Cross-gain modulation between pairs of counter-propagating pulses within a semiconductor optical amplifier is used as a pulse delay detector. Unlike previous designs based on differential photodiodes, the difference between average powers of the pulse trains after propagation are deduced from the voltage difference between two contacts on the SOA, eliminating the photodiodes and two optical couplers. Simulations show the design can be improved by adding a third contact. The linearity, sensitivity and noise performance of the design equal or surpass the original design.
©2005 Optical Society of America
The comparison of phase and timing of modulated optical waveforms is critical to the design of all-optical clocks using phase-locked loops . Awad et al.  have proposed a novel device for measuring the delay between two pulse trains using cross-gain modulation in a Semiconductor Optical Amplifier (SOA). In their design, the two pulse trains are injected into opposite ends of the SOA, so that they counter-propagate. The pulse trains are conditioned to have equal pulse energies and low duty-cycles (short pulses). If input pulses in one direction precede the opposite-traveling pulses, they will benefit from high gain in the SOA, and reduce the gain for the opposite-traveling pulses. Simply comparing the time-averaged output powers at the ends of the SOA will indicate the relative delays of the pulses. Awad et al.  used couplers and photodiodes to detect the powers of the counter propagating waves exiting the SOAs as shown in Fig. 1. The photocurrents are fed into a low-speed differential amplifier to obtain a signal proportional to the relative timing of the pulses.
In this paper, a simplified arrangement dispensing with the photodiodes and couplers is proposed, as shown in Fig. 2. This uses the difference in the contact voltages on a 2-section SOA to deduce the relative powers exiting the SOA. This scheme has the advantage of fewer optical components and easier integration, since no photodiode processing steps are required. The performance of the device was tested using numerical simulations, which indicated very good linearity, high sensitivity and a first-order transient response with a time-constant of 300 ps. Furthermore, if a long 3-contact is introduced between end electrodes of SOA, the sensitivity of the scheme can be improved and also made independent of input power.
Previously, Awad’s  device has been simulated as part of a photonic circuit design for optical-time division multiplexed (OTDM) signal demultiplexing . This paper extends that simulation by introducing a multi-contact model of the Semiconductor Optical Amplifier (SOA). The device parameters are as in . The model predicts the carrier densities under each contact, and so is able to deduce the contact voltage.
Figure 3 shows a simplified simulation schematic from VPIcomponentMaker™ Active Photonics, for a 3-contact SOA, though the length of the center contact can be reduced to zero. The optical pulses generators (one for each signal direction) comprise: bit generators (used to provide strings of 1’s); electrical pulse generators (with the ability to specify a periodic timing jitter); lasers (assumed to convert the electrical pulses to optical pulses perfectly in this simulation). A variable delay module can apply swept or step-increases in time delay to one input of the SOA. The pulse rate is 10 Gpulses/s with a width of 12.5 ps and a peak power of 1 mW.
The SOA model has four optical ports, representing two bidirectional ports in the real device, on the left and right. The optical input ports are fed with the counter-propagating waves from the optical pulse generators. The optical output ports are fed to photodiode models. The difference of the photocurrents is calculated and fed to an oscilloscope model. The top input port of the SOA model allows different bias currents to be applied to each contact of the SOA. The current per unit length was kept constant in all of the simulations at 20 mA/(63 µm). The top outputs of the model also produce time waveforms of the average carrier densities under each contact. These are converted to voltages using a heterojunction model with an ideality factor of 2 and a temperature of 300 K. The simulations were operated at a sampling rate of 2.56 THz, giving a time resolution of better than 400 ps. The simulations were run for sufficiently long for all outputs to reach a steady state.
Figure 4 shows the output current of the photodiode’s differential receiver for the circuit of Awad et al.  when one period of sinusoidal jitter is applied to the forward pulses, over a period of 32 pulses. The SOA has 2-contacts, each 190-µm long, though it behaves as a single-contact SOA for the purposes of this explanation. The jitter amplitude is 15 ps peak to peak. The backward pulses reach the photodiode connected to the -ve input of the differential receiver, to produce negative-going spikes: the forward pulses produce positive spikes. If the pulses are synchronized, they will perfectly cancel, as happens at the beginning, middle and end of the Fig. 4. In the first half of the plot, the backward pulses lead. This means that they receive more gain from the SOA, as they stimulate the recombination of carriers so reduce the gain available for the forward pulses. If the differential photocurrent is passed through a low-pass filter, then the filter’s output will indicate a negative voltage when the backward-pulses lead, and a positive voltage for when the forward pulses lead.
Figure 5 shows the output voltage of the Contacts’ Differential Receiver for our proposed scheme, obtained during the same simulation as Fig. 4. This plot shows large negative spikes of the backward pulses during the first half of the simulation, and positive-going spikes in the second half of the simulation. However, the charge storage in the SOA has effectively integrated the waveform compared with the photodiodes’ output. This aside, the plot shows that the differential contact voltage is an indication of the time delay.
A simple explanation for the operation of the 2-contact delay measurement is as follows. The contacts are connected to constant current sources of equal magnitude. We assume that the carrier lifetime is assumed to be far longer than the pulse width, the transit time of pulses through the SOA and the delay between the pulse trains. Consider a single low-power pulse incident on the left-hand facet of an SOA. This pulse will grow exponentially as it propagates along the SOA, from left to right (“forwards”). At the right facet of the SOA, the pulse will have grown to sufficient power that stimulated recombination becomes significant, reducing the carrier density and gain under the right contact. If a pulse is then input to the right facet of the SOA, to travel backwards along the SOA, it will experience this reduced gain and not grow strongly as it propagates towards the left contact. Therefore, the carrier density under the left contact will not be reduced as much as the carrier density under the right contact was. This imbalance in carrier densities will cause a differential voltage across the contacts. In the absence of pulses within the SOA, the carrier density relaxes towards a steady-state, causing the differential contact voltage to be a function of time delay.
From the simple explanation, it is unclear whether the device will exhibit sufficient linearity, sensitivity and speed to be useful, or be better than the photodiode design.
3.1 Number and lengths of contacts
The voltage change at the contacts relies on having a large change in carrier density below the contacts. A simple model of heterostructure junction voltage V with carrier density N, ignoring resistive voltage drops, is :
where: η is the heterostructure ideality factor, k is Boltzmann’s constant, T is the junction temperature, q is the electronic charge and Ni is the intrinsic carrier density. It is clear that the voltage change will be greatest at the ends of the device, where the optical powers, so the stimulated recombination is highest . A long contact will average the voltage underneath it (due to the bulk resistance of the contact to the active region). Thus, it is advantageous to have two short contacts close to the facets of the SOA, and a third contact over the centre region of the SOA, just to provide current to the center region .
Figure 6 shows the effect on peak-peak output voltage (neglecting the spikes) for a 15 ps peak-peak delay, of using a 3-contact SOA for various lengths of center contact. In all cases the end contacts were 126-µm long each and the current density was maintained constant along the SOA. The three traces correspond to different peak input powers. The shortest center contact is 126-µm: this gives a total SOA length equal to the 2-contact simulations. In this case, the output voltage swing is improved from 0.85 mV to 1.14 mV by having 3 rather than 2 contacts. For longer center contacts and low input powers, the sensitivity improves by a factor of 4, because of the extra amplification provided by the center section of the SOA. However, for high input powers, the center section becomes gain-saturated, giving little benefit of a long length. Usefully, long center contacts give a sensitivity (volts per unit delay) independent of input power.
The linearity of the output versus time delay is important if the device is to be used over a wide range of delays, rather than as part of a delay-locked loop that locks to a single value of delay. To measure the linearity, the delay of the forward pulses was swept and the mean output of the contacts and the photodiodes calculated. A 380-µm center contact was used, with 1-mW peak pulses of 12.5 ps width.
Figure 7 shows the mean output versus delay between the pulses. The 50 ps delay corresponds to the forward pulses lying between the backward pulses. The best linearity is obtained around this point. Both schemes show similarly-good linearity. Note that the photodiodes produce a photocurrent. A responsively of 1 A/W is assumed, with perfect coupling from the SOA to the photodiodes. Use of 50% couplers would reduce this current by 50%, and coupling losses to the facet would introduce at least another 3-dB loss from the SOA to the coupler. The input signal would also be attenuated by the coupler and the facet coupling loss. The sensitivity of the contacts is 188 µV/ps assuming a pulse input power just inside the amplifier’s facets of 1 mW peak.
3.3 Noise spectra
For noise calculations, the following simulations use a population inversion parameter (the absolute carrier density divided by the carrier density in excess of the transparency density) of 2 in the SOA, photodiodes with shot noise, followed by amplifiers with 10-11 A/root-Hz input noise current. The noise spectrum is displayed on an RF spectrum as the electrical power into 1-ohm in a 78-MHz bandwidth.
Figure 8 shows the noise spectra of the photodiode and contact schemes. These show similar signal to noise ratios close in to the signal (at DC). However, the photodiode shows a flat frequency spectrum (there is no bandwidth limitation on the photodiode), whereas the contact noise is filtered by the carrier storage in the SOA. Investigations identified that the noise in both cases was from amplified spontaneous emission (ASE) within the SOA. In the case of the photodiode, this wideband optical noise mixes with itself to produce wideband electrical noise (ASE × ASE) over the simulation bandwidth. Awad et al.  used optical bandpass filters to reduce this noise.
3.4 Transient response
As indicated by Fig. 4, the transient response of the photodiode scheme is dominated by the electrical bandwidth of the photodiodes and subsequent amplifiers. Figure 5 showed that the contact voltage responded more slowly. To investigate further, a simulation was devised where the delay was subject to a step increase of 10 ps after the system had reached a steady-state with zero delay. The voltage output was integrated into 50 ps blocks and the pulse rate increased to 20 Gpulses/s. This filtered out any rippled between the pulses. The response was fitted to a V(t)=V ∞(1- exp(-t/τ)) function, and this revealed a good fit over 3 orders of magnitude, with a timeconstant, τ, of 293 ps, giving a bandwidth of over 500 MHz. This bandwidth is set by the effective carrier lifetimes within the SOA .
A simplified method of detecting the relative delay between two optical pulse trains has been devised and tested using numerical simulations. This method offers good performance using fewer components than previous schemes, and allows integration onto a photonic circuit. The method uses a 2- or 3-contact SOA. The 3-contact scheme has the advantage that the sensitivity of the device is independent of the pulses’ powers at input powers >1 mW.
We should like to than VPIphotonics (www.vpiphotonics.com) for the use of their simulator VPIcomponentMaker™Active Photonics for the simulations in this paper.
References and links
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