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.
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.
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.
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 propose a novel, wideband spectrum analyzer based on spectral hole burning (SHB) technology. SHB crystals contain rare earth ions doped into a host lattice, and are cooled to cryogenic temperatures to allow sub-MHz hole burning linewidths. The signal spectrum is recorded in an SHB crystal by illuminating the crystal with an optical beam modulated by the RF signal of interest. The signal's spectral components excite those rare earth ions whose resonance frequencies coincide with the spectral component frequencies, engraving the RF spectrum into the crystal's absorption profile. Probing this altered absorption profile with a low power, chirped laser while measuring the transmitted intensity results in a time-domain readout of the accumulated RF signal spectrum. The resolution of the spectrum analyzer is limited only by the homogeneous linewidth of the rare earth ions (< 1 MHz when the SHB crystal is cooled to cryogenic temperatures). The spectrum analyzer bandwidth is limited by the inhomogeneous linewidth and by the electro-optic modulator bandwidth, both of which can be > 20 GHz.
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.
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.
Operation of a wideband, versatile optical spectrum analyzer for radio-frequency (RF) signals is demonstrated. The device is based on spectral hole burning (SHB). The demonstration features 2.3-GHz instantaneous bandwidth, 500-kHz resolution, and a 32-dB dynamic range. A true RF signal, transferred to the optical carrier with the help of a Mach-Zehnder modulator, is analyzed with optical carrier suppression and zooming capabilities. This is to the authors' knowledge the largest instantaneous bandwidth ever demonstrated for a SHB-based processor in rare-earth-doped crystals.