A novel approach to analytically evaluate the bit error probability in optically preamplified direct-detection systems is presented, which can take into account the effects of pulse shaping, chirping, filtering at the transmitter and the receiver, both pre- and postdetection, chromatic dispersion, and ASE noise. The method is computationally very fast in that the saddle point integration method for solving the resulting line integral of a particular moment generating function is adopted. A closed-form approximation for the bit error probability is also provided, which is within 0.01 dB from the exact numerical results.

Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering

We present a comprehensive treatment of optically preamplified direct detection receivers for non-return-to-zero (NRZ) and return-to-zero (RZ) on/off keying modulation, taking into account the influence of different (N)RZ optical pulse shapes, specified at the receiver input, and filter transfer functions; optical Fabry-Perot filters (FPFs) and Bragg gratings as well as electrical fifth-order Bessel and first-order RC low-pass filters are considered. We determine optimum optical and electrical filter bandwidths and analyze the impact of bandwidth deviations on receiver sensitivity. Optimum receiver performance relies on a balance between noise and intersymbol interference (ISI) for NRZ transmission, while for RZ reception detection noise has to be traded against filter-induced signal energy rejection. Both for NRZ and 33% duty cycle RZ, optical filter bandwidths of around twice the data rate are found to be optimum. Receivers using RZ coding are shown to closely approach the quantum limit, and thus to outperform NRZ-based systems by several decibels. We further analyze the impact of important degrading effects on receiver sensitivity and optimum receiver bandwidths, including receiver noise, finite extinction ratio, chirp, and optical carrier frequency (or optical filter center frequency) fluctuations.

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Optimum filter bandwidths for optically preamplified NRZ receivers

We report electric field-induced modulation of absorption in PbS nanocrystal quantum dots across the spectral region 600–2000nm, encompassing the entire telecommunications band. The maxima in the electroabsorption spectra correspond with the positions of the first excitonic peak, confirming the predominance of excitonic broadening as the basis for the observed effect. We estimate the change in dipole moment to be on the order of 20 D in 7nm diameter PbS nanocrystals compared to previously-reported ∼100D in CdSe.

/pdf/pbs-quantum-dot-electroabsorption-modulation-across-the-4q5hyunp8k.pdf

PbS quantum dot electroabsorption modulation across the extended communications band 1200-1700 nm

A Gaussian approach (GA), which takes into account the influence of arbitrary optical and electrical filters, is proposed to analytically evaluate the performance of optically preamplified receivers. This GA also takes into account the effects of waveform distortion in the signal and in the signal-amplified spontaneous emission beat noise. Exact expressions for the mean and variance of the current at the decision circuit input are derived, which explicitly present the dependence on the optical and electrical filter transfer functions and take into account the presence or absence of a polariser. This GA is computationally much faster and simpler than more rigorous methods and the accuracy of its sensitivity estimates is investigated for different optical and electrical filters. It is shown that the GA predicts the optimal optical filter bandwidth very reasonably. Discrepancies below 1.2 dB are found between its sensitivity estimates and rigorous estimates. The assessment of the optical filter detuning impact on the receiver sensitivity is also investigated with this GA. Discrepancies less than 1 dB are found between the GA estimates and rigorous estimates. The GA sensitivity estimate's accuracy is also investigated in the presence of intersymbol interference (ISI) and very accurate predictions are obtained by the GA for significant ISI.

https://ieeexplore.ieee.org/iel5/2197/20364/00940560.pdf

Gaussian approach for performance evaluation of optically preamplified receivers with arbitrary optical and electrical filters

A monolithically-integrated semiconductor optical transmitter that can index tune to any transmission wavelength in a given range, wherein the range is larger than that achievable by the maximum refractive index tuning allowed by the semiconductor material itself (i.e. Δλ/λ>Δn/n). In practice, this tuning range is >15 nm. The transmitter includes a Mach-Zehnder (MZ) modulator monolithically integrated with a widely tunable laser and a semiconductor optical amplifier (SOA). By using an interferometric modulation, the transmitter can dynamically control the chirp in the resulting modulated signal over the wide tuning range of the laser.

Tunable laser source with monolithically integrated interferometric optical modulator

The transmission and chirp characteristics are described for two types of semiconductor Mach-Zehnder modulators, distinguished by the differential phase shift between the two arms of the interferometer in the unbiased state. The conventional modulator has a differential phase shift of 0 radians, while the /spl pi/-shift modulator has a differential phase shift of /spl pi/ radians. The nonlinear dependence on the applied voltage of the attenuation and phase constants of the optical signal propagating in the p-i-n waveguide leads to different characteristics for the two modulators. The influence of the splitting ratio of the Y-junctions is considered for single-arm and dual-arm (push-pull) modulation formats. The /spl pi/-shift modulator is shown to yield better transmission performance for 10 Gb/s systems compared to the conventional modulator.

Modulation characteristics of semiconductor Mach-Zehnder optical modulators

A technique is presented for evaluating the probability of error for an optically preamplified receiver with a fiber Fabry-Perot optical filter of arbitrary bandwidth between the preamplifier and photodiode. The technique permits simultaneous consideration of the distortion due to modulator chirp and fiber dispersion, the optical filter and the baseband electrical filter. The optical filter is characterized by a Lorentzian passband response, and the quadrature noise processes due to the amplified spontaneous emission are represented by Karhunen-Loeve expansions. For an arbitrary optical filter bandwidth, the evaluation of the probability of error depends explicitly on the details of the Karhunen-Loeve expansion. The solution procedure is general and consequently can, in principle, be applied to other filter passband responses. The influence of the bandwidths of the optical and electrical filters on the performance of a 10 Gb/s system is assessed.

C. Lawetz

Papers

Modulation characteristics of semiconductor Mach-Zehnder optical modulators

Performance of optically preamplified receivers with Fabry-Perot optical filters