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Nonlinear correction of spectrally recovered, RF spectral features, readout with high frequency-chirped laser fields

Louis Joseph Oberto

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

Frequency-chirped readout of spectral features from spatial-spectral (S2) materials, as a result of spectral hole-burning, has been in use as a radio-frequency (RF) spectrum analyzer for well over a decade. Previously, a signal processing deconvolution algorithm had been developed that enabled faster chirping, such that the chirp rate 'K' could be much greater than the desired resolution bandwidth (RBW). This broke past conventional limits for spectroscopic detection, which states that one needs to dwell on a spectral feature of width gamma for a time 1/gamma. For a chirp, this would mean that the square root of the chirp rate would need to be less than the RBW. For chirp rates on the order of gamma 2 or higher, nonlinearities begin to appear in detected signals depending on optical absorption depth, the chirp rate, and burned hole depths. Even with this algorithm, distortions still persist when very deep holes are burned in a high absorbing material, while the chirp rate is still very high. However, resolving spectral features under these conditions is desirable to increase the dynamic range of the SA. A new nonlinear signal processing technique that removes the nonlinearity has been developed, recovering the distorted signals. It was applied to RF signals spectrally absorbed in two different Tm 3+: YAG crystals, with measured absorption lengths of 1.9 and 2.5. The new algorithm is shown to work on multiple spectral holes simultaneously. Signals as wide as 1 MHz and as small as 300 kHz were recovered for a chirp rate of about 11.88 MHz/microsecond. These results show that very fast chirp rates could be used for highly absorbing materials, with deeply burned spectral holes. This could enable ultra-sensitive readout of a spectrum spanning hundreds of gigahertz, while pushing the dynamic range higher.

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IEEE Photonics Technology Letters•Oct 24, 2005•41 citations
Frequency-chirped readout of spectral features from spatial-spectral (S2) materials, as a result of spectral hole-burning, has been in use as a radio-frequency (RF) spectrum analyzer for well over a decade. Previously, a signal processing deconvolution algorithm had been developed that enabled faster chirping, such that the chirp rate 'K' could be much greater than the desired resolution bandwidth (RBW). This broke past conventional limits for spectroscopic detection, which states that one needs to dwell on a spectral feature of width gamma for a time 1/gamma. For a chirp, this would mean that the square root of the chirp rate would need to be less than the RBW. For chirp rates on the order of gamma 2 or higher, nonlinearities begin to appear in detected signals depending on optical absorption depth, the chirp rate, and burned hole depths. Even with this algorithm, distortions still persist when very deep holes are burned in a high absorbing material, while the chirp rate is still very high. However, resolving spectral features under these conditions is desirable to increase the dynamic range of the SA. A new nonlinear signal processing technique that removes the nonlinearity has been developed, recovering the distorted signals. It was applied to RF signals spectrally absorbed in two different Tm 3+: YAG crystals, with measured absorption lengths of 1.9 and 2.5. The new algorithm is shown to work on multiple spectral holes simultaneously. Signals as wide as 1 MHz and as small as 300 kHz were recovered for a chirp rate of about 11.88 MHz/microsecond. These results show that very fast chirp rates could be used for highly absorbing materials, with deeply burned spectral holes. This could enable ultra-sensitive readout of a spectrum spanning hundreds of gigahertz, while pushing the dynamic range higher.
A new nonlinear signal processing algorithm for recovery of narrow and high-contrast spectral features for fast chirping tunable laser spectroscopy is described. The prior linear spectral feature recovery algorithm used only linear signal processing techniques. The new algorithm uses nonlinear signal processing to improve the linear recovery algorithm by estimating and removing nonlinearities resulting from the combination of chirping faster than the conventional spectroscopic limit, large absorption depth, and high-contrast spectral features. In this context, “nonlinearities” refers to the difference between the feature-size-dependent recovered spectral features and a properly scaled version of the actual spectral features. The new nonlinear algorithm was tested on a set of spectrally narrow holes burned into the inhomogeneous line, both theoretically and experimentally. Experimental data included multiple sets of spectral holes of different depths and widths <1 MHz, which were spectrally burned into cryogenic Tm3+:YAG and readout using a chirp rate of 11.88 MHz/μs. This technique improves the qualitative and quantitative spectral estimates made by spectral-holeburning-based RF spectrum analyzers, but can be applied to any tunable laser spectroscopy applications that require fast measurement of multiple high-contrast and narrow spectral features.
We demonstrate an RF spectrum analyzer based on spectral-hole burning (SHB) that operates with unity probability of intercept and resolution under 100 kHz. An SHB crystal, which consists of rare-earth ions doped into a crystal host, records the power spectrum of an RF signal modulated onto an optical carrier as a series of spectral holes that persist for about 10 ms. While the crystal's homogeneous and inhomogeneous linewidths place the fundamental limits on resolution and bandwidth, respectively, the practical limits depend on the lasers used to interrogate the record stored in the crystal's absorption profile. Up to now, SHB spectrum analyzers have used chirped beams from externally modulated, stabilized lasers, which have linewidths of under 10 kHz but cannot chirp over much more than octave bandwidths, or directly modulated diode lasers, which can chirp over more than 20GHz but have linewidths of about 1 MHz. Switching to chirped fiber lasers, which have natural linewidths of under 2 kHz and chirping linewidths on the order of 10 kHz, produces a measurement with fine resolution without any laser stabilization. In addition, by chirping the fiber laser with a sufficiently fast piezo, the resulting chirp could extend over tens of gigahertz in under 10 ms, yielding both fine resolution and broad bandwidth without extraordinary stabilization schemes.
We present experimental results for what is to our knowledge the first spectral-hole-burning based rf spectrum analyzer to cover 10 GHz of rf analysis bandwidth. The rf signal of interest is modulated onto an optical carrier, and the resultant optical sidebands are burned into the inhomogeneously broadened absorption band of a Tm3+:YAG crystal. At the same time a second, frequency-swept laser reads out the absorption profile, which is a double-sideband replica of the rf spectrum, and thus the rf spectrum can be deduced after spectral calibration of the nonlinear readout chirp. This initial demonstration shows spectral analysis covering 10 GHz of bandwidth with >5500 spectral channels and provides 43 dB of dynamic range.
We propose performing ultrawideband RF spectrum analysis using spectral-hole-burning (SHB) crystals, which are crystal hosts lightly doped with rare earth ions such as Tm3+ or Er3+. Cooling SHB crystals to cryogenic temperatures suppresses phonon broadening, narrowing the ions' homogeneous linewidths to <100 kHz; local inhomogeneities in the crystal lattice shift the individual ionic resonances such that they're distributed over a bandwidth of 20 GHz or in some structurally disordered crystals to up to 200 GHz. Illuminating an SHB crystal with a beam modulated with multiple RF sidebands digs spectral holes in the crystal's absorption profile that persist for the excited state lifetime, about 10 ms. The spectral holes are a negative image of the modulated beam's spectrum. We can determine the location of these spectral holes by probing the crystal with a chirped laser and measuring the transmitted intensity. The transmitted intensity is the double-sideband spectrum of the original illumination blurred by a 100 kHz Lorentzian and mapped into a time-varying signal. Scaling the time series associated with the transmitted intensity by the instantaneous chirp rate yields the spectrum of the original illumination. Postprocessing algorithms undo distortion due to swept laser nonuniformities and ringing induced by fast chirp beams, eliminating the need for long dwell times to resolve narrow spectral features. Because the read and write processes occur simultaneously, SHB spectrum analyzers can operate with unity probability of intercept over a bandwidth limited only by the inhomogeneous linewidth. These capabilities make SHB spectrum analyzers attractive alternates to other approaches to wideband spectrum analysis.
A readout using a frequency-chirped laser is investigated in a spectrum analyzer with spectral-hole-burning (SHB). An analysis based on the Bloch equations is presented for the spectral distortion due to a fast readout, and a recovery algorithm is developed for the distortion. The experiment of a SHB spectrum analyzer is executed to demonstrate the optical spectral distortion due to fast readout. The experimental spectral distortion is recovered by the recovery algorithm developed from the Bloch equations.
We demonstrate the first 10-GHz instantaneous bandwidth radio-frequency spectrum analyzer based on spectral hole burning in Tm/sup 3+/:YAG. It exhibits 10 000 frequency channels and a resolution better than 1 MHz. Thanks to the fast and linear chirping capabilities of the laser used, it has a potential 100% probability of interception and a response time in the millisecond range. Its linear dynamic range of 16 dB is presently essentially limited by the modest amount of optical power available and can be further improved.