Complex-Fourier-transform integrated-optic spatial heterodyne spectrometer using phase shift technique

Abstract

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.

Spectrum retrieval using circular shift procedure in complex Fourier-transform integrated-optic spatial heterodyne spectrometer

“…2b. Since every spectral range shifted downwards as the temperature increased, part of the light spectrum (ii) penetrated the adjacent range and this condition was completely different from that in our previous work [2]. In the transform, the elements for both spectra were shifted to the right and the last element still had a 90 % value against the peak of the waveform (ii).…”

“…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.…”

Progress and technical challenge for planar waveguide devices: silica and silicon waveguides

“…A phase-shift method was also proposed to generate a quadrature output from each MZI [34]. A complex Fourier transformation to a series of complex data comprising the in-phase and quadrature outputs derives the spectrum over entire FSR.…”

Detailed calculation of spectral noise caused by measurement errors of Mach–Zehnder interferometer optical path phases in a spatial heterodyne spectrometer with a phase shift scheme

“…We have already proposed an advanced version of the SHS, namely the complex Fourier-transform integrated-optic SHS [4], which generates two different outputs from each MZI set in the in-phase and quadrature states. We report that the noise level obtained by applying the root mean square (rms) operation including arithmetic and ensemble averaging to the spectral noise that distributes over the free spectral range (FSR) of our SHS is proportional to the rms error of the phase measurement.…”