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Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation
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Image of FIG. 1.
FIG. 1.

A schematic of a laser with delayed optical feedback.

Image of FIG. 2.
FIG. 2.

A schematic of the photonic integrated device that we study in this work.19 It consists of a single frequency DFB, two semiconductor optical amplifiers (SOA1 and SOA2), a photodiode (PD) and a passive waveguide. HR-coating: high reflection coating for optical feedback, AR-coating; anti-reflection coating for avoiding extra optical feedback.

Image of FIG. 3.
FIG. 3.

The power spectra and the absolute values of the autocorrelation for the injection current to SOA1 mA (a,b), 10 mA (c,d), and 15 mA (e,f). In these examples, the injection currents to SOA2 and DFB are fixed at 5 mA and 35 mA, respectively. For a comparison of the signal amplitudes, the power spectrum of the laser noise observed for mA is shown in figure (a). Dotted lines represent (b), (d), and (f).

Image of FIG. 4.
FIG. 4.

A schematic of experimental setup for measuring the effect of noise amplification in a laser device with delayed optical feedback. OSC; digital oscilloscope (50 GS/s, bandwidth 12.5 GHz).

Image of FIG. 5.
FIG. 5.

Time trace of the chaotic light intensity. The upper panel represents the pulse current. In this example, the low level and high level of the pulse are respectively 0 mA and 5 mA.

Image of FIG. 6.
FIG. 6.

Four temporal waveforms of chaotic intensity starting from an initial state. The injection current is applied to SOA1 at time . The values of the injection current are 5 mA (a), 10 mA (b), 15 mA (c).

Image of FIG. 7.
FIG. 7.

Time dependence of the probability density of the chaotic light intensity signals for . The dotted curve represents the probability density obtained from a single long chaotic time series in the case of the same injection current value.

Image of FIG. 8.
FIG. 8.

The time dependence of the deviation from the invariant probability density for J = 5 mA (a), 10 mA (b), 15 mA (c). Dotted lines represent (a), (b), and (c).

Image of FIG. 9.
FIG. 9.

Time dependence of the Shannon's entropy.

Image of FIG. 10.
FIG. 10.

Time dependence of the Shannon's entropy of the XOR-ed bit sequences.


Generic image for table
Table I.

Results of NIST Special Publication 800-22(rev. 1a) statistical tests. For each test, 100 samples of 1 Mbit sequences and significance level were used. “Success” denotes that the P-value of the uniformity of p-value is larger than 0.0001, and that the proportion of the bit sequences satisfying p-value for 100 samples is larger than 0.960150377. For the tests which produce multiple P-values and proportions, the worst case is shown.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation