Effect of 1/f-type FM noise on semiconductor-laserlinewidth residual in high-power limit

The FM-noise spectrum and the linewidth of 1.3 μm DFB (distributed feedback) semiconductor lasers measured in the high-power state up to 20 mW are discussed. A 5-MHz residual linewidth is observed in the high-power limit. The FM-noise spectrum consists of white noise and 1/f noise. The spectral density of the white noise is reduced by the increase in the output power, whereas that of the 1/f noise is unchanged, which means that the linewidth residual in the high-power limit is caused by the 1/f noise rather than the white noise. The impact of the 1/f-type FM noise on coherent optical communication systems is also discussed     

1/f frequency noise effects on self-heterodyne linewidthmeasurements

The effects of a 1/f frequency noise on self-heterodyne detection are described, and the results are applied to the problem of laser diode linewidth measurement. The self-heterodyne autocorrelation function and power spectrum are evaluated for both the white and the 1/ f components of the frequency noise. From numerical analysis, the power spectrum resulting from the 1/f frequency noise is shown to be approximately Gaussian, and an empirical expression is given for its linewidth. These results are applied to the problem of self-heterodyne linewidth measurements for coherent optical communications, and the amount of broadening due to 1/f frequency noise is predicted     

Wavelength dependence of 1/f noise in the light output oflaser diodes: an experimental study

The optical power emitted by a monomode GaAlAs laser is filtered with a monochromator. The 1/f noise in the filtered emission is found to be directly dependent on the noncoherent emission, such as S_pαP_nc^m. Here s_p is the spectral density of the 1/f fluctuations, P_nc is the average noncoherent power, m=3/2 under spontaneous emission, and m=4 in the superradiation and laser regions. Study of the 1/f noise in the optical power in a band centered at the laser wavelength and with variable bandwidth shows three operating regions. (1) LED region (at low currents): the fluctuations with a 1/f spectrum are uncorrelated in wavelength. (2) Superradiation region (at currents close to the threshold): the fluctuations are correlated. (3) Laser region: the 1/f noise apparently is dominated by noncoherent emission within a small optical band around the laser wavelength     

Carrier synchronization for homodyne and heterodyne detection ofoptical quadriphase-shift keying

Through analysis and simulation, the authors investigated the performance of four carrier-synchronization techniques suitable for both homodyne and heterodyne detection of optical quadriphase-shift keying: the discrete-time decision-directed loop, the analog decision-directed loop, the Costas quadriphase loop, and the fourth-power phase-locked loop. Accounting for shot noise, laser phase noise, and feedback delay, they optimize the loop natural frequency and specify laser-linewidth requirements. The performance discrepancy between the best and worst of these loops is found to be small; accounting for inherent loop delays only, the linewidth requirements range from ΔvT<2.5×10^-5 to ΔvT<5.2×10^-5, where Δv is the beat laser linewidth and T is the baud interval. Hence other considerations, such as ease of implementation, will govern the design choice for most practical systems. For the case when propagation delays in the feedback loop are significant, a simple and accurate method for estimating the laser-linewidth requirement and corresponding optimal natural frequency is presented     

Feedback phenomena in a semiconductor laser induced by distantreflectors

Multiple pass resonances in the noise spectrum and low-frequency self-oscillations in asymmetric geometrical configurations are described. The double peaked structure of the external cavity resonance f_c (at c/2L), the `subharmonic cascading' from f_c, and the generation of subharmonics of a modulated injection current are detailed. The exact field intensity distribution in the passive external resonator is shown to command these phenomena which reveal intermingled spatial and dynamical effects. The different behaviors are related to the characteristic curves of the laser. The authors have found that when the external cavity laser operates in its unstable regime, a locking of the otherwise randomly distributed intensity drops can occur giving a narrow resonance in the noise spectrum. In addition, based on the authors' observations, adapted rate equations are built starting from the Lang and Kobayashi model. Results show an adequate match between theory and experiments for the detailed microwave spectra, multiple pass resonances of the external cavity, and low-frequency resonances     

Noise caused by semiconductor lasers in high-speed fiber-opticlinks

Theoretical and experimental results are presented for the signal-to-noise (S/N) ratio caused by mode partition noise, intensity noise, and reflection-induced noise in optical data links. Under given conditions an additional noise source with a S /N ratio of 20 dB will cause a power penalty of 1 dB in order to maintain a 10^-9 bit error rate. From numerical simulations the authors predict the maximum allowable dispersion in the presence of mode partition noise to be approximately 40% of a clock period. This figure is almost independent of bit rate and laser structure and agrees well with the measurements and with results of other workers. Numerical simulations of a buried-heterostructure and a TJS laser were carried out at four bit rates from 565 Mbit/s to 4.5 Gbit/s and the measurements were done at 2.2 Gbit/s using a TJS laser     

A novel multilevel coherent optical system: 4-quadrature signaling

A novel multilevel coherent optical system is proposed. It is based on the exploitation of the property that the electromagnetic field propagating in a single-mode optical fiber can be represented by a four-dimensional vector whose components are the phase and quadrature terms of the two polarization components of the electrical field. This allows a wider use of the resources of the electromagnetic field for information transmission in order to obtain a spectrally efficient modulation format with a limited end. The net performance gain with respect to multilevel amplitude and phase modulation (N-APK) and N-PSK increases with an increase in the number of levels N. For instance, for N=32 the gain is 1.6 and 7.7 dB with respect to N-APK and N-PSK systems. The effect of laser phase noise on the system performance is evaluated     

Theory of linewidth for multielectrode laser diodes with spatiallydistributed noise sources

A general theory of linewidth for single-frequency semiconductor lasers is presented. The effects of spatially distributed noise sources together with spatially varying carrier and photon densities and injection current are analyzed in a rigorous manner by solution of the scalar wave equation. A new rate equation for the electric field is derived, in which the longitudinal effects are represented in the form of the weight functions C_N(z) and C_S(z). These functions express the sensitivity of the (output) field to local changes in carrier and photon density at the position z. For Fabry-Perot laser's the z dependence of the C factors is shown to be negligible, in agreement with the fact that spatial hole burning is not considered to be important for Fabry-Perot lasers. For distributed-feedback (DFB) lasers, however, the z dependence is shown to be very significant     

Bounding the capacity of saturation recording: the Lorentz modeland applications

The authors consider the problem of bounding the information capacity of saturation recording. The superposition channel with additive Gaussian noise is used as a model for recording. This model says that for a saturation input signal, x(t) (i.e., one that can assume only one of two levels), the output can be expressed as y(t)=x˜(t)+z(t ) where x˜(t) is a filtered version of the input x(t) and z(t) is additive Gaussian noise. The channel is described by the impulse response of the channel filter, h(t), and by the autocorrelation function of the noise. A specific example of such a channel is the differentiated Lorentz channel. Certain autocorrelation and spectrum expressions for a general Lorentz channel are derived. Upper and lower bounds on the capacity of saturation recording channels are described. The bounds are explicitly computed for the differentiated Lorentz channel model. Finally, it is indicated how the derived bounds can be applied in practice using physical measurements from a recording channel     

All-optical frequency conversion in a traveling-wave semiconductorlaser amplifier

All-optical frequency conversion over the entire gain spectrum of a traveling-wave semiconductor laser amplifier is analyzed by numerical solution of a nonlinear wave equation system. The wavelength dependence of the gain coefficient g, the linewidth enhancement factor α, the differential gain dg/dN, and the gain saturation effect are contained in the model. The method yields a high conversion efficiency and a converted signal output power up to 10 dBm is obtainable. It is shown that the input signal power can vary by three orders of magnitude with nearly no degradation of the conversion efficiency. By means of the input powers, the conversion efficiency can be maximized. The dependence of the conversion efficiency is analyzed for fixed input powers. Simultaneous conversion of an optical data signal to several wavelengths is analyzed. The requirements for the output filter are outlined     

Limiter-discriminator detection of a coherent optical heterodyneM-ary CPFSK receiver

The performance of a coherent optical M-ary continuous-phase frequency-shift-keying (CPFSK) receiver using limiter-discriminator (L-D) detection is investigated. It is shown that L-D detection of CPFSK optical signals offers the best performance for a large normalized IF beat spectral linewidth, ΔνT. When the modulation index is unity, the receiver is immune to laser phase noise and can produce (M/4) exp (-SNR) symbol error probability, which may be considered as the upper bound if the optimal modulation index is used (SNR is the signal-to-noise ratio per symbol). Optimum modulation indexes are 0.8 and 1 at ΔνT=1% and ΔνT=2%, respectively, for M=4, 8, and 16     

Performance analysis of optical heterodyne PSK receivers in thepresence of phase noise and adjacent channel interference

A phase-shift-keying (PSK) optical heterodyne receiver using synchronous detection by means of a Costas phase-locked loop (PLL) is investigated. Taking into account the laser phase noise and adjacent channel interference (ACI), an expression of the phase error variance is derived and error probability calculation is performed. Plots of the error probability versus the number of photons per bit are presented as a function of the optical domain channel spacing (D) and for several linewidth-to-bit-rate ratios (δf/R_b ). Relative sensitivity penalties, based on the performance with and without ACI, are evaluated for several combinations of D and δf/R_b. It is shown that, if lasers with larger linewidths are used, the frequency separation between optical carriers has to be increased in order to allow the same relative sensitivity penalty     

Asymptotic distortion spectrum of clipped, DC-biased, Gaussiannoise [optical communication]

Consider a zero-mean, stationary Gaussian process g(t ), to which a large positive constant A has been added. Define a distortion process h_A(t) as equal to g(t)+A when the latter is negative and equal to zero otherwise. The author calculates the power spectrum of the process h_A(t) asymptotically as A becomes large. The results have application for estimating the nonlinear-distortion power in the recovered signal when many frequency-multiplexed subcarriers collectively modulate a laser's output power, as would be the case for CATV transmission over an optical fiber. The process h_A(t) then models the nonlinear distortion caused by occasional clipping of the DC-biased laser input     

Wideband frequency-response measurement of optical receivers usingoptical heterodyne detection

Measurements have been carried out using 1.3-μm distributed-feedback laser diodes (DFB-LDs). The frequency difference of the LDs is continuously varied with temperature changes of a few degrees and the spectral linewidth of one of the LDs is narrowed by optical feedback using a grating. Wideband, highly sensitive measurement has been achieved for a p-i-n photodiode and a Ge avalanche photodiode from DC to 20 GHz. The result is compared with that of the pulse spectrum analysis (PSA) method. Although the finite pulsewidth in the PSA method causes roll-off in the frequency response, the optical heterodyne method has the advantage for very wideband frequency response measurement. The S/N ratio in the optical heterodyne method can be made as high (~40 dB) as that of the PSA method by narrowing the spectral linewidth of DFB-LDs     

Origin of residual semiconductor-laser linewidth in high-powerlimit

The FM noise spectrum and the spectral width of semiconductor lasers are measured in the high-power state up to 20 mW. The FM noise spectrum consists of the white noise and the 1/f noise. The spectral density of the white noise is suppressed by the increase in the output power, whereas that of the 1/f noise is kept constant. This fact means that the residual linewidth in the high-power limit is caused by the 1/f noise rather than the white noise     

Correlation between 1/f fluctuations in the two outputbeams of a laser diode

The coherence function of 1/f noise fluctuations in the optical output from the two laser facets is derived from a simple model. At low power, the coherence is shown to be dependent on the optical absorption in thermal equilibrium. The coherence function can be used to determine the absorption coefficient. In the superradiation region, the coherence function increases strongly with power toward its maximum value of one. It remains one above threshold. Experimental findings on a channeled-substrate-planar laser are in good agreement with the author's theory     

Novel method of estimation flicker frequency noise in lasers

A simple method is proposed for the precise measurement of flicker (1/f) frequency noise in lasers. The method is based on measurement of the Allan variance of beat signals produced by delayed self-heterodyning. A simple relation between measured variance and frequency-noise spectrum is derived analytically. Measurement on a 1.5-μm semiconductor laser diode is presented. It is pointed out that since the method possesses the great advantage of insensitivity to optical power fluctuations, it can be widely used for precisely testing laser frequency quality     

Gaussian feedback capacity

The capacity of time-varying additive Gaussian noise channels with feedback is characterized. Toward this end, an asymptotic equipartition theorem for nonstationary Gaussian processes is proved. Then, with the aid of certain matrix inequalities, it is proved that the feedback capacity C_FB in bits per transmission and the nonfeedback capacity C satisfy C⩽C_FB ⩽2C and C⩽C_FB⩽ C+1/2     

Theory of FM clicks with Brownian motion phase noise

Lasers that are used for coherent optical communication exhibit phase instabilities which can be modeled as a Brownian motion. The effect that such a disturbance has on limiter-discriminator detection of FM signals received in additive Gaussian noise is investigated. Although a new theory must be developed to calculate FM click rates (and prove them finite), no effects are found which would preclude the use of such a detector with Brownian phase noise. In particular, for binary FM transmission at rate R, discriminator detection will result in 1 dB of degradation or less if B_pn/R<0.002, B_pn being the linewidth of the unmodulated carrier