Nonzero Linewidth Research Articles

Temporal Cavity Soliton Interaction in Passively Mode-Locked Semiconductor Lasers

Weak interactions of temporal cavity solitons resulting from gain saturation and recovery in a delay differential model of a long cavity semiconductor laser were studied numerically and analytically using an asymptotic approach. This paper shows that in addition to the usual soliton repulsion leading to a harmonic mode-locking regime, soliton attraction is also possible in a laser with a nonzero linewidth enhancement factor. It is shown numerically that this attraction can lead either to pulse merging or to pulse bound-state formation.

All-Optical Phase Memory Circuit Based on Two Coupled Lasers and External Optical Injection

We propose a volatile static all-optical memory capable of storing phase information of a slowly-varying electric field. The scheme and its realization (a memory circuit) are based on two mutually coupled lasers subject to external optical injection. The proposed circuit has a single optical input for write and hold operations and two opposite-sign outputs for reading the memory. The proposed circuit operates with a single wavelength of light, a single direction of propagation, and without a need to switch the state of polarization. We prove mathematically that the proposed arrangement has equilibrium points that may discreetly quantify and store the phase in a bistable manner. The circuit is studied numerically for solid-state and semiconductor lasers with zero and non-zero linewidth enhancement factors, respectively. Simulations based on a rate equation system confirm the essential findings. Using typical parameters of a semiconductor laser and optimizing for a possibly wide range of operation, the write-read operations were simulated using PRBS-9 at the rate of 1 Gb/s with negligible errors. The proposed circuit will enable integrated memory implementations for future all-optical signal processing and computing systems.

CW Emission and Self-Pulsing in a III-V/SiN Hybrid Laser With Narrow Band Mirror

We report on how external cavity III-V/SiN hybrid lasers operate in regimes of ultra-damped relaxation oscillations or in CW unstable dynamical regimes (self-pulsing or approaching turbulence) as a consequence of mirror dispersion, non-zero linewidth enhancement factor, and four-wave mixing in the gain medium. The impact of the dispersive mirror bandwidth and different mirror effective lengths on the laser tolerance to external optical feedback is also discussed.

Single-particle excitations in disordered Weyl fluids

We theoretically study the single particle Green function of a three dimensional disordered Weyl semimetal using a combination of techniques. These include analytic $T$-matrix and renormalization group methods with complementary regimes of validity, and an exact numerical approach based on the kernel polynomial technique. We show that at any nonzero disorder, Weyl excitations are not ballistic: they instead have a nonzero linewidth that for weak short-range disorder arises from non-perturbative resonant impurity scattering. Perturbative approaches find a quantum critical point between a semimetal and a metal at a finite disorder strength, but this transition is avoided due to nonperturbative effects. At moderate disorder strength and intermediate energies the avoided quantum critical point renormalizes the scaling of single particle properties. In this regime we compute numerically the anomalous dimension of the fermion field and find $\eta= 0.13 \pm 0.04$, which agrees well with a renormalization group analysis ($\eta= 0.125$). Our predictions can be directly tested by ARPES and STM measurements in samples dominated by neutral impurities.

Widely Continuous Tunable ps Pulse Train Generation Based on SOA Nonlinear Dynamics

We propose a simple setup based on nonlinear dynamics in a semiconductor optical amplifier (SOA) and solitonic compression for the generation of stable and tunable repetition rate picosecond (ps) optical pulses. A quantum-well SOA is used to amplify electrical-optic-modulated rectangular optical signal, during which the nonlinear amplification process induces front-edge distortion. Due to the non-zero linewidth enhancement factor, the front-edge distortion can be isolated by the optical filtration of the chirped frequency component, which eventually becomes Gaussian-like pulse train of tens of ps FWHM pulsewidth. Following a stage of solitonic compression and a stage of pedestal suppression, we are able to obtain a train of 1-ps high-quality pulses for which the root mean square timing jitter is $C$ -band.

Low Temperature Properties of Inhomogeneous Magnetic Multilayers

System of two magnetic layers with nonuniform distribution of anisotropy parameter and exchange coupled by nonmagnetic spacer is studied by means of the Green function approach. Our attention is focussed on the elementary excitations and low temperature magnetisation behavior. The spin wave parameter B in the Bloch law T 3/2 is found as an oscillatory function of a spacer thickness. The e ects of damping leading to non-zero line-width of ferromagnetic resonance peaks are also taken into account. As a result the dependence of resonance line-width on parameters characterizing system under consideration is obtained for the case of uniform anisotropy parameter and for quadratic distribution of this parameter in magnetic layers, respectively.

Spectral line shape profile of rovibrational transitions of CO embedded in p-H2 crystals studied by high resolution IR diode laser spectroscopy

Line profiles of rovibrational transitions of CO embedded in p-H(2) crystals were studied by high resolution midinfrared diode laser spectroscopy. The line profile analysis for the R(0)(parallel), R(0)(perpendicular), P(1)(parallel), and P(1)(perpendicular) transitions shows that spectral line shapes are well reproduced by a convolution of Gaussian and Lorentzian functions. The temperature dependence of the Lorentzian Gamma(L)(T) and Gaussian widths Gamma(G)(T) shows that there is a nonzero linewidth contribution to each at the T = 0 K limit. The main part of the Lorentzian width Gamma(L)(T = 0) shows anisotropy in the hcp structure and is explained by spontaneous decay of the rotational excited state energy to phonon modes. A smaller part of Gamma(L)(T = 0) is attributed to inhomogeneous broadening due to the point defects of other CO molecules in the crystal. On the other hand, the Gaussian width Gamma(G)(T = 0) is explained by inhomogeneous broadening due to dislocations. In the T > 0 region, Gamma(L)(T) shows strong temperature dependence but Gamma(G)(T) does not. The center frequencies of the R(0)(perpendicular) and P(1)(parallel) transitions show blueshifts and those of the R(0)(parallel) and P(1)(perpendicular) transitions show redshifts with increasing temperature. This phenomenon is explained by a decrease in the anisotropy in the crystal field, which is caused by the averaging of thermal lattice fluctuations. Furthermore, the contribution of vibration and rotation to the linewidth is discussed.

Slow and superluminal light in semiconductor optical amplifiers

An effective mechanism to achieve slow and superluminal light can be achieved in semiconductor optical amplifiers via wave mixing processes due to nonzero linewidth enhancement factor.

Modulation resonance enhancement in SCH quantum-well lasers with an external Bragg reflector

The modulation response of a semiconductor laser can be enhanced by coupling it to an external cavity with frequency-selective feedback. This creates a comb of transmission bands where the modulation response is high, at the cavity round-trip frequency and its harmonics. In a previous publication, we related the bandwidths of these bands to the material and structural parameters of a bulk laser. We showed that a nonzero linewidth enhancement factor together with a nonzero intermediate facet reflectivity lead to deep nulls close to the peaks of these transmission bands. This suggests that quantum-well (QW) lasers, which have a low linewidth enhancement factor, may give a better performance than bulk lasers. To test this hypothesis, we have extended our analysis to model QW lasers coupled to a fiber grating. Carrier transport, carrier heating, intraband carrier fluctuations, and nonparabolic band structures are considered. We show that electron carrier transport and amplitude-phase coupling in the separate-confinment-heterostructure (SCH) layer contribute to the nulls in the modulation response. Therefore, the apparent advantage of having a reduced linewidth enhancement factor that we found in our previous analysis cannot be fully realized by using QW lasers.

Preamplifier ASK system performance with incomplete ASK modulation: influence of ASE and laser phase noise

Present extensions of the rigorous model of Jacobsen and Garrett and of the Gaussian approximation of Tonguz and Kazovsky for the performance of optically amplified direct detection ASK receivers. These new models take into account incomplete ASK modulation, nonzero laser linewidth, and spontaneous emission noise from the optical amplifier in both polarization control (PC) and polarization diversity (PD) receiver configurations. The penalty associated with the polarization diversity configuration is shown to be consistently under 1 dB for a wide range of ASK modulation depths. The penalty due to the noise in the orthogonal polarization decreases with ASK modulation depth. We find optimum optical filter bandwidths and linewidth-induced performance penalties as a function of ASK modulation depth and linewidth. We provide detailed tables of optimum filter bandwidths for bath PC and PD receivers using both the rigorous method and the Gaussian approximation; the Gaussian approximation frequently underestimates the optimum bandwidth values. A linewidth-induced floor in the minimum usable ASK modulation depth is found for nonzero linewidth and a fixed optical filter bandwidth. Though the Gaussian approximation is found to be accurate within 1.5 dB in all computed cases for optimum optical filter bandwidths, it does not predict the floor accurately in the case of a nonoptimum filter bandwidth.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the linewidth of microcavity lasers

In a recent letter by G. P. Agrawal and G. R. Gray [Appl. Phys. Lett. 59, 399 (1991)] the frequency and phase noise of vertical-cavity surface-emitting microlasers is calculated using rate equations and Langevin noise sources. In this letter we re-examine their calculations and get different results. Specifically, we predict that an increase of the spontaneous emission coupling coefficient will not necessarily lead to an increase in linewidth. It is also found that the reported ‘‘anomalous linewidth enhancement’’ is present in all lasers with a nonzero linewidth enhancement factor.

Influence of laser phase on 400-Mbit/s coherent optical DPSK system

The influence of laser phase noise on a 400-Mb/s optical DPSK (differential phase-shift keying) system is experimentally investigated with linewidths ranging from 1.2 MHz to 8 MHz. This range corresponds to linewidth to bit rate ratios epsilon of 0.33-2%. The system performance with these nonzero linewidths is evaluated against a negligible linewidth performance baseline. The sensitivity degradation at a bit error rate of 10/sup -9/ increases from 1.8 to 7 dB as epsilon is increased from 0.33-1%. When epsilon is increased beyond 1%, bit error rate floors higher than 10/sup -9/ develop. These findings agree well with the existing theories and allow the generalization of these results to other bit rates, as well as establishing practical criteria for lasers to be used in DPSK systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

M-ary FSK Performance for Coherent Optical Communication Systems Using Semiconductor Lasers

This paper describes the design and performance of an M ary frequency shift keyed (FSK) signaling and demodulation scheme for an optical communication system using semiconductor lasers and heterodyne detection. Frequency or phase noise in semiconductor lasers causes spectral spreading, producing a nonzero linewidth laser signal. This degrades communication performance when compared to a system using an ideal laser with zero linewidth. We present estimates of the bit error rate (BER) performance of M -ary frequency shift keying (FSK) with noncoherent demodulation in the presence of white Gaussian frequency noise and additive channel noise. This is typical of an optical system using semiconductor lasers and heterodyne detection. Estimates use the union-Chernoff bound with a simplified channel model to predict the effects of frequency noise. Two effects of frequency noise are identified: signal attenuation or suppression, and crosstalk. These cause an offset in the BER curve from the BER in the absence of frequency noise, and an error rate floor, respectively. The error rate floor is lower than previously predicted. When performance is not crosstalk limited, M -ary FSK is found to perform better than binary FSK with the same system bandwidth constraints, as would be predicted if ideal lasers are used. Theoretical results are compared with Monte Carlo simulations of the system.

The effect of spurious intensity modulation in semiconductor diode lasers on the performance of optical heterodyne frequency shift-keyed communications systems

Analytical expressions are derived for the bit-error rate (BER) of an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -ary frequency shift-keyed (FSK), heterodyne, optical communication system with noncoherent demodulation in the presence of spurious intensity modulation (SIM) and frequency noise. The SIM degradation of an FSK system, implemented with semiconductor diode lasers, is estimated for lasers with zero and nonzero linewidths and will be discussed for a distributed feedback laser operating at 1.5μm and a channeled substrate planer laser operating at 0.83 μm. The SIM power penalty is typically less than 1 dB, but can exceed 1 dB for 2-, 4-, and 8-ary FSK at data rates above 1 Gbit/s.

Theoretical analysis of heterodyne optical receivers for transmission systems using (semiconductor) lasers with nonnegligible linewidth

We present a general theoretical model of receivers for coherent optical communication systems where transmitters and local oscillators having nonzero linewidth are used. Key issues in the model are the concept of single realization measurements of a stochastic intermediate frequency, and development of the probability density function for this stochastic process. Analytical results are derived for heterodyne ASK and dual filter FSK receivers and include the shot-noise limit, the asymptotic error-probability limits in ASK and FSK receivers, the influence of the IF on receiver noise, and the effective local oscillator strength. Detailed numerical results for typical p-i-n-FET wide-band receivers illustrate the influence on receiver sensitivity of IF filter bandwidth and relative threshold setting in ASK systems and of modulation index and IF filter bandwidth in FSK systems. A receiver sensitivity penalty for nonzero linewidth is found to be, for IF linewidths of 0.1 to 0.3 of the bit-rate, 3 to 9 dB in optimum ASK receivers, and 2 to 8 dB in optimum FSK receivers. Thus DFB lasers of linewidth 5 to 20 MHz could be used without external cavities in simple systems with near-ideal performance, which could find application wherever the great multiplexing advantage of coherent systems is a prime advantage. We present some guidelines for system design based on the results of this work.

Initial or thermally controlled impurity trapping of muons in niobium?

We have studied muon depolarization in some very well characterized samples of niobium (pure Nb with <1 ppm impurities and Nb doped with 15 at.ppm N and 53 at.ppm Ta, respectively). This has allowed us to separate the influence of substitutional and interstitial impurities on theμSR linewidthσ. The purest sample shows a low but non-zero linewidth from 0.1 to 70 K. Ta-doping increases the width strongly below 20 K. while N-doping gives a broad maximum between 30–70 Kand a considerable width below 20 K. Conventional two-trap models cannot explain the occurrence of a linewidth significantly lower that that predicted for staticμ + and constant over a wide temperature range. A consistent explanation of these three observations can however be obtained from the following model: In pure Nb only a fraction of the muons is self-trapped thermally; the other muons do not form small polarons but remain in a propagating metastable nonlocalized state. Impurities can catalyse further initial polaron formation, decreasing the metastable fraction. This process causes temperature-independent plateaus inσ up to the detrapping temperature. The muons localized at shallow traps (Ta induced) can diffuse at higher temperatures and be trapped again at deeper traps (associated with the N-impurities).

Limitations of spin-wave theory inT=0spin dynamics

The $T=0$ dynamics of a family of one-dimensional quantum spin systems with fully ordered (ferromagnetic or spin-flop) ground states is investigated. By rigorous calculations, it is demonstrated that the $T=0$ dynamic structure factor is, in general, not a $\ensuremath{\delta}$ function as predicted by linear spin-wave theory but characterized by more complicated structures with nonzero linewidths. The exact result approaches the spin-wave result in the classical limit $s\ensuremath{\rightarrow}\ensuremath{\infty}$. The results of this study demonstrate how quantum effects may invalidate spin-wave theory even in the presence of saturated magnetic long-range order. Hence the failure of spin-wave theory is not necessarily linked to the absence or strong reduction of long-range order typical for one-dimensional quantum spin systems. The unreliability of spin-wave theory has therefore to be suspected also for the dynamics of three-dimensional quantum spin systems where the long-range order is always strong at $T=0$.

Lifetime of zero sound in liquid3He

Zero-sound excitations in liquid 3He at 0.02K and at the pressure of the saturated vapour have been studied using neutron inelastic scattering techniques. The results for the frequencies of the zero-sound excitations are in agreement with the measurements of Skold and co-workers. The results also show a non-zero linewidth for the excitations with wave-vector transfers 0.45 AA-1<Q<0.8 AA-1, which suggests that modification to the current theories is required.