ICTON 2013 Tu.D5.1 978-1-4799-0683-3/13/$31.00 ©2013 IEEE 1 High Resolution Fourier-Transform Microspectroscopy Based on Spiral Silicon Waveguides Aitor V. Velasco*, Pavel Cheben, María L. Calvo*, Mirosław Florjańczyk, Przemek J. Bock, André Delâge, Jens H. Schmid, Jean Lapointe, Siegfried Janz, Dan-Xia Xu and Martin Vachon National Research Council Canada, Ottawa, Ontario, K1A 0R6, Canada Tel: (001) 6139931624, Fax: (001) 6139907656 e-mail: Pavel.Cheben@nrc.ca *Universidad Complutense de Madrid, 28040 Madrid, Spain Tel: (0034) 913944629, Fax: (0034) 913944914, e-mail: avillafr@ucm.es ABSTRACT We report a spatial heterodyne Fourier-transform spectrometer consisting of an array of Mach-Zehnder interferometers (MZI) implemented in silicon microphotonics. Optical path differences between the MZI arms increase linearly along the array, generating a wavelength-dependent interferogram which enables the retrieval of the source spectrum with a single measurement. Optical delays were implemented with Si-wire waveguides arranged in tightly coiled spirals to achieve a high resolution in a reduced footprint. Our spectral retrieval algorithm compensates phase and amplitude errors arising from fabrication imperfections by using a transformation matrix based on the calibration data. A wavelength resolution of 40 pm within a free spectral range of 0.75 nm is demonstrated. Keywords: spectroscopy, Fourier transform, silicon waveguides, spectral retrieval. 1. INTRODUCTION Compact spectrometers with high-resolution and small footprint are required for a wide range of applications, including optical communications, biological and environmental sensing, and space instrumentation [1]. Additionally, a large optical throughput (étendue) is also required for the analysis of spatially extended and incoherent sources. Planar waveguide devices such as arrayed waveguide gratings (AWG) [2], echelle gratings [3,4], lattice filters [5], ring resonators [6] and sidewall grating filters [7,8] provide high spectral resolution in a small device footprint, but are largely limited in terms of optical throughput. This limitation can be overcome by spatial heterodyne Fourier-transform (SHFT) spectrometers [9-12], which benefit from the intrinsically large étendue of the Michelson interferometer [13]. In particular, the SHFT concept can be implemented with an array of Mach-Zehnder interferometers (MZI) with linearly increasing optical path differences between MZI arms across the array [10]. This configuration provides a wavelength-dependent stationary interferogram from which the source spectrum can be retrieved by mathematical analysis. Here we demonstrate a silicon waveguide SHFT spectrometer chip consisting of a MZI array with tightly coiled spiral structures [14]. A high spectral resolution of 40 pm is demonstrated for a compact device with a footprint of 12 mm 2 . Furthermore, the disclosed spectral retrieval algorithm compensates phase and amplitude errors, circumventing the need of dedicated phase shifting circuits [15]. 2. OPERATION PRINCIPLE The SHFT microspectrometer is implemented in silicon-on-insulator (SOI) waveguides as an array of N Mach- Zehnder interferometers with linearly increasing optical path differences. Compact optical delays are achieved with Si-wire waveguides coiled in tight spirals, benefiting from the high mode confinement and small bend radius of the SOI platform. For a given input spectral distribution within the free spectral range (FSR) of an ideal device without phase errors, the MZI array generates a discretized stationary interferogram Y(x i ):     0 cos 2 FSR i i Y x B xd      (1) where B is the incident spectral density, x i is the path delay of the i-th MZI, and     σ L is the shifted wavenumber, relative to the Littrow wavenumber σ L at which the maxima of the MZI transfer functions are aligned [10]. The input spectrum can be retrieved from the wavelength-dependent interferogram with a discrete cosine transform. Wavelength resolution (δλ) and FSR of the spectrometer are determined by the maximum optical path difference (ΔL max ) and the number of interferometers [14]: 2 0 max g L n     (2) 2 N FSR   (3) where λ 0 is the device operational central wavelength and n g is the waveguide group index.