We describe a configuration of the integrated-optic spectrometer based on Fourier-transform spectroscopy. The original source spectrum has been successfully retrieved with 20 GHz resolution by the spectrometer implemented in a silica-based planar waveguide.

We report that a spectrum can be retrieved with a planar waveguide spatial heterodyne spectrometer (SHS) incorporating an active phase-shift scheme, where the phase shifts are distributed around π/2. This was confirmed experimentally with an SHS that had 32 interleaved Mach-Zehnder interferometers and whose free spectral range was 625 GHz. The phase shifts ranged from 0.71 to 2.2 rad against the target of π/2 rad.

Proposed is a phase shift method that employs a planar waveguide spatial heterodyne spectrometer (SHS) to reveal the input light spectrum. A complex Fourier transformation derives the spectrum directly without any mathematical assumptions, thus eliminating the need for the Lagrange interpolation or deconvolution techniques. The available spectral range is one free spectral range of the SHS and is twice as wide as that available with the conventional method based on a Fourier cosine transformation.Introduction: High-resolution and miniaturised spectrometers without moving parts have great potential for use in optical fibre communication networks, environmental sensing and medical diagnostics. Spatial heterodyne spectroscopy (SHS) is an interferometric technique that uses the Fourier transformation of stationary interference patterns from Mach-Zehnder interferometers (MZIs) [1]. The planar waveguide version of the SHS architecture is a key approach since the MZI array is fabricated on one substrate.The actual optical delays of the fabricated MZIs are likely to deviate from the designed values and the phase error frozen in each MZI prevents us from deriving the input light spectrum. The development of a signal processing procedure for revealing the light spectrum is an important issue because of its practical applications. This Letter reports a phase shift method that obtains the spectrum without using the Lagrange interpolation [1] or deconvolution [2] techniques. We generate a quadrature output from each MZI and apply a complex Fourier transformation to a series of complex data comprising the in-phase and quadrature outputs.

Described is a noteworthy characteristic of a spatial heterodyne spectrometer featuring a complex Fourier transformation, namely that the spectrum can be retrieved by using a circular shift procedure when it is distributed over two adjacent spectral ranges. Retrieval is demonstrated by changing the temperature of the array and causing the spectrum to penetrate the adjacent spectral range.Introduction: A spatial heterodyne spectrometer (SHS) is an instrument that uses the Fourier transformation of a stationary interference pattern from a Mach-Zehnder interferometer (MZI) array [1]. The optical path differences between the two arms of the individual MZIs are designed to increase at equal intervals, which we denote as DL. Since the conventional SHS is based on the Fourier cosine transformation, the spectrum of the light launched into the MZI array should be finite only in the left half of the particular spectral range s/DL to (s + 1)/DL in wavenumber units, where s is an integer. When the spectrum is distributed either down to the Littrow wavenumber s/DL or over the centre (s + 1/2)/ DL, the spectral part outside the half range is folded over into the same range, resulting in the fatal deformation of the calculated waveform. This is the origin of the generation of blind regions where in practice we cannot measure the spectral components.We have proposed an advanced version of the SHS, namely the complex Fourier-transform integrated-optic SHS [2, 3], which generates in-phase and quadrature outputs at individual MZIs and acquires two interference patterns. This Letter reports a characteristic of our SHS, which is that the correct waveform of the spectrum can be retrieved even when it is distributed over two adjacent spectral ranges and therefore no blind regions are generated. The waveform is derived by circular shifting the Fourier transform when the spectrum is bandlimited to fall within the width 1/DL.