Weak gratings in silicon-on-insulator for spectral filters based on volume holography

Abstract

We demonstrate integrated holographic grating filters, that can be designed towards any desired target spectrum. A straightforward design method transforms this target spectrum into a weak effective refractive index variation. The filters are implemented in high-contrast SOI by modulating the width of the shallow etched sides of a ridge waveguide. Measurements show that this is a promising approach to integrate flexible and versatile filters on photonic chips to enable more complex applications. c 2013 Optical Society of America OCIS codes: 000.0000, 999.9999.Silicon-on-Insulator (SOI) has emerged as a popular platform for photonic integrated circuits, mainly because of its high refractive index contrast and its compatibility with CMOS fabrication technology [1]. As the latter technology becomes even more refined, more functionality and complexity can be added to the photonic chips. This creates a need for more flexible and versatile spectral filters. Filters based on photonic crystals, arrayed waveguide gratings or ring resonators are well understood and have excellent performance [2, 3]. Still, even with these devices it is difficult to obtain filters with complex transfer functions.The principles of volume holography, a powerful method for encoding optical information [4], present a solution. Allowing light to travel over a large distance through a holographic grating structure, significantly increases the opportunities for light processing. The resolution of a holographic spectral filter is closely related with the scatter strength of the grating, which means a very low refractive index contrast is desirable for highresolution filters. A high-resolution holographic filter is therefore not straightforward to realize in a strong contrast material system such as SOI. In this paper we demonstrate holographic filters that were implemented by modulating the width of the shallow etched sides of an SOI ridge waveguide.The filters are designed in a very direct and elegant way, translating the targeted transfer function into a weak refractive index variation. Any grating can be represented by a variation of the effective refractive index n eff along the propagation direction x:A grating is weak if the index variation ∆n(x) is small (∆n(x) ≪ n eff,0 ). Because the scatter strength is low, it is justified to neglect second-order reflections. This means that a pulse E 0 δ(t) interacts with the grating by producing a single reflection at each point x with anα R E 0 Δn(x) at t 2n eff,0 x c = Fig. 1. The impulse response of the grating consist of one contribution from every position x. This contribution has a amplitude related to ∆n(x) and arrives at a time related to x.amplitude of E R = α R E 0 ∆n(x), where α R is a constant [5]. As indicated in Fig. 1, this reflection is delayed by a transit time of t = 2n eff,0 x c . The response to the impulse E 0 δ(t) in reflection becomes E R (t) = α R E 0 ∆n ct 2n eff,0 .The spectral transfer function of this filter can then be calculated as the Fourier transform of E R /E 0 :

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“…This means that the coupling strength is lithographically defined and can be varied by mask design only. Also, by mask design only, more complex grating transfer functions can be realized, such as apodized gratings and multiple‐channel gratings . Another approach is to use very low coupling strength to realize long gratings, having fiber Bragg grating‐like performance.…”

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“…Notice that WBGs can be designed using a similar set of analysis and synthesis tools as FBGs [65]. Recent developments have enabled fabrication of WBGs with complex grating profiles [66][67][68].…”

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“…It is worth noting that other authors have arrived at the same Fourier transform design method by approaching the problem from the point of view of volume holography [14], and the application of coupled-mode theory to weakly coupled gratings [15][16][17][18]. However, these approaches were either constrained to the low reflection limit or the authors concentrated on tailoring the phase in a high reflection limit.…”