflectance measurements from TM-polarized incidence. These values are listed in Figure 9C.

Figure 11

Comparison of experimental results with theoretical spectra calculated by considering incident beam to have rays varying between θ = 0 to θ_max. The θ_max values used for structures 1, 2, 3, and 4 respectively are 0.35, 0.35, 0.35 and 0.6° respectively. The integration has been performed using trapezoidal method.