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Journal of the Optical Society of America B

Rate equation reformulation including coherent excitation: application to periodic protocols based on spectral hole-burning

Yoann Attal, Perrine Berger, Loïc Morvan, P. Nouchi, Daniel Dolfi, T. Chanelière, Anne Louchet-Chauvet

Published May 3, 2018• 1 citation
Publisher

Abstract

A large number of signal-processing protocols are based on recording a spectral pattern via spectral hole-burning in an inhomogeneously broadened absorption profile. We present a simulation method specifically designed for periodic excitation sequences leading to the creation of a spectral pattern. This method is applicable to any multilevel atomic structure. The atomic variables’ coherent dynamics are solved for a single temporal excitation step. The result is expressed as an equivalent population transfer rate. This way, the whole sequence is described as a matrix product and the steady state of the system under periodic excitation is easily derived. The propagation through the atomic medium is fully decoupled from the temporal evolution. We apply this method to the engraving of a spectral grating in a large-absorption Tm:YAG sample for wideband spectral analysis.

DOI
10.1364/josab.35.001260

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A large number of signal-processing protocols are based on recording a spectral pattern via spectral hole-burning in an inhomogeneously broadened absorption profile. We present a simulation method specifically designed for periodic excitation sequences leading to the creation of a spectral pattern. This method is applicable to any multilevel atomic structure. The atomic variables’ coherent dynamics are solved for a single temporal excitation step. The result is expressed as an equivalent population transfer rate. This way, the whole sequence is described as a matrix product and the steady state of the system under periodic excitation is easily derived. The propagation through the atomic medium is fully decoupled from the temporal evolution. We apply this method to the engraving of a spectral grating in a large-absorption Tm:YAG sample for wideband spectral analysis.
Summary form only given. Complex spectral gratings, accumulated to nearly steady-state in a short-term persistent inhomogeneously broadened optical transition, have been demonstrated by repeated application of a pair of frequency stabilized and low power-optical pulses (i.e. continuous programming). Provided the grating is not saturated, it can perform continuous correlation of an amplitude and/or phase modulated optical waveform at multi-gigahertz rates with large time-bandwidth products. The present work demonstrates continuous programming of a complex spectral grating, representing a 30-bit pattern and 4 microsecond time delay, to and beyond steady state. Grating accumulation and maintenance is observed by applying a probe pulse (identical to the pattern) after each programming pulse pair. Each probe stimulates an optical coherent transient emitted signal that represents the correlation of the pattern and probe. The probe was non-destructive to the grating, and consequently did not interfere with programming. The frequency reference was a transient, regenerating spectral hole created by the optical carrier in the same inhomogeneously broadened transition.
A complex spectral grating is accumulated by repeated application of a pair of low-power optical programming pulses to a short-term persistent inhomogeneously broadened transition in Tm:YAG at 4.5 K and then probed to investigate the buildup dynamics. The necessary frequency stability is obtained by locking a cw Ti:sapphire laser to a regenerating transient spectral hole in the same transition. Grating accumulation is demonstrated for both a periodic spectral grating, representing a true-time delay, and a complex spectral grating, permitting correlation-based pattern recognition. This work is a step toward demonstrating an optical coherent transient continuously programmed continuous processor.
In this work, we present a model that describes the atomic reaction to a periodic excitation in a general case. Starting with a holeburning material, we aim at computing the steady state of the atoms of interest within the whole bulk material. This work is composed of three steps. In the first one, we generalize the optical Bloch equations to any atomic structure, keeping as long as possible the Bloch sphere picture that can provide good intuition and a better understanding of the atomic response than a huge set of equations.
We propose a protocol for storage and retrieval of photon wave packets in a $\ensuremath{\Lambda}$-type atomic medium. This protocol derives from spectral hole burning and takes advantages of the specific properties of solid-state systems at low temperature, such as rare-earth ion-doped crystals. The signal pulse is tuned to the center of the hole that has been burnt previously within the inhomogeneously broadened absorption band. The group velocity is strongly reduced, being proportional to the hole width. This way the optically carried information and energy are carried over to the off-resonance optical dipoles. Storage and retrieval are performed by conversion to and from ground-state Raman coherence by using brief $\ensuremath{\pi}$ pulses. The protocol exhibits some resemblance with the well-known electromagnetically induced transparency process. It also presents distinctive features such as the absence of coupling beam. In this paper we detail the various steps of the protocol, summarize the critical parameters, and theoretically examine the recovery efficiency.
Several investigations have shown that in some systems stimulated photon echoes may be obtained over times much longer than the excited state relaxation time T11,2. It has been claimed that the mechanism for this anomalously long storage time is the formation of a frequency dependent modulation of the ground state population which persists because of spectral hole-burning1. Such a population grating produced by coherent multipulse excitation and spectral hole-burning has been measured only in a few cases3.
We apply Fourier-transform spectral interferometry to complete phase and intensity characterization of a chirped filter engraved in a persistent spectral hole-burning (PSHB) material. The conjugated transfer function of a grating pair compressor is stored in a PSHB material as an accumulated spectral hologram that behaves as a pulse stretcher. By directing the diffracted pulse back through the compressor, we verified that the PSHB stretcher’s transfer function is indeed conjugated to that of the grating pair compressor. We have extended the spectral phase analysis to regions where the engraved structure is much narrower than the spectrometer’s resolution.