Noise in Brillouin Based Information Storage

We theoretically and numerically study the efficiency of Brillouin-based opto-acoustic data storage in a photonic waveguide in the presence of thermal noise and laser phase noise. We compare the physics of the noise processes and how they affect different storage techniques, examining both amplitude and phase storage schemes. We investigate the effects of storage time and pulse properties on the quality of the retrieved signal, and find that phase storage is less sensitive to thermal noise than amplitude storage.

: data pulses are depleted by the write-pulse, exciting an acoustic wave inside the waveguide, with some energy gained by the write-pulse. Retrieval process in (c) and (d): a read-pulse interacts with the acoustic wave, both become depleted and the energy is used to regenerate the original sequence of data pulses. The retrieval efficiency is limited by the acoustic lifetime of the phonons. 55 2.1. Brillouin coupled mode equations 56 We consider a waveguide of length oriented along the coordinate axis, in which an optical data stream propagates in the positive direction. The interaction between the two optical fields and the acoustic field can be described by the coupled system [18, 19]

Numerical simulation of noise
where 1 ( , ) and 2 ( , ) are the envelope fields of the data pulse (pump) and read/write pulse 57 (Stokes) respectively, which correspond to mode fields with frequency/wavenumber ( 1,2 , 1,2 ). random phase terms 1,2 are statistically uncorrelated Brownian motions described by must obey the condition Θ = ( + 1/2) where = 0, 1, 2, .... This is because once 84 the data pulse is depleted completely, the transfer of energy reverses and the data pulse is 85 regenerated [23][24][25]. The dependence of the pulse-area on may seem deceptive at first, but 86 since 0 is also dependent on these two effects cancel out.

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The storage efficiency tells us how effective the storage system is, and may be defined as the 88 ratio of the total output data power | out ( )| 2 to the total input data power | data ( )| 2 [10]: For our simulations we use the parameters summarized in Table 1. We assume a high gain   Gaussian pulses of the same peak power p0 , while zeros are represented by gaps of duration bit .

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For phase storage, we use the same scheme as in quadrature phase-shift keying (QPSK) with gray 124 coding [31], where bit pairs are assigned a unique phase, namely 11 = 45°, 01 = 135°, 00 = 225°125 and 10 = 315°. For a given input information packet, we quantify the retrieval accuracy in both 126 storage schemes via the packet error rate (PER). This is similar to the bit error rate (BER) of 127 a binary stream, except that we count correct 8-bit packets as opposed to counting individual 128 correct bits. Therefore, the PER is the ratio of correctly retrieved packets with respect to the 129 input data, and has a value 0 ≤ PER ≤ 1.

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In the amplitude storage case, we encode bits=1 into Gaussian pulses of full-width at half-131 maximum (FWHM) 1 , while bits=0 are represented by gaps of duration bit in the data sequence.

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By default, we choose all pulses to have a phase of 0°. In the retrieval stage, the output data power 133 | out ( )| 2 is separated into equal intervals of length bit . We use a dynamic threshold technique:  In the phase storage case, we encode bit-pairs into 4 different phases, as shown in Fig. 3(a),  Fig. 4. First, we observe 160 in Fig. 4(a) and (b) that the storage efficiency in both storage schemes is higher as we increase 161 the peak write pulse power, as the pulse area is lower than the optimum value given by Eq. (5).

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We have numerically simulated the Brillouin storage of different data packets with thermal and 207 laser noise, using amplitude storage and phase storage techniques in a photonic waveguide.

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Through these computer simulations, we have shown that phase encoded storage allows for longer  Data underlying the results presented in this paper are not publicly available at this time but may be obtained 225 from the authors upon reasonable request.