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Physical Review A

Frequency-chirped readout of spatial-spectral absorption features

Tiejun Chang, R. Mohan, Ming Tian, Todd L. Harris, Wm. Randall Babbitt, K.D. Merkel

Published Dec 8, 2004• 17 citations
Publisher

Abstract

This paper examines the physical mechanisms of reading out spatial-spectral absorption features in an inhomogeneously broadened medium using linear frequency-chirped electric fields. A Maxwell-Bloch model using numerical calculation for angled beams with arbitrary phase modulation is used to simulate the chirped field readout process. The simulation results indicate that any spatial-spectral absorption feature can be read out with a chirped field with the appropriate bandwidth, duration, and intensity. Mapping spectral absorption features into temporal intensity modulations depends on the chirp rate of the field. However, when probing a spatial-spectral grating with a chirped field, a beat signal representing the grating period can be created by interfering the emitted photon echo chirped field with a reference chirped field, regardless of the chirp rate. Comparisons are made between collinear and angled readout configurations. Readout signal strength and spurious signal distortions are investigated as functions of the grating strength and the Rabi frequency of the readout pulse. Using a collinear readout geometry, distortions from optical nutation on the transmitted field and higher-order harmonics are observed, both of which are avoided in an angled beam geometry.

DOI
10.1103/physreva.70.063803

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Journal of the Optical Society of America B•Nov 9, 2018•0 citations
This paper examines the physical mechanisms of reading out spatial-spectral absorption features in an inhomogeneously broadened medium using linear frequency-chirped electric fields. A Maxwell-Bloch model using numerical calculation for angled beams with arbitrary phase modulation is used to simulate the chirped field readout process. The simulation results indicate that any spatial-spectral absorption feature can be read out with a chirped field with the appropriate bandwidth, duration, and intensity. Mapping spectral absorption features into temporal intensity modulations depends on the chirp rate of the field. However, when probing a spatial-spectral grating with a chirped field, a beat signal representing the grating period can be created by interfering the emitted photon echo chirped field with a reference chirped field, regardless of the chirp rate. Comparisons are made between collinear and angled readout configurations. Readout signal strength and spurious signal distortions are investigated as functions of the grating strength and the Rabi frequency of the readout pulse. Using a collinear readout geometry, distortions from optical nutation on the transmitted field and higher-order harmonics are observed, both of which are avoided in an angled beam geometry.
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.
Spatial spectral holographic (SSH) systems have applications in signal processing including spectrum analysis to optical correlation. Beam splitters and material interactions can affect the phase relationships between fields in separate spots in the material (or fields bypassing the material). Interferometric methods allow for these phase shifts to be exploited for two primary uses: the isolation of fields generated by the material and the amplification of signals and the amplification of signals in the chirped readout of programmed spectra. Stimulated photon echoes are used as the basis of SSH material-based optical systems and have been suggested as a protocol for optical quantum memory. These applications require the stimulated echo field to be isolated from a probe field. Current methods take an angular approach to isolating fields. An alternative approach uses interferometric methods to isolate fields in a way that can be implemented in a photonic integrated circuit. This dissertation will present a mathematical model for the isolation of stimulated photon echoes in both a 2-port Mach-Zehnder interferometer and a 4-port interferometer designed to emulate the isolation achieved via the angular "Box-Geometry" using interferometric methods. Experimental stimulated photon echo studies in a Mach-Zehnder interferometer built around a sample of 0.01% Tm 3+ : LiNbO 3 will demonstrate the principle of interferometric isolation of stimulated photon echoes. Maxwell-Bloch simulations will be used to demonstrate the principle of echo isolation in the 4-port interferometer. Use of the chirped interferometric readout of programmed spectra is demonstrated for SSH grating processing and spectrum analysis is shown in experiments in a sample of 0.01% Tm 3+ : LiNbO 3. Improvements to signal-to-noise ratio over traditional readout are seen by using a strong local oscillator in both applications. In spectrum analysis applications, the recovery of the proper spectral line shape is demonstrated, and SNR improvements are shown for a given read power. In the grating experiments, a non-linear noise floor was shown that created a constraint on the usable read power for these experiments. In this case, the interferometric readout was able to produce an improvement in the signal-to-noise ratio that could not be achieved using a stronger read power.
The role of weakly chirped pulses (time bandwidth product, DeltanuDeltatau<0.61) on three-pulse photon echo signals has been systematically studied. Pulses with varying chirp were characterized with frequency resolved optical gating (FROG) and used to measure spectrally resolved three-pulse photon echoes of a dye in solution. The weakly chirped pulses give rise to markedly different echo signals for population times below approximately 100 fs. The chirped pulses can decrease or enhance spectral signatures of an excited state absorption transition in the echo signal. Furthermore, the observed dephasing dynamics depend on the phase of the electric fields. Simulations based on a three-level model and the electric fields retrieved from the FROG traces give a good agreement for photon echo experiments with both transform limited and chirped pulses. The simulations also allow for a numerical investigation of effects of chirp in two-dimensional spectroscopy. For a two-level system, the chirped pulses result in nonelliptical two-dimensional spectra that can erroneously be interpreted as spectral heterogeneity with frequency dependent dephasing dynamics. Furthermore, chirped pulses can give rise to "false" cross peaks when strong vibrational modes are involved in the system-bath interaction.
An investigation is reported of the characteristic features of a four-wave mixing of a chirped signal with bandwidth- limited pump waves in a resonant medium modeled by a two- level scheme. Analytic estimates are obtained and a numerical analysis is made of the combined influence of various mechanisms (spatial phase matching, a finite nonlinear response time, and phase cross-modulation) on the spectral composition and on the temporal behavior of the fourth pulse. Conditions are found for achieving, with practically undetectable distortions, phase conjugation of a chirped signal accompanied by shortening of the pulse envelope and narrowing of the spectrum of the phase- conjugate wave.
A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved quasidegenerate three-pulse scattering experiments is presented. The third-order phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separated sets of closely spaced energy levels. Equations for calculating the electric field of four-wave-mixing signals generated by path-length delayed pulses are given. It is found that the phase of the signal field is determined by the excitation pulse phases, the dynamics of the nonlinear polarization decay, the product of four transition dipole matrix elements, and by a pulse-delay-dependent phase modulation at the frequency of the first dipole oscillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decay. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), but can be real and negative for some four-level Raman processes. The pulse-delay-dependent phase modulation treated here is closely related to the interferometric pulse-delay-dependent amplitude modulation observed in some collinear experiments, and plays a role in producing photon echos in inhomogeneously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model appropriate for condensed-phase dynamics are presented. The ability of pulse-delay-dependent phase modulation to encode the frequency of the initially excited dipole onto the phase of the signal field can be exploited to examine energy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.
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.