Timing jitter in semiconductor lasers under pseudorandom wordmodulation

Timing jitter of semiconductor lasers under pseudorandom word modulation was studied at 1 Gb/s. For lasers biased above threshold the timing jitter was Gaussian in distribution, with a turn-on timing jitter amplitude τ=2σ=±6 ps. For lasers biased below threshold, the turn-on timing jitter showed two peaks of Gaussian distribution, with an amplitude τ=60±10 ps and separated by about 80 ps. This phenomenon is due to a pattern-dependent effect of the laser turn-on delay. Theoretical calculations show that for data transmission above 2.2 Gb/s, the laser has to be biased above threshold to avoid excessive (>0.5 dB) jitter-induced power penalty     

Memory diagram of single-mode semiconductor lasers

A memory diagram, i.e., regions where pattern effects appear at the output of the laser, in the bias-current-versus-modulation-period plane is obtained, both by numerical simulation of the rate equations and by using an analytical approach. A simple method, based on the superposition of the turn-on time probability distribution for the periodic sequence . . .1111. . . of input bits and the turn-on time probability distribution obtained for repetitive gain switching, is used to describe the response of the laser to a pseudorandom word modulation of the injection current     

Mode partition noise of nearly single-mode semiconductor lasersmodulated at GHz rates

A new method to calculate very low errors due to mode partition noise in nearly single-mode semiconductor lasers has been developed. The laser is intensity modulated at GHz rates. The method allows us to obtain the error for a periodic sequence of input bits as a function of the threshold gain difference for different values of the bias current, above and below threshold, injected current in the ON state and modulation frequency. It is shown that bounds for the error under pseudorandom modulation conditions can be obtained from the periodic and gain switching sequences. The required threshold gain difference for an error of 10^-9 is calculated, and it is shown to increase with the current in the ON state. We also observe pattern effects at the output of the laser, for bias current above threshold, due do the pseudorandom sequence of input bits. For a special value of the bias current slightly below threshold, these patterns effects are suppressed and the error is independent of the modulation frequency and of the modulation regime     

The effect of external optical feedback on timing jitter in modulated laser diodes

Laser diodes with optical feedback are numerically modeled using single-mode rate equations. The effects of the optical feedback on the pulse turn-on delay and timing jitter are examined, for gain-switching, periodic and pseudorandom modulation formats. It is shown that there is a change in turn-on delay and a considerable increase in the timing jitter due to the changes in the output power distributions as optical feedback increases. The cause of the increased jitter is found to be the additional intensity noise introduced by the optical feedback.<>     

Analysis of bit-error rate of vertical-cavity surface-emitting lasers modulated at high speed

A theoretical study of single and multimode vertical-cavity surface-emitting lasers (VCSELs) subject to pseudorandom modulation of the current at a rate of 10 Gb/s is performed. Eye diagrams, probability density functions of the power at the decision time, averaged turn-on delay, and timing jitter are analyzed for different values of the on- and off-state currents. Bit sequences where errors occur are identified. Extensive simulations have been performed to obtain the bit-error rate (BER) for the back-to-back configuration. We find that the BER performance of single-mode VCSELs is better than the one obtained with multimode VCSELs when the off-state current is smaller than the threshold current. The same result is obtained when the off-state current is larger than the threshold value, providing that the on-state current is large enough. However, BER in single-mode VCSELs is greater than in multimode VCSELs when the off-state current is equal to the threshold current. BER performance is also better for multimode VCSELs when the off-state current is larger than the threshold value, if the on-state current is small enough.     

The effect of external optical feedback on the turn-on delaystatistics of laser diodes under pseudorandom modulation

The turn-on delay statistics of laser diodes with optical feedback are investigated by numerical modeling. Under pseudorandom modulation the optical feedback causes an increase in the average turn-on delay and multiplies and jitter considerably. The jitter increase due to optical feedback is largest at highest bias currents. Optical feedback from an external reflectivity of greater than 0.1% can destroy the pattern effects which occur for some operating conditions     

Dynamic spectra of 1.3-µm InGaAsP lasers under pseudorandom word modulation

The dynamic spectra of 1.3-μm InGaAsP lasers were studied under low-duty-cycle pulse modulation and under 180- and 432-Mbit/s psendorandnm pulse modulation. The average dynamic spectra of these lasers differ from their dc-bias spectra, and also show variation betweeh low-duty-cycle pulse modulation and pseudorandom pulse modulation due to local heating effect. Under pseudorandom word modulation, no distinctive pulse-to-pulse variation in average dynamic spectra was observed. Transient damping times of the individual longitudinal mode of the average dynamic spectra of 2-4 ns were observed in the turn-on stage. Carrier buildup and decay of the side modes are the cause of these spectral transient responses. Essentially, the same average dynamic spectra were observed at 180 and at 432 Mbit/s where the time slot is less than the transient damping time in the turn-on stage. This suggests that the transient damping time of the individual longitudinal mode in the turn-off stage is much faster than that in the turn-on stage when the laser is biased below threshold. This result is supported by simple calculations from the rate equations which show that when the laser is biased below threshold, the transient damping time in the turn-off stage can be an order of magnitude faster than that in the turn-on stage.     

Measurement and simulation of the turn-on delay time jitter ingain-switched semiconductor lasers

The turn-on delay time jitter of four different unbiased gain-switched laser types was determined by measuring the temporal probability distribution of the leading edge of the emitted optical pulse. One single-mode 1.5-μm distributed feedback laser and three multimode Fabry-Perot lasers emitting at 750 nm and 1.3 μm were investigated. The jitter was found to decrease for all lasers with increasing injection current. For multimode lasers it decreases from 8 ps excited slightly above threshold down to below 2 ps at three times the threshold current. The jitter of the distributed feedback (DFB) laser is a factor of 3-5 larger than the jitter of the three multimode lasers. A model for predicting the turn-on delay time jitter is presented and explains the experiments quantitatively     

Operation range of VCSEL-interconnect links with“below-threshold”-biasing

Biasing lasers below threshold in interconnect links yields a lower effort for the monitoring circuitry, but it leads to a significant turn-on jitter due to the bit-pattern effects and spontaneous emission. An analytical expression describing the probability density function (pdf) of the total turn-on delay for a single-mode vertical-cavity surface-emitting laser (VCSEL) biased below threshold is derived, which accounts for both bit-pattern effects and spontaneous emission. In a high speed digital transmission system both timing jitter as well as the signal-to-noise ratio (SNR) limit the system-performance, which can be measured by the resulting bit-error rate (BER). The measured BER is compared with the calculated BER yielding good agreement. Therefore, following the quite general guideline as presented here, the operation range for “below-threshold”-biased VCSEL-interconnect links can be determined     

High-speed digital modulation characteristics of oxide-confined vertical-cavity surface-emitting lasers-numerical simulations consistent with experimental results

The vertical-cavity surface-emitting laser (VCSEL) is a preferred light source for short-distance high-speed fiber-optic communication links. We simulate the digital modulation behavior of typical oxide-confined VCSELs under realistic working conditions with a comprehensive model that includes the detailed geometry when calculating the optical fields and that accurately accounts for the dynamic effects of carrier density and temperature on the modal distributions. The intrinsic output characteristics of single- and multimode VCSELs were studied as functions of bias and modulation depth under a 2/sup 7/-1 pseudorandom bit sequence current modulation at 2 and 10 Gb/s. The data were used to create numerical eye diagrams that show, e.g., the significant impact of the bit pattern history and the noise on the timing jitter in both single- and multimode VCSELs. For the single-mode VCSEL, the choice of the bias current and modulation depth was less critical due to its higher damping of the relaxation oscillations. The simulated VCSELs were fabricated and experimentally evaluated. The measured eye diagrams showed the same characteristic features as those in the simulations.     

Differentail Board/Backplane Optical Interconnects for High-Speed Digital Systems Part II: Simulation Results

For pt.I see ibid., vol.11, no.7, p.1234-49 (1993). The performance of a DC-coupled fully-differential interconnect is analyzed in terms of the deterministic vertical and horizontal eye closure at Gb/s for different optical power levels and extinction ratios in the two complementary arms. Two types of transmitters are investigated, one based on an ideal optical modulator switch (IOMS) and the other based on conventional modulation of two separate lasers. In general, it is found that the timing jitter increases when the imbalance between the power levels in the two arms increases, when the difference between the laser turn-on delay in the two arms increases, and when the receiver and transmitter bandwidth is reduced. To achieve low latency and to accept a maximum power imbalance of 4-5 dB at the receiver, the IOMS and the lasers should be modulated to produce an extinction ratio of at least 10 dB, and the lasers should be biased above threshold. If low latency is not the main concern, an improvement in the maximum tolerable imbalance can be obtained with regular laser modulation by biasing the lasers below threshold. The fitter can be reduced and the maximum tolerable imbalance be increased if faster receivers and transmitters are employed     

Analysis of true jitter arising from pulse-stuffing schemes

In synchronous digital hierarchy and plesiochronous digital hierarchy networks, it is frequently necessary to recover a data clock from a gapped clock derived from stuff information present at the desynchronizer. In this paper, a comprehensive analysis of the timing jitter resulting from phase-locked loop-type desynchronizers is presented. This analysis is different from the conventional analysis where the jitter is represented using a phase-error sequence. It is shown that such a simplified approach cannot accurately describe the jitter at the output of the desynchronizer. From the detailed analysis, it is also shown how the use of threshold modulation at the synchronizer reduces the low-frequency jitter at the desynchronizer. It has been demonstrated in the paper that when threshold modulation is used at the synchronizer, the dominating low-frequency jitter terms cannot be explained by the conventional jitter analysis methods. Therefore, in future networks, where tighter jitter performances are to be imposed on the synchronizers, jitter characterization using the proposed true jitter analysis technique would be very useful.     

Statistical properties of the spectrum of light pulses in fastpseudorandom word modulation of a single-mode semiconductor laser

The spectrum of single-mode laser pulses generated by fast pseudorandom word modulation is studied numerically for return-to-zero and nonreturn-to-zero control signals. We analyze both statistics and the worst cases for the frequency chirp during each optical pulse, and we study the connection between these frequency chirps and the turn-on times. We show that patterns in the modulation signal sequences contribute to chirp noise. The worst case values of the turn-on time and the chirp range are very similar in the two modulation schemes, hence, the optimum choice depends mainly on the characteristics of the decision circuit and on the driver and detector bandwidths     

Turn-on jitter in nearly single-mode injection lasers

Computer modeling confirms recent experimental observations and shows that photon absorption and spontaneous emission cause as much as 50-60 ps jitter in the turn-on time delay of lasers with large mode-suppression ratios. Careful selection of the bias point can reduce this jitter to about 12 ps. Statistics are presented for the expected power level at fixed sampling time during the turn-on, and for the fluctuation in time delay for the laser power to rise to one-half the equilibrium power output.     

Jitter Accumulation for Periodic Pattern Signals

It is important to accurately evaluate and reduce jitter accumulation in long-haul digital repeatered lines. Jitter accumulation caused by random pattern signals has already been analyzed. However, periodic pattern signals such as pseudorandom signals are usually used to measure jitter accumulation. This paper describes the difference between the jitter accumulation for both signals and the necessary conditions to accurately estimate jitter accumulation for random pattern signals by using periodic pattern signals. First, it is shown theoretically that systematic jitter for periodic signals saturates, showing a ripple pattern. The limit of increase is determined by the ratio of tank bandwidth and pattern repetition frequency. Up to a certain number of regenerators determined by the ratio, systematic jitter increases in rough proportion to thesqrt{N}slope. It is also shown that the equation to estimate random pattern jitter accumulation is determined by the measured value for periodic pattern signals. Second, jitter characteristics are simulated by optical signal circulating experiments. The results are in agreement with the analysis. In addition, the reduction effects on periodic signal jitter accumulation caused by timing signal delay and nonlinearity of the limiter in the timing circuit are shown.     

Effects of current modulation on timing jitter of single-modesemiconductor lasers in short external cavities

Turn-on jitter of single-mode semiconductor lasers with modulated injection current and weak optical feedback exhibits periodic oscillations as a function of the length of the external cavity, under configurations appropriate for packaged laser diodes. Numerical results for both periodic and pseudorandom word modulation show that the oscillations persist even when increasing the external cavity length to a few millimeters. It is found that under particular positions of the external reflector a large increase of jitter occurs as compared with the jitter without optical feedback     

Modeling rare turn-on events of injection lasers

An efficient numerical method based on photon statistics and rate equations is developed to simulate rare turn-on events of injection lasers. Results indicate that: (1) during the transient stage, with a probability of 10^-9, the side-mode suppression ratio can deteriorate by three orders of magnitude from its steady-state value; (2) there is a turn-on jitter for the main mode, even when the side mode is missing; and (3) the slower the risetime of the laser output the less the transient mode partitioning. The effects of gain compression and driving condition on the transient turn on are discussed     

Fundamental Bit-Error-Rate Limits of In-Line Optical Regeneration by Synchronous Intensity Modulation: An Analytical Gaussian-Statistics Model

Fundamental limits of optical regeneration by in-line synchronous intensity modulation are evaluated through a simple Gaussian-statistics analysis. Regeneration is shown to involve three processes: asymptotic stabilization of signal-to-noise ratio, asymptotic stabilization of timing jitter, and instrinsic conversion of timing jitter into intensity noise. The model also includes filtering, which is shown to reduce or suppress amplitude noise. Key system parameters, which are valid regardless the origin of noise and jitter (amplification, interaction, collisions), are identified for the regime of “infinite” transmission, where the bit-error rate becomes distance-invariant. These parameters make it possible to predict the level and distance at which the bit-error rate converges, thus enabling rapid analytical evaluation and optimization of system performance. Novel effects such as transition from intensity-noise-limited to timing-jitter-limited regimes (or the reverse) and eye reopening with distance have been identified and analyzed for the first time.     

An integrated direct-coupled 10-Gb/s driver for common-cathode VCSELs

An all- npn integrated driver for directly modulating common-cathode vertical-cavity surface-emitting lasers (VCSELs) at high speeds (such as 10 Gb/s) is proposed and experimentally demonstrated. Special biasing techniques allow the output transistors to operate with small collector-emitter voltages while maintaining their fast current-switching capabilities. A current-splitting technique in the output stage minimizes the transients through the bias source and reduces jitter and overshoot.