Correction for phase-shift deviation in a complex Fourier-transform integrated-optic spatial heterodyne spectrometer with an active phase-shift scheme

Takada, K.; Aoyagi, H.; Okamoto, K.

doi:10.1364/ol.36.001044

Cited by 15 publications

(11 citation statements)

References 5 publications

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“…1a. When the number of MZIs is N, the normalised in-phase and quadrature outputs [3] from the (k + 1)th MZI are DP (I)…”

Section: Principlementioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

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

Takada¹,

Aoyagi²,

Okamoto³

2012

Electron. Lett.

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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.

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“…1a. When the number of MZIs is N, the normalised in-phase and quadrature outputs [3] from the (k + 1)th MZI are DP (I)…”

Section: Principlementioning

confidence: 99%

mentioning

confidence: 99%

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

Takada¹,

Aoyagi²,

Okamoto³

2012

Electron. Lett.

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“…In this procedure, the influence of phase and amplitude errors is compensated, since the actual MZI transmittance functions (as measured in the calibration step) are used instead of an ideal cosine function. This yields a robust result compared to the conventional cosine transform technique, which requires an active compensation of the phase errors [15]. Figure 3 shows signal spectra, experimentally retrieved using our device and algorithm, for a single monochromatic source (solid curve), a doublet of two monochromatic lines separated by 56 pm (dotted curve), and a doublet of two monochromatic lines separated by 80 pm (dashed curve).…”

mentioning

confidence: 96%

“…This is a consequence of nonorthogonality of the base of the cosine transform in the presence of phase errors. A solution to incorporate this effect to the model of the discrete Fourier cosine transform was proposed [15]; however, it required phase correction circuits and multiple measurements at varying temperatures.…”

mentioning

confidence: 99%

High-resolution Fourier-transform spectrometer chip with microphotonic silicon spiral waveguides

et al. 2013

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We report a stationary Fourier-transform spectrometer chip implemented in silicon microphotonic waveguides. The device comprises an array of 32 Mach-Zehnder interferometers (MZIs) with linearly increasing optical path delays between the MZI arms across the array. The optical delays are achieved by using Si-wire waveguides arranged in tightly coiled spirals with a compact device footprint of 12 mm 2 . Spectral retrieval is demonstrated in a single measurement of the stationary spatial interferogram formed at the output waveguides of the array, with a wavelength resolution of 40 pm within a free spectral range of 0.75 nm. The phase and amplitude errors arising from fabrication imperfections are compensated using a transformation matrix spectral retrieval algorithm. In a typical configuration, a waveguide array of MachZehnder interferometers (MZIs) with increasing path differences are used to implement the SHS concept [9,10]. For such a geometry, the source power spectrum and the output interferogram are related by the cosine FT. A similar MZI array geometry, including phase-correction circuits using independent heaters for each MZI, has also been demonstrated [13]. However, when long optical path delays are required for high spectral resolution, similar configurations yield prohibitively large devices.In this Letter, we present a compact FT spectrometer chip, in which a high spectral resolution of 40 pm with a compact device size is achieved by using tightly coiled spiral waveguide structures in an MZI array. Furthermore, a spectral retrieval algorithm with phase and amplitude error compensations is demonstrated for the first time to the best of our knowledge, obviating the need for dedicated phase correction circuits. The FT spectrometer is implemented as an array of N MZIs in silicon-on-insulator (SOI) waveguides (Fig. 1). Each MZI comprises a reference arm of constant length and a delay arm with a spiral waveguide. The length of the delay arm, i.e., spiral length, linearly increases by ΔL across the array. The high refractive index contrast of the SOI platform and the waveguide bend radius of ∼5 μm readily allows the making of spirals with geometrical lengths of over a centimeter within an area only a few hundred micrometers in diameter.For a given input spectral distribution, the dispersive property of the MZI array results in a wavelengthdependent spatial interferogram at the outputs of the array. The relation between the input spectral distribution and the interferogram Ix i is unambiguous within

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“…The experimental spectral response of the MZIs of the array showed phase and amplitude errors from the ideal sinusoidal MZI spectrum, caused by fabrication deviations and other experimental interference, such as Fabry-Perot cavity effects and ambient fluctuations. These deviations result in a degeneration of the orthogonality of the transformation base and prevent the use of classical FT spectral retrieval algorithms without active compensation of phase errors [21]. Instead, our spectral retrieval technique is based on a system of linear equations defined by the MZI transmittance functions.…”

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confidence: 99%

Optical fiber interferometer array for scanless Fourier-transform spectroscopy

et al. 2013

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We report a spatial heterodyne Fourier-transform spectrometer implemented with an array of optical fiber interferometers. This configuration generates a wavelength-dependent stationary interferogram from which the input spectrum is retrieved in a single shot without scanning elements. Furthermore, fabrication and experimental deviations from the ideal behavior of the device are corrected by spectral inversion algorithms. The spectral resolution of our system can be readily scaled up by incorporating longer optical fiber delays, providing a pathway toward surpassing current spectroscopy resolution limits.

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Correction for phase-shift deviation in a complex Fourier-transform integrated-optic spatial heterodyne spectrometer with an active phase-shift scheme

Cited by 15 publications

References 5 publications

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

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

High-resolution Fourier-transform spectrometer chip with microphotonic silicon spiral waveguides

Optical fiber interferometer array for scanless Fourier-transform spectroscopy

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