Spectral measurements with superresolution based on periodic modulation of the spectrum

Abstract

We extend the approach recently applied for achieving spatial and temporal superresolution to spectral measurements with superresolution. The light passes previously through a filter with a periodic spectral response. Owing to the spectral modulation, the parts of the spectrum Fourier transform are shifted and transmitted through the passband of the Fourier transform of the spectrometer instrumental function. Thus, all the parts of the spectrum Fourier transform are recorded by the spectrometer and then restored by a special procedure. An inverse Fourier transform gives the spectrum restored with superresolution. We numerically demonstrate more than tenfold enhancement of the resolution by using a sampled fiber Bragg grating for spectral modulation.

Measurement of subpicosecond optical waveforms using a resonator-based phase modulator

“…The variation of the Fourier coefficients of periodic modulation was also applied for spectral measurements with superresolution [29].…”

Periodic modulation-based spectral and temporal superresolution with a single measurement

“…We introduce a superresolution factor which is defined as the ratio of the full width of the signal Fourier transform to that of the system passband. For instance, the superresolution factor was 2-3 in [8], 5.5 in [3], 12.5 in [15], and 20 in [16].…”

“…Higher harmonics of modulation lead to enhancement of superresolution. For spectral superresolution, the object spectrum to be measured is spectrally modulated by a filter with a sinusoidal [8] or a periodic spectral response with higher modulation harmonics [15,16]. In the measurements of periodic ultrashort optical pulses with temporal superresolution, the pulses are temporally modulated, for instance, by a Mach-Zehnder modulator [9] or a resonator-based optical phase modulator [10].…”

Enhancement of resolution of optical spectrum analysers with thermally tuned sampled fibre Bragg grating

“…Spectral magnification, analogous to spatial and temporal ones, was proposed [9] and experimentally implemented [10] with a magnification factor of 105, but the maximum spectral range was only 14 GHz. A method based on periodic spectral modulation of the spectrum to be measured has recently been proposed [11]. This technique is an extension of the methods applied for spatial and temporal measurements [12] to the spectral domain.…”

“…Instead of 2N + 1 different shapes of the modulation function f(v) [11], we propose to use a single form of the modulation function and to shift it spectrally 2N + 1 times. This shifting is implemented by heating the SFBG (see Fig.…”