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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Bit error rates for a photon echo memory

Jin Y. Choi, John F. Walkup, Thomas F. Krile, David J. Mehrl

Published Nov 5, 1998• 1 citation
Publisher

Abstract

The noise characteristics of the photon echo memory have been investigated. The photon echo memory has the ability to store many bits of information in a diffraction-limited spot, thereby dramatically increasing the storage density. The temporal Fourier transform of the input data sequence is written into the inhomogeneous absorption profile of the recording medium. Data are encoded by means of temporal modulation onto the waveform of a finite duration data beam. Individual bits are not localized to a specific spectral channel; instead, they are stored throughout a region of spectral-addressing space, In order to store and recall the input data accurately, the Fourier transform of the input data sequence must be narrower than the inhomogeneous bandwidth. In the photon echo memory mechanism, there are several factors affecting the system bit error rate such as finite-width write/read pulses, echo efficiency, shot noise, thermal noise, etc. The accuracy of the echo output depends on those system factors. In this paper we formulate a simple model of the photon echo system, and by analyzing this model we derive the relationship between the characteristics of the echo output signal and several factors such as the bandwidth of the system, echo efficiency, atom excited state population fluctuations, shot noise, and thermal noise.

DOI
10.1117/12.330424

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The noise characteristics of the photon echo memory have been investigated. The photon echo memory has the ability to store many bits of information in a diffraction-limited spot, thereby dramatically increasing the storage density. The temporal Fourier transform of the input data sequence is written into the inhomogeneous absorption profile of the recording medium. Data are encoded by means of temporal modulation onto the waveform of a finite duration data beam. Individual bits are not localized to a specific spectral channel; instead, they are stored throughout a region of spectral-addressing space, In order to store and recall the input data accurately, the Fourier transform of the input data sequence must be narrower than the inhomogeneous bandwidth. In the photon echo memory mechanism, there are several factors affecting the system bit error rate such as finite-width write/read pulses, echo efficiency, shot noise, thermal noise, etc. The accuracy of the echo output depends on those system factors. In this paper we formulate a simple model of the photon echo system, and by analyzing this model we derive the relationship between the characteristics of the echo output signal and several factors such as the bandwidth of the system, echo efficiency, atom excited state population fluctuations, shot noise, and thermal noise.
The photon-echo memory[1], or the time-domain optical data storage, resembles the hole-burning memory [2] in that the inhomogeneous absorption line of a material is employed as a storage medium and the information is stored in it as a frequency-dependent absorption change with the resolution determined by the homogeneous width. Having the common memory capacity N given by the inhomogeneous-to-homogeneous width ratio, both types of memories share common problems like low-temperature operation, spectral diffusion and so on. Although a storage medium is common, storage techniques are definitely different for the two memories. The photon-echo memory utilizes the temporal interference effect between a reference pulse and a data pulse and their interference pattern is stored as a population grating in the frequency domain. In this sense this is a time-domain analog of holography where the spatial interference pattern between a reference beam and a data beam is stored in a medium as a population grating in the real space. Like the spatially diffracted beam from the read beam gives the information stored in the hologram, the “temporally diffracted pulse", or the photon echo, after the read pulse can give the information stored in the inhomogeneous distribution.
The diffraction-limited spot size of a focused laser beam puts an upper boundary on the storage densities in conventional optical data storage. This can be overcome by storing multiple bits of data in each spatial location. In materials with an inhomogeneously broadened absorption line, such as crystals doped with rare-earth ions, frequency can be used as an additional addressing dimension. In some materials the number of spectral channels can be as high as 107. Spectral data storage can be done using coherent transient interactions between light and atoms and can be described in terms of photon echo processes. In this Master's Project the swept-carrier time-domain (SCTD) approach, a hybrid between frequency- and time-domain approaches, is used. An overview of the theory is given, followed by a description ofthe set-up and equipment. A maximum of 330 bits of data have been stored in one spatial location. The necessary conditions for successful storage and retrieval of data have been examined and suggestions are given on how to extend the results further.
The first analysis to our knowledge of the optical data storage density of photon-echo storage is presented. Mainly considering signal-to-noise ratio performance, we calculate the obtainable storage density for data storage and processing using photon echoes to be approximately 100 times the theoretical limit for conventional optical data storage. This limit is similar to that theoretically calculated for data storage by use of persistent spectral hole burning. For storage times longer than the upper-state lifetime the highest densities can, however, be obtained only if all the excited atoms decay, or are transferred, to a different state than that from which they were originally excited. The analysis is restricted to samples with low optical density, and it also assumes that for every data sequence, writing is performed only once. It is therefore not directly applicable to accumulated photon echoes. A significant feature of photon-echo storage and processing is its speed; e.g., addressing 1 kbyte/(spatialpoint) permits terahertzread and write speeds for transitions with transition probabilities as low as 1000 s(-1).
The photon echo memory is one of the most attractive optical memories in terms of memory capacity and access speed. Fundamentally, the storage capacity and access speed are limited by the inhomogeneous bandwidth of the material. In reality, however, the storage capacity and data rates are further limited by several kinds of imperfections in the memory process. One of the main limiting factors is the noise caused by several sources. In this dissertation we categorize these noise sources into three groups, time domain noise, frequency domain noise, and detection noise. For each noise group, we create models and characterize the noise properties. We then simulate each noise model in the computer and compare the results with the analytical results. Experimental results are also presented. Those experimental results yield insight into the photon echo memory system and its physical noise characteristics. The dissertation concludes with an interpretation of the noise modeling approach described and proposes fiiture directions for this research area.
We present the results of analytical and numerical calculations of the amplitude and temporal shape of photon echoes produced in optically thick absorbing media. In particular, we are interested in echo output signals that mimic the temporal shape of one of the input pulses (the data pulse). Echo recall efficiencies of temporally structured data pulses exceeding unity can be obtained in optically thick media while preserving the information content of the data pulse. We find that the relationship between the maximum echo efficiency and the Beer's length at which that maximum is attained is nearly linear. This linear relation holds well beyond the optimal absorption length predicted by linear theory for both two-pulse photon echoes and three-pulse stimulated photon echoes. These results have significance in the development of optical coherent transient memory and processing systems, where previous calculations predicted recall efficiencies of only a few percent.