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Chinese Physics B

Characteristics of spectral-hole burning in Tm 3+ :YAG based on the perturbation theory

Shiyu Zhang, Xiurong Ma, Shuanggen Zhang, ChenLei, Xia-Yang Wang, Kuanlin Mu, Song Wang

Published May 30, 2014• 4 citations
Publisher

Abstract

In this paper, the physical mechanism of the interaction between electromagnetic wave and spectral-hole burning crystal material is investigated in detail. In the small signal regime, a perturbation theory model is used to analyze the mechanism of spectral-hole burning. By solving the Liouville equation, three-order perturbation results are obtained. From the theoretic analysis, spectral-hole burning can be interpreted as a photon echo of the zero-order diffraction echo when the first optical pulse and the second optical pulse are overlapped in time. According to the model, the spectral-hole width is dependent on the chirp rate of the reading laser. When the chirp rate is slow with respect to the spectral features of interest, the spectral hole is closely mapped into time domain. For a fast chirp rate, distortions are observed. The results follow Maxwell—Bloch model and they are also in good agreement with the experimental results.

DOI
10.1088/1674-1056/23/6/060304

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 28, 2005•2 citations
In this paper, the physical mechanism of the interaction between electromagnetic wave and spectral-hole burning crystal material is investigated in detail. In the small signal regime, a perturbation theory model is used to analyze the mechanism of spectral-hole burning. By solving the Liouville equation, three-order perturbation results are obtained. From the theoretic analysis, spectral-hole burning can be interpreted as a photon echo of the zero-order diffraction echo when the first optical pulse and the second optical pulse are overlapped in time. According to the model, the spectral-hole width is dependent on the chirp rate of the reading laser. When the chirp rate is slow with respect to the spectral features of interest, the spectral hole is closely mapped into time domain. For a fast chirp rate, distortions are observed. The results follow Maxwell—Bloch model and they are also in good agreement with the experimental results.
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 report on light slowing down in a rare earth ion doped crystal by persistent spectral hole burning. The absence of motion of the active ions, the large inhomogeneous broadening, the small homogeneous width and the long lifetime of the hyperfine shelving states make this material convenient for the burning of narrow persistent spectral holes. Since the hole can be burnt long before the arrival of the input signal, there is no need for a strong coupling field, illuminating the sample simultaneously with the input signal, in contrast with procedures such as Electromagnetically Induced Transparency or Coherent Population Oscillations. Analyzing the slowing down process, we point out the role played by off resonance atoms where most of the incoming information is carried over while the pulse is confined within the sample.
There have recently been several studies of the performance of laser frequency stabilization using spectral holes in solids, instead of an external cavity, as a frequency reference. Here an analytical theory for Pound-Drever-Hall laser frequency stabilization using spectral hole-burning is developed. The interaction between the atomic medium and the phase modulated light is described using a linearized model of the Maxwell-Bloch equations. The interplay between the carrier and modulation sidebands reveals significant differences from the case of locking to a cavity. These include a different optimum modulation index, an optimum sample absorption, and the possibility to lock the laser in an inherent linear frequency drift mode. Spectral holes in solids can be permanent or transient. For the materials normally used, the dynamics and time scales of transient holes often depend on population relaxation processes between ground state hyperfine levels. These relaxation rates can be very different for different solid state materials. We demonstrate, using radio-frequency pumping, that the hyperfine population dynamics may be controlled and tailored to give optimum frequency stabilization performance. In this way also materials with initially non-optimum performance can be used for stabilization. The theoretical predictions regarding the inherent linear frequency drift is compared to experimental data from a dye laser stabilized to a spectral hole in a Pr(3+)3+:Y(2)SiO(5) crystal.
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.