METHOD FOR PHYSICAL RANDOM NUMBER GENERATION USING A VERTICAL CAVITY SURFACE EMITTING LASER

Abstract

A method for physical random number generation includes the steps of: modulating the gain of a vertical-cavity surface-emitting laser periodically from the lower threshold to the upper threshold and back; maintaining the gain per round trip positive for a longer period than the round trip time of the cavity; maintaining the net gain per round trip negative for a longer period than the round trip time of the cavity, in order to create optical pulses of random amplitude; detecting the optical pulses; converting the optical pulses into electrical analog pulses; and digitising the electrical analog pulses into random numbers.

Claims

1. A method comprising: modulating a gain of a vertical-cavity surface-emitting laser periodically from below a regime of spontaneous emission to above a regime of stimulated emission to create optical pulses of random amplitude; detecting, before the optical pulses reaches a maximum value, the optical pulses; converting the optical pulses into electrical analog pulses; and digitizing the electrical analog pulses into random numbers.

2. The method of claim 1, wherein detecting the optical pulses comprises detecting the optical pulses via a fast photodiode.

3. The method of claim 1, wherein modultating the gain comprises setting a biasing current point of the vertical-cavity surface-emitting laser below a threshold level and adding an additional modulating current.

4. The method of claim 3, wherein the additional modulating current varies between 2 mA and +2 mA.

5. The method of claim 1, wherein digitizing the electrical analog pulses comprises digitizing the electrical analog pulses via an 8-bit digitizer or a comparator.

6. The method of claim 5, wherein the comparator operates as a 1-bit resolution digitizer.

7. The method of claim 1, wherein modulating the gain comprises: maintaining gain per round trip positive for a longer period than a round trip time of a cavity of the vertical-cavity surface-emitting laser; and maintaining net gain per round trip negative for a longer period than the round trip time of the cavity, to create optical pulses of random amplitude.

8. An apparatus comprising: a vertical-cavity surface-emitting laser; an electric pulse diver configured to modulate a gain of the vertical-cavity surface-emitting laser periodically from below a regime of spontaneous emission to above a regime of stimulated emission to create optical pulses of random amplitude; an optical detector configured to detect, before the optical pulses reaches a maximum value, the optical pulses and convert the optical pulses into electrical analog pulses; and a digitizer configured to digitize the electrical analog pulses into random numbers.

9. The apparatus of claim 8, wherein the optical detector comprises a fast photodiode.

10. The apparatus of claim 8, wherein the electric pulse diver is configured to set a biasing current point of the vertical-cavity surface-emitting laser below a threshold level and add an additional modulating current.

11. The apparatus of claim 10, wherein electric pulse diver configured to add the additional modulating current such that the additional modulating current varies between 2 mA and +2 mA.

12. The apparatus of claim 8, wherein the digitizer comprises an 8-bit digitizer or a comparator.

13. The apparatus of claim 12, wherein the comparator comprises a 1-bit resolution digitizer.

14. The apparatus of claim 8, wherein the electric pulse diver configured to modulate the gain of the vertical-cavity surface-emitting laser by: maintaining gain per round trip positive for a longer period than a round trip time of a cavity of the vertical-cavity surface-emitting laser, and maintaining net gain per round trip negative for a longer period than the round trip time of the cavity, to create optical pulses of random amplitude.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] FIG. 1 shows a scheme of the method of the invention;

[0012] FIG. 2 shows the time dependent traces (left) and corresponding spectra (right) of train pulses as in the method of the invention;

[0013] FIG. 3 represents the time-dependent trace (left) and spectrum (right) of a train of pulses for a VCSEL that stays always above threshold in contrast with FIG. 2;

[0014] FIG. 4 shows the time dependent trace of several pulses (right) captured by an oscilloscope together with their statistical distribution of intensity (left); and

[0015] FIG. 5 is a representation of several pulses captured by an oscilloscope.

DETAILED DESCRIPTION

[0016] There are different VCSEL structures for implementing embodiments of the invention. The driving current applied to the VCSEL to modulate its gain consists of two parts: a bias current and a modulating current. It is essential that the sum of those (i.e. the total current applied) take the VCSEL from below (regime of spontaneous emission) to above threshold (regime of stimulated emission) and back continuously. FIG. 1 shows a possible scheme for implementing the process of the invention. A generator (electrical pulse driver) delivers current pulses to a VCSEL that produce a train of optical pulses with varying amplitude that can be detected by a photodiode (PD). When the VCSEL is taken from below to above threshold and back again at each pulse, the intensity pattern becomes random and can be digitised into a random number sequence.

[0017] FIG. 2 shows an example of the train of pulses (intensity as a function of time) detected by the photodiode and displayed by an oscilloscope, together with the corresponding spectra (intensity as a function of wavelength). On the left, the time dependent traces can be seen, while on the right, the corresponding spectra of a train of pulses with varying amplitude at different bias currents, 2, 2.5 and 3 mA (pulse/modulation frequency 200 MHz) can be found. The modulating current varies from about 2 mA to +2 mA. Under these conditions, the VCSEL goes from below-to-above-to-below threshold during the formation of each pulse. Despite a periodic modulation of the current (always with the same value from pulse to pulse), the optical intensity of the pulses varies. In some instances, the optical pulses reach their maximum amplitude right after the current is taken to above threshold while in other cases it takes a while before the pulses reach their maximum intensity. In other instances, the pulses are essentially absent (they do not grow). In this way, a train of pulses with random intensity is generated, which can be subsequently detected and digitised into random numbers.

[0018] FIG. 3 clearly shows that in the case the VCSEL current is not taken below threshold, i.e. the current is modulated from slightly above threshold to farther above threshold, the intensity of the different optical pulses does not change over time. The time dependent trace (left) and corresponding spectrum (right) of a train of pulses with constant amplitude and different pulse/modulation frequency, for a bias current of 4 mA is shown. The modulating current varies from about 2 mA to +2 mA. Under these conditions, the VCSEL stays always above threshold. There is also a clear difference between corresponding spectra (FIGS. 2 and 3 bottom): in the case of random intensity patterns there exists a side lobe at long wavelength, which is essentially absent in the case of constant intensity patterns. Such a side lobe indicates that when the modulation brings the laser from below to above the threshold level, a new mode is generated. For certain pulses, the gain experienced by the predominant mode is reduced, with its consequent smaller growth, while it is larger for the side mode. The fact that the gain for the predominant mode is reduced in the pulses with lower intensity is also in agreement with the absence of the relaxation oscillation peaks at the beginning of each pulse.

[0019] The generated random optical intensity pattern has a typical distribution as shown in FIG. 4. The time dependent trace of several pulses (right) captured by the oscilloscope together with their statistical distribution of the intensity (left) can be seen in this graph. The statistical distribution corresponds to more than 30000 pulses. Pulse/modulation frequency is 1 GHz, bias current of 1.7 mA and modulating current varies from about 2 mA to +2 mA. Note that the time dependent behaviour of the random intensity and the corresponding distribution may depend on parameters such as geometry and materials of VCSEL structure, bias current, modulating current, pulse/modulation frequency, temperature, etc. For example, there is a clear increase in the entropy at higher frequency, which is evident when going from 100 to 400 MHz (FIG. 5) and even more at 1 GHz (FIG. 4). This is due to the fact that the shorter the current pulse the lower the growth experienced by the light pulse; i.e. there is not sufficient time for the light pulse to grow to significant intensities within its duration when the random effect occurs. In FIG. 5, the time dependent trace of several pulses captured by the oscilloscope is shown. Pulse/modulation frequency is 100 MHz (top), 200 MHz (middle) and 400 MHz (bottom), the bias current is 3 mA and the modulating current varies from about 2 mA to +2 mA.

[0020] The gain-switching mechanism is used to modulate the output of the laser source. By injecting electrical carriers into the active region, through the application of an electrical signal, the gain of the laser can be changed. In particular, by setting the biasing current point of the laser below a threshold level and adding an additional modulating current, a sequence of optical pulses can be produced. During the pulse generation the laser continuously goes from below to above threshold. While doing this, a secondary lobe appears in the laser spectrum. The produced train of optical pulses undergoes strong amplitude variations due to the presence of this new spectral feature. The optical pulses are then recorded with a photodetector that converts the optical signal into an electrical signal. Finally, the electronic signal can be converted into a digital signal by means of a digitisation process, which can include high-resolution digitisers, e.g. 8 bit digitisers, or a simple comparator acting as a 1-bit resolution digitiser.

[0021] Changes and modifications in the specifically-described embodiments may be carried out without departing from the principles of the present invention, which is intended to be limited only by the scope of the appended claims as interpreted according to the principles of patent law including the doctrine of equivalents.