Dual spectral filters with multi-layered grating waveguide structures

Promising configurations for dual spectral filters based upon grating-waveguide structures are presented. In these configurations, the parameters of the multimode waveguide and grating are carefully chosen to achieve dual resonances at two different pre-determined wavelengths. Specifically, the grating-waveguide structure resonates for each pre-selected wavelength with a different waveguide mode. Theoretical and experimental results reveal that the resonance wavelengths can be accurately selected and that the resonance spectral bandwidths can be less than 1 nm with high contrast ratios. PACS: 42.25.Fx; 42.79.Ci; 42.79.Dj Optical filters based upon diffraction anomalies from gratings have been extensively investigated for many years. The diffraction anomaly phenomenon was first investigated by Wood [1], who observed very strong variations in the intensity of the diffracted spectral orders over narrow frequency bands. Wood’s observation was followed by numerous theoretical and experimental investigations that dealt with the resonance behavior in reflection gratings [2–8]. These investigations have been expanded to resonance anomalies in grating–waveguide structures (GWS) and have included new theoretical and experimental developments [9–18]. In general, filters based on GWS are designed to reflect the incoming light at one specific wavelength. Indeed, extremely narrow resonance bandwidths on the order of 0.1 nm have been obtained [19, 20]. Here we present an advanced GWS design and fabrication procedures which enable the selection of two pre-determined resonance wavelengths. We show that it is possible to accurately control each of the resonance wavelengths, so as to obtain two simultaneous filters, thereby extending the range of applications of GWS. ∗Corresponding author. (Fax: +972-8/934-4109, E-mail: [email protected]) 1 Basic principles of GWS The basic configuration of a GWS is schematically shown in Fig. 1. It is composed of a thin dielectric or semiconductor waveguide layer and an additional transparent layer in which a grating is formed. Below these is a substrate and above is a superstrate. When such a GWS is illuminated with an incident light beam, most of the beam is directly transmitted, while the rest is diffracted, trapped in the waveguide layer and subsequently partially rediffracted outwards. At a specific resonant wavelength and angular orientation of the incident beam, the rediffracted beam interferes destructively with the transmitted beam, so that the incident beam is completely reflected from the GWS. In general, the resonance bandwidths are limited by the losses that are caused by material and fabrication defects. In the most basic form, the resonance wavelength λ0 in GWS is related to the grating period Λ as follows: nspk sin θ+mK (Λ)= nwgk (λ0) cosψ , (1) where nsp is the refractive index of the superstrate layer above the structure, nwg is the refractive index of the waveguide layer, and θ and ψ are the angle of incident light and the angle of diffracted light, respectively, as shown in Fig. 1. k = 2π/λ0 is the light wavevector at resonance, K = 2π/Λ the grating wavevector, and m an integer (m = 1, 2, 3, . . . ) where m = 1 is used in the simplest case of a single-mode waveguide. Following Tien and Ulrich [21], we derive an implicit equation to relate waveguide thickness W and grating periodΛ, assuming the thin grating approximation, as Wnwgk sinψ (Λ)=Φsb (Λ)+Φsp (Λ)+ (m −1)π , (2) where ψ (Λ) is a function of the period Λ in accordance with (1) and Φsb (Λ) and Φsp (Λ) are the phases accumulated by the waves trapped in the waveguide each time they are totally internally reflected from the waveguide–substrate and waveguide–superstrate surfaces, respectively. The phases Φsb