Decision-driven phase-locked loop for optical homodyne receivers: Performance analysis and laser linewidth requirements

Optical homodyne receivers based on decision-driven phase-locked loops are investigated. The performance of these receivers is affected by two phase noises due to the laser transmitter and laser local oscillator, and by two shot noises due to the two detectors employed in the receiver. The impact of these noises is minimized if the loop bandwidthBis chosen optimally. The value of Boptand the corresponding optimum loop performance are evaluated in this paper. It is shown that second-order phase-locked loops require at least 0.8 pW of signal power per every kilohertz of laser linewidth (this number refers to the system with the detector responsivity 1 A/W, dumping factor 0.7, and rms phase error 10°). This signal power is used for phase locking, and is, therefore, lost from the data receiver. Further, the maximum permissible laser linewidthDelta vis evaluated and for second order loops with the dumping factor 0.7 found to be 3.1 × 10^-4. Rb, where Rb(bit/s) is the system bit rate. ForR_{b} = 100Mbit/s, this leads toDelta v = 31kHz. For comparison, heterodyne receivers with noncoherent postdetection processing only requireDelta v = 0.72-9MHz forR_{b} = 100Mbit/s. Thus, the homodyne systems impose much more stringent requirements on the laser linewidth than the heterodyne systems. However, homodyne systems have several important advantages over heterodyne systems, and the progress of laser technology may make homodyning increasingly attractive. Even today, homodyne reception is feasible with experimental external cavity lasers, which have been demonstrated to haveDelta vas low as 10 kHz.     

Decision-driven phase-locked loop for optical homodyne receivers: Performance analysis and laser linewidth requirements

Optical homodyne receivers based on decision-driven phase-locked loops are investigated. The performance of these receivers is affected by two phase noises due to the laser transmitter and laser local oscillator, and by two shot noises due to the two detectors employed in the receiver. The impact of these noises is minimized if the loop bandwidthBis chosen optimally. The value of Boptand the corresponding optimum loop performance are evaluated in this paper. It is shown that second-order phase-locked loops require at least 0.8 pW of signal power per every kilohertz of laser linewidth (this number refers to the system with the detector responsivity 1 A/W, dumping factor 0.7, and rms phase error 10°). This signal power is used for phase locking, and is, therefore, lost from the data receiver. Further, the maximum permissible laser linewidthDeltanuis evaluated and for second order loops with the dumping factor 0.7 found to be3.1 times 10^{-4} cdot R_{b}, where Rb(bit/s) is the system bit rate. ForR_{b} = 100Mbit/s, this leads toDeltanu = 31kHz. For comparison, heterodyne receivers with noncoherent postdetection processing only requireDeltanu = 0.72-9MHz forR_{b} = 100Mbit/s. Thus, the homodyne systems impose much more stringent requirements on the laser linewidth than the heterodyne systems. However, homodyne systems have several important advantages over heterodyne systems, and the progress of laser technology may make homodyning increasingly attractive. Even today, homodyne reception is feasible with experimental external cavity lasers, which have been demonstrated to haveDeltanuas low as 10 kHz.     

Performance analysis and laser linewidth requirements for optical PSK heterodyne communications systems

An optical PSK heterodyne communications receiver is investigated. The receiver is based on the decision-directed phase-locked loop. The performance of the phase-locked loop subsystem is analyzed taking into account both shot noise and laser phase noise. It is shown that for reliable phase locking (rms phase error less than 10°), heterodyne second-order loops require at least 6771 electrons/s per volt every hertz of the laser linewidth. This number corresponds to the limit when the loop dumping factor η is infinitely large; ifeta = 0.7, then the loop needs 10 157 electrons/(s . Hz). If the detector has a unity quantum efficiency andlambda = 1.5 mum, the above quoted numberers give 0.9 pW/ kHz foreta rightarrow inftyand 1.35 pW/kHz fornu = 0.7. The loop bandwidth required is also evaluated and found to be155 Deltanu, whereDeltanuis the laser linewidth. Finally, the linewidth permitted for PSK heterodyne recievers is evaluated and found to be2.26 cdot 10^{-3} R_{b}where Rbis the system bit rate. ForR_{b}=100Mbit/s, this leads toDeltanu < 226kHz. Such and better linewidths have been demonstrated with laboratory external cavity lasers. For comparison, ASK and FSK heterodyne receivers are much more tolerant to phase noise,-they can tolerateDeltanuup to 0.09 Rb. At the same time, homodyne receivers impose much more stringent requirements on the laser linewidth (Deltanu < 3 cdot 10^{4} R_{b}).     

Multichannel coherent optical communications systems

Balanced coherent receivers perform substantially better than single-detector receivers in multichannel optical fiber FDM communications systems since the balanced approach eliminates the direct-detection and signal-cross-signal interference. The permissible channel spacingDdepends on the intermediate frequency fIF, on the bit rate Rb, and on the modulation/demodulation format. In particular,Dincreases by 2 Hz for every 1-Hz increase of the fIF. The signal-to-interference ratio SIR, as defined in the text, provides a simple measure of the amount of the interference generated by undesired channels. The criterion SIR = 30 dB is selected in this paper and leads to the following minimum channel spacings: for heterodyne systems,3.8R_{b}for FSK,9.5R_{b}for ASK, and12.4R_{b}for PSK; for homodyne systems,7.5R_{b}for ASK and10.5R_{b}for PSK. Simultaneous transmission of several channels generates an excess shot noise studied here for the first time. If the local oscillator power is 40 dB above the received signal power and 2000 channels are transmitted without optical prefiltering, the excess shot noise power penalty is less than 1 dB.     

Optimum optical power splitting ratio of decision drivenphase-locked loop in BPSK optical homodyne receiver

In a BPSK optical homodyne receiver that utilizes a decision-driven phase-locked loop, the splitting ratio of the received power and that of the local oscillator power are very important parameters in achieving high receiver sensitivity. This paper determines the optimum setting of these parameters considering the influence of the relative intensity noise of the local oscillator and the thermal noise of the preamplifier. The optimum splitting ratio of the local oscillator power to the Q-arm is found to be 0.5. The splitting ratio of the received power to Q-arm is obtained as a function of laser linewidth. The optimum setting of the received power and the local oscillator power Is independent of the relative intensity noise of the local oscillator, the thermal noise of the preamplifier and the bit rate, At the optimum splitting ratios, required beat linewidth is obtained as 1.3×10 ^-3/T_b(τ/T_b≪1) and 2.99×10 ^-3/τ(τ/T_b≫1), where T_b is the bit duration and τ is the loop propagation delay time. We show that the total power penalty of 0.8 dB from the shot noise limit can be realized with the relative intensity noise of -170 dB/Hz and equivalent input noise current of 10 pA/√(Hz), even if an imperfect balanced receiver is utilized; quantum efficiency ratio of the twin-photodetector is 0.96, propagation time difference T/T_b is 0.01. To confirm the theoretical model, a BPSK homodyne detection experiment is performed and good agreement is found between theoretical and experimental results     

1/f noise in n-channel silicon-gate MOS transistors

It is found that equivalent gate noise power for l/f noise in n-channel silicon-gate MOS transistors at near zero drain voltage at room temperature is empirically described by two noise terms, which vary asK_{1}(q/C_{ox}) (V_{G} -V_{T})/f and K_{2}(q/C_{ox})^{2}/f, where V_{G}is gate voltage, VTis threshold Voltage, and Coxis gate-oxide capacitance per unit area. Unification of carrier-density fluctuation (McWhorter's model)and mobility fluctuation (Hooge's model) can account for the experimental data. The comparison between the theory and experiment shows that the carrier fluctuation term K2is proportional to oxide-trap density at Fermi-level. The mobility fluctuation term K1is correlated to K2, being proportional toradic K_{2}. The origin of this correlation is yet to be clarified.     

Electromigration and low-frequency resistance fluctuations in aluminum thin-film interconnections

Low-frequency noise spectra originating from resistance fluctuations in Al films during electromigration were measured in the absolute temperature and current density intervals327 leq T leq 396K and1.34 times 10^{6} leq j leq 2.22 times 10^{6}A/cm². The values of SR, the resistance power spectral density, at 20 × 10^-3Hz allowed the construction of an Arrhenius plot from which a grain-boundary activation energy value of about 0.6 eV was deduced. This value lies in the range of values found by other authors using different techniques. A first attempt to model the observed dependence of SRonjandTis also described.     

Laser-stimulated atomic migration

The effects of stimulated Raman scattering (SRS) and of infrared (IR) absorption on the scattering at defects leading to atomic migration in solids is evaluated in detail for certain systems.DeltaE/kT approx sum u_{ic}^{2}/langleu_{i}u_{i}rangle, whereDeltaEis the activation energy, uicis the many-body critical displacement in a migration event, andlangleu_{i}u_{i}rangleis the equal-time correlation function including anharmonic terms. Using the equal-time correlation for the defect lattice in the harmonic approximation, we getDeltaE/kT_{eff} propto 1/sum h[2(n_{s} + n_{e}) + 1]where Teffincludes both neand nsthe externally and thermally excited phonon numbers, respectively. The phonon rate density required for an observable effect of SRS or IR absorption on diffusion in solids isn_{e}^{(c)}c_{s}/V approx 10^{26} - 10^{27}phonons/s.cm², wheren_{e}^{(c)}is a critical number of high wave-vector laser-stimulated phonons, cs, is the sound velocity, and V, the volume per atom. In KCI at 110 K, theory shows thatn_{e} = 0.2can produce a factor of 10 effect on the reorientation of Na:FAcenters. Anharmonic effects onlangleu_{i}u_{i}ranglewere calculated and numerical estimates indicate that they would be experimentally observable for large ne. It is found that some of the effects reported here probably contribute, in part, to the permanent damage tracks caused by high-power laser beams in solids and provide an internal source for the initiation of microcracks. In addition, the direction of the stimulated phonon wave vector is shown to produce a directional effect in the control of atomic migration.     

Exact evaluation of laser linewidth requirements for optical PSKhomodyne communication systems with balanced PLL receivers

The power penalty induced by imperfect phase recovery in PSK homodyne communication systems with balanced phase-locked loop receivers are exactly evaluated. Optimum phase deviations between the mark-state and the space-state bits are used in this study. This study for the first time shows the imperfect-phase-recovery-induced power penalty as a function of laser linewidth with optimum phase deviations considered. It can be estimated from the theoretical result that an optimal balanced PLL receiver requires the laser linewidth as Δν⩽1.15×10^-6× (bit rate) in contrast to the previous reported one Δν⩽5.88×10^-6× (bit rate). We also point out here that the previously reported laser linewidth requirement was wrongly estimated     

Optical Phase Locking by Local Oscillator Phase Dithering

A new type of optical phase-locked loop (OPLL), called the dither loop, is mathematically analyzed. The dither loop extracts a phase-error signal by applying a small phase disturbance to the local oscillator laser, and synchronously demodulating the resulting power fluctuation in the output signal of the receiver. The dither loop is superior to other OPLL designs, because it does not need the transmission of a residual carrier, it employs a 180deg/3-dB hybrid, an ac-coupled front end, and it accepts a large variety of input signals. Furthermore, in a dither loop, the amount of power which is fed to the phase-locking branch can be adaptively controlled within the receiver. The analysis first focuses on an expression for the phase detector gain in a dither loop. Using a linearized model, the phase-error variance due to phase dithering, white frequency noise induced phase noise and shot noise is evaluated. A simplified expression for the power penalty generated by the phase dither signal is presented. In a more complex calculation, the overall power penalty due to phase dithering and the residual phase error is found. This allows us to synthesize a design rule for dither loops with optimum performance measures. The design rule determines all relevant system parameters, based on specified values of the system bit rate, the laser linewidth, the photodiode responsivity and the required bit-error rate     

Interferometric Noise Characterization and Suppression in Optical CDMA Networks

A solution for suppressing multiple-access interference and incoherent interferometric noise in 2-D optical code-division multiple access (CDMA) networks is demonstrated using a dispersion-imbalanced loop mirror containing a 15-m heavily GeO$_{2}$-doped fiber. From the experimental study of the degradation caused by noise, bit-error-rate (BER) measurements in a two-user system having coherent, partially coherent, and incoherent interferometric noise without the dispersion-imbalanced loop mirror exhibit error floors above BER $=10 ^{-6}$. Including the dispersion-imbalanced loop mirror before the receiver allows error-free transmission, and reduces the power penalty from the noise by 7 dB. The solution presented increases the receiver sensitivity and accentuates the flexibility of the optical CDMA networks.      

Ellipse rotation studies in laser host materials

Using a TEM00qnear Gaussian mode ruby laser system we report the first experimental measurements of intensity induced changes of optical polarization (ellipse rotation) in a cubic crystalline medium, YAG, for which we obtain the nonlinear susceptibilitieschi_{3}^{1221} (- omega, omega, omega, -omega) = 6.34 times 10^{-15}ESU andfrac{1}{2} (chi_{3}^{1111} + chi_{3}^{1221} - 2chi_{3}^{1212}) = 7.18 times 10^{-15}ESU, accurate to better than ±7 percent relative tochi_{3}^{1221} (- omega,omega,omega, -omega)for liquid CS2. These values are compared with further results obtained for fused quartz and two laser glasses. Moreover, by time resolving the ellipse rotation data we demonstrate the capability to plot ellipse rotation versus input power on a single laser shot, thus increasing the practical feasibility of the technique and introducing the possibility of resolving transient contributions to the measurement.     

A Super-Tripling Technology Used in Radio-Over-Fiber Systems for Multiservice Wireless Signals Within a Millimeter-Wave Band

A super-tripling technology used in radio-over-fiber systems is presented in this letter for the optical generation and multiplexing of multiservice wireless signals within a millimeter-wave band. To realize the technology, optical carrier suppression is followed by optical single sideband with suppressed carrier modulation in the central station and optical stopband filtering in the base station is utilized. With the technology, 38.5-GHz amplitude shift keying and 41-GHz differential phase-shift keying signals both with 1.25-Gb/s data bit rate were demonstrated experimentally, and power penalties of about 1 dB at a bit-error rate of $10^{-8}$ were obtained after both signals transmitted over 10 km fiber. The spurious-free dynamic range of the link was measured to be 65 $hbox{dB}cdothbox{Hz}^{2/3}$ for the 38.5-GHz channel and 70 $hbox{dB}cdothbox{Hz}^{2/3}$ for the 41-GHz channel, both with the phase-noise at about ${-}$70 dBc/Hz.      

Noise temperature in silicon in the hot electron region

The noise temperature as a function of the applied field has been measured on an epitaxial silicon layer at the frequencies 2 GHz and 4 GHz. It has been found that the experimental results are in good agreement with the theory given by Moll. It is shown that for noise calculations in silicon field-effect transistors with pronounced carrier velocity saturation the noise temperature Tnversus field E may be approximated byT_{n}/T_{0}= 1 + γ(E/E_{c})^{2}with T0= lattice temperature, Ec= saturation field, γ = const.     

Mutual information of the white Gaussian channel with and without feedback

The following model for the white Gaussian channel with or without feedback is considered: begin{equation} Y(t) = int_o ^{t} phi (s, Y_o ^{s} ,m) ds + W(t) end{equation} wheremdenotes the message,Y(t)denotes the channel output at timet,Y_o ^ {t}denotes the sample pathY(theta), 0 leq theta leq t. W(t)is the Brownian motion representing noise, andphi(s, y_o ^ {s} ,m)is the channel input (modulator output). It is shown that, under some general assumptions, the amount of mutual informationI(Y_o ^{T} ,m)between the messagemand the output pathY_o ^ {T}is directly related to the mean-square causal filtering error of estimatingphi (t, Y_o ^{t} ,m)from the received dataY_o ^{T} , 0 leq t leq T. It follows, as a corollary to the result forI(Y_o ^ {T} ,m), that feedback can not increase the capacity of the nonband-limited additive white Gaussian noise channel.     

Carrier synchronization for 3- and 4-bit-per-symbol optical transmission

We investigate carrier synchronization for coherent detection of optical signals encoding 3 and 4 bits/symbol. We consider the effects of laser phase noise and of additive white Gaussian noise (AWGN), which can arise from local oscillator (LO) shot noise or LO-spontaneous beat noise. We identify 8- and 16-ary quadrature amplitude modulation (QAM) schemes that perform well when the receiver phase-locked loop (PLL) tracks the instantaneous signal phase with moderate phase error. We propose implementations of 8- and 16-QAM transmitters using Mach-Zehnder (MZ) modulators. We outline a numerical method for computing the bit error rate (BER) of 8- and 16-QAM in the presence of AWGN and phase error. It is found that these schemes can tolerate phase-error standard deviations of 2.48/spl deg/ and 1.24/spl deg/, respectively, for a power penalty of 0.5 dB at a BER of 10/sup -9/. We propose a suitable PLL design and analyze its performance, taking account of laser phase noise, AWGN, and propagation delay within the PLL. Our analysis shows that the phase error depends on the constellation penalty, which is the mean power of constellation symbols times the mean inverse power. We establish a procedure for finding the optimal PLL natural frequency, and determine tolerable laser linewidths and PLL propagation delays. For zero propagation delay, 8- and 16-QAM can tolerate linewidth-to-bit-rate ratios of 1.8/spl times/10/sup -5/ and 1.4/spl times/10/sup -6/, respectively, assuming a total penalty of 1.0 dB.     

Electronic processes at grain boundaries in polycrystalline semiconductors under optical illumination

The dependence of minority carrier lifetime (τ) on the doping concentration Nd, grain sizedand interface state density Nisat the grain boundaries in (n-type) polycrystalline semiconductors has been calculated analytically. The recombination velocity at grain boundaries is enhanced by the diffusion potential Vdadjacent to the boundaries, and ranges fromsimeq 10^{2}to 10⁶cm . s^-1depending on Nisand Nd. Under illumination, the population of the interface states is altered considerably from its dark level and as a result, Vddecreases to that value which maximizes recombination (equal concentrations of electrons and holes at the boundary). This causes τ to decrease with increasing Nd. Sample calculations for polycrystalline silicon show that for low angle boundaries with interface state densities ofsimeq 10^{11}cm^-2eV^-1, τ decreases from 10^-6to 10^-10s as the grain size is reduced from 1000 to 0.1 µm (forN_{d} = 10^{16}cm^-3). For a constant grain size, τ decreases with increasing Nd. The open-circuit voltage of p-n junction solar cells decreases fortau leq 10^{-7}s, whereas that for Schottky barrier cells remains at its maximum value untiltau lsim 10^{-8}s.     

Optimum design for high-power and high-efficiency GaAs Hi-Lo IMPATT diodes

Optimum structure parameters of GaAs hi-lo IMPATT diodes to give a high-efficiency and a high-output power are experimentally determined in the frequency range from 7 to 18 GHz. The highest efficiency is obtained at any frequency when a diode has a punch-through factor of about 0.6 and is depleted with an electric field strength of 10 kV/cm at the end of the lo region under operation. The optimum lo-region carrier concentration to achieve the highest efficiency and the upper limit of a junction area to obtain a high-output power without decreasing efficiency are found to be simply related to frequency by the following equations:(N_{L})_{opt} = (4 times 10^{14}) cdot (f/7)^{3}cm^-3and(S_{j})_{max} = (20 times 10^{-4}) cdot (f/10)^{-1.9})cm²), respectively, wherefis in gigahertz.     

The performance of optical phase-locked loops in the presence of nonnegligible loop propagation delay

The optical phase-locked loop is analyzed taking into account shot noise, phase noise, and loop propagation delay. The degradation of loop phase error due to propagation delay is evaluated in terms of the delay bandwidth productomega_{n} cdot tau_{D}. This product was found to have a maximum value of 0.736 for absolute loop stability. The resulting effect on a Costas loop system optimized for zero time delay is discussed. It is found that in order to maintain a 10^-9BER system performance withxi = 1/2^{0.5}, R = 0.85A/W,P_{DATA} = -59.2dBm, and a 1-MHz beat linewidth, the delay time must be kept below 1.8 ns. If the beat linewidth increases to 15 MHz this figure drops to 0.12 ns.     

Hot-electron-induced MOSFET degradation at low temperatures

The n-channel LDD MOSFET lifetime is observed to followtau=(A/I_{d})(I_{sub}/I_{d})^{-n}from 77 to 295 K when the device is stressed near the maximum Isub. Here Idis the drain current andAis the proportionality constant. The experimental result indicates thatnis approximately 2.7 and is independent of temperature. However, the proportionality constantAfollowsA = A_{0} exp (-E_{a}/kT), withE_{a} = 39meV. The smaller proportionality constant at low temperatures suggests that hot-electron injection (HEI) degradation is caused by the electron trapping in the oxide.