Chirp Factor Research Articles

Novel Solitary Pulses for a Variable-Coefficient Derivative Nonlinear Schrödinger Equation

A derivative nonlinear Schrodinger equation with variable coefficient is considered. Special exact solutions in the form of a solitary pulse are obtained by the Hirota bilinear transformation. The essential ingredients are the identification of a special chirp factor and the use of wavenumbers dependent on time or space. The inclusion of damping or gain is necessary. The pulse may then undergo broadening or compression. Special cases, namely, exponential and algebraic dispersion coefficients, are discussed in detail. The case of exponential dispersion also permits the existence of a 2-soliton. This provides a strong hint for special properties, and suggests that further tests for integrability need to be performed. Finally, preliminary results on other types of exact solutions, e.g., periodic wave patterns, are reported.

Bandwidth and stability enhancement of optical parametric amplification using chirped ferroelectric superlattice

We report a theoretical analysis and numerical simulation of bandwidth and stability enhancement in optical parametric amplification (OPA) when using chirped periodically poled KTiOPO 4. Calculation results show that the bandwidth and stability are enhanced significantly by the use of a chirped grating. Temperature-gradient and fanned gratings are introduced and chirp factors of them are deduced and calculated. The use of a fanned grating flattens the Quasi-phase-matching response and improves the efficiency. Finally, we propose a method to reduce the instability induced by an unstable pump.

Chirp Control of an Electroabsorption Modulator to be used for Regeneration and Wavelength Conversion at 40 Gbit/s in All-Optical Networking

Chirp control to produce low or negative values of chirp at the output of an electroabsorption modulator (EAM) is an important mechanism for reducing the signal degradation due to chromatic dispersion in high-speed transmission over standard single-mode fibre. An analytical model for the chirp performance of an EAM capable of optical regeneration and simultaneous wavelength conversion operating at 40 Gbit/s is derived. A chirp control approach is identified using this model by exploring the tradeoff between the α-parameter describing the chirp factor (based on the nonlinear absorption coefficients) and bias voltage requirements of an EAM. In particular, an optimum range of bias voltage is determined to ensure reduced chirp operation when a two-tone signal (i.e., comprised of bias and modulating voltages) is applied to the EAM. It is also demonstrated for large signal operation at 40 Gbit/s that the optimum range of reverse bias voltage is between 0 and 2 V to obtain low values for the chirp factor (between +1 and −2) in order to facilitate the necessary chirp control in all-optical networking. In addition, it is identified that at 40 Gbit/s higher positive values of the second- and third- order nonlinear coefficients of chirp must be avoided when operating at reverse bias voltages less than 1 V.

Unbroadened-spectrum chirped Modulation: effects of the chirp-inducing mechanism on the spectral broadening in LiNbO/sub 3/ Modulators

The spectrum of a chirped optical nonreturn-to-zero data stream obtained by an external Mach-Zehnder modulator (MZM) is analyzed. We demonstrate that it is possible to induce chirp without broadening the optical spectrum by employing an MZM with optical power unbalancing in the two waveguides. For standard chirped MZMs (different electric fields on the two arms), such as z-cut LiNbO/sub 3/ modulators, the broadening as a function of chirp factor is measured for comparison.

Chirp and linewidth enhancement factor of 1.55 µm VCSEL with buried tunnel junction

Chirp characteristics of a 1.55 µm vertical-cavity surface-emitting laser (VCSEL) employing a buried tunnel junction are reported for the first time. From the measurements the linewidth enhancement factor αH is derived and presented.

Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL

Small-signal frequency modulation response and chirp characteristics of a tunable, optically-pumped 1.6 µm vertical cavity surface emitting laser (VCSEL) based on microelectromechanical at wavelength tuning are presented for the first time. From the measurements the linewidth enhancement factor αH has been derived and is discussed.

Chirp-Inducing Mechanisms in Mach–Zehnder Modulators and Their Effect on 10 Gb/s NRZ Transmission Studied Using Tunable-Chirp Single Drive Devices

We study the effects of different mechanisms inducing chirp in single-drive Mach-Zehnder modulators (MZM). In particular, we compare the effect of optical power splitting ratio unbalance with radio frequency modulation unbalance on the two interferometer arms. The better transmission performances of optically unbalanced modulators are ascribed to the different shape of time resolved chirp factor. Finally, we demonstrate error-free uncompensated transmission over 130-km fiber span.

Pulse linewidth and lifetime broadening study of multi-pulse pumped distributed feedback dye lasers

Results on characterization of spectral width and lifetime broadening mechanism in picoseconds multiple-pulse pumped distributed feedback dye lasers (DFDL) is presented. An experimental study was carried out to investigate the impact of pump pulse energy, dynamic grating length and dye concentration on the spectral width and lifetime characteristics of single and multi-pulse pumped DFDL. To implement this study the solution of Rh6G in ethanol was pumped by 2nd harmonic of a passively q.switched and modelocked ND:YAG laser. Further to study the effect of grating chirp factor on spectral characteristics of the luminescence spectra of the DFDL, the dye cell was pumped by multiple time delayed pulses. Results show that pump power, grating length, dye concentrations and temperature effects cause spectral and life time broadening of simultaneously oscillating multiple lasing lines.

Sampled-grating DBR laser integrated with SOA and tandem electroabsorption modulator for chirp-control

Chirp-controlled optical modulation is demonstrated using a voltage division scheme applied to a long-section phase modulator to compensate for the positive chirp of an electroabsorption modulator arranged in a tandem configuration. Both modulators are integrated with a semiconductor optical amplifier (SOA) and a sampled-grating distributed Bragg reflector (DBR) laser. The effective chirp factor can be controlled from +1 to -0.86 with less than 2 dB penalty in extinction ratio and insertion loss.

Power penalty analysis for realistic weight functions using differential time delay with higher-order dispersion

In this paper, the power penalty analysis for approximate and realistic weight functions has been presented for combating the pulse broadening effects of group-velocity dispersion in a fiber-optic communication link using differential time delay method including higher-order dispersion terms. The expressions for root mean square (RMS) phase deviation, optimum chirp factor and figure of merit have been evaluated for approximate and realistic systems. We show that the optimum value of chirp factor corresponds to dispersion compensation. The power penalty graphs for second-, third-, and fourth-order dispersion and their combinations have been presented for distance up to 300 km for this chirp factor for different weight functions. It is observed that the power penalty for realistic weight functions is less in comparison with the approximated weight function. It has also been shown that it is possible for a short pulse to propagate without significant broadening over the lengths many times longer than the usual dispersion length of fiber.

Influence of a Fabry–Perot etalon on a chirped optical pulse

Taking into consideration the fact that the output from a Fabry–Perot etalon is formed on the basis of the interference of the multi-reflected beams of the input pulse that enters the etalon, an analytical expression of the output pulse intensity has been derived for an input chirped Gaussian pulse passing through an etalon. Using the expression, the temporal width and the peak power of the output pulse is investigated. Results show that for a given etalon, the chirp factor and the width of the input pulse have intense effects on the width and the peak of the output pulse.

Improved estimation of hyperbolic frequency modulated chirp signals

This article deals with parameter estimation of product signals consisting of hyperbolic FM and chirp factors. A computationally simple algorithm that decouples estimation of the chirp parameters from those of the hyperbolic FM part is presented. It relies on a simple data transformation that removes the hyperbolic FM component, leaving one with the simpler problem of estimating chirp parameters. For the latter, the high-order ambiguity function (HAF) is adopted. Schemes for estimating the hyperbolic FM parameter are also proposed. The method improves on existing approaches and is shown to provide performance close to the Cramer-Rao bound.

Numerical simulation of a silicon-on-insulator waveguide structure for phase modulation at 1.3 μm

This paper presents an analysis of a silicon-on-insulator (SOI) waveguide structure to be used for phase modulation at 1.3 /spl mu/m. The device consists of a two-dimensional (2-D) strip waveguide and a p/sup +//N/sup -//N/sup +/ lateral diode to realize the effective index modulation by free-carrier injection. We have calculated that an effective index modulation between 5/spl middot/10/sup -4/ and 10/sup -3/ could be obtained with current densities in the range from 500 to 1600 A/cm/sup 2/. A detailed numerical simulation of the device transient response is also reported. We demonstrate that an effective index modulation of 5/spl middot/10/sup -4/ could be obtained with a cutoff frequency of about 100 MHz. The phase modulator has a predicted figure-of-merit (FoM) of 160/spl deg//V/mm and a chirp factor of 25. Due to its full compatibility with complementary metal-oxide-semiconductor (CMOS)-SOI technology, the device is interesting for low-cost silicon-based optoelectronic systems.

Efficient modeling of the optical properties of MQW modulators on InGaAsP with absorption edge merging

The optical properties of quantum wells on Ga/sub x/In/sub 1-x/As/sub 1-y/P/sub y/ are investigated. The dielectric function /spl epsiv/(/spl omega/) is calculated with a density matrix formalism valid for excitonic transitions as well as for the interband absorption including band mixing. With two simple approximations, the required number of overlap integrals is greatly reduced, allowing a fast and efficient exciton calculation. The calculated results are compared with measurements at 77 K and at a room temperature of 300 K. Furthermore, we present a field-induced heavy and light hole absorption merging for a Ga/sub x/In/sub 1-x/As/sub 1-y/P/sub y/-based modulator for the first time. It can he operated at a wavelength /spl lambda/=1.55 /spl mu/m, showing a very large absorption change and a small negative chirp factor, which is recommended for a low bit error rate.

Evaluation of the chirp parameter of aMach-Zehnder intensity modulator

A simple and accurate technique for evaluating of the chirp factor of Mach-Zehnder modulators is presented. The method is based on the dependence of the α parameter of the modulators on the applied bias voltage. It is shown that experimental results and theory are in very good agreement.

Frequency dependence of the chirp factor in 1.55 mu m distributed feedback semiconductor lasers

The authors report on measurements of the chirp factor versus modulation frequency and bias for 1.55 mu m distributed feedback lasers. A scanning Michelson interferometer is used to measure the phase response of the optical field under small-signal modulation of the injection current. The magnitude of the phase response is then quantified in terms of an effective chirp factor corresponding to the well known alpha -parameter. The authors find this factor to increase monotonically and nearly double as the modulation frequency increases from below to above the resonance frequency of the relaxation oscillation. The results contradict the commonly held view of alpha as a constant parameter for a given laser structure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Mode selection and spatial hole burning suppression of a chirped grating distributed feedback laser

A new kind of distributed feedback (DFB) laser with a linearly chirped grating is proposed and investigated theoretically for the first time. The eigenmodes of the chirped grating DFB (CG-DFB) and the field intensity distribution are calculated. With a suitable cavity length and chirp factor, the threshold gain difference to the next competence mode can be very large and will keep the single longitudinal mode stable. The chirp factor can be chosen to make the field intensity distribution quite uniform and at the same time keep the threshold gain difference large. This behavior effectively suppresses spatial hole burning and hence makes CG-DFB lasers that are stable single mode at high power, and with a narrow linewidth.

Sonics and ultrasonics : Signal processing by parametric interactions in delay-line devices Kino, G.S., Ludvik, S., Shaw, H.J., Shreve, W.R., White, J.M., Winslow, P.K. SU-20 (April 1973) 162–173

According to coherence theory and Mandel’ definition of coherence time, the analytical expressions for the complex degree of temporal coherence and coherence time of chirped Gaussian pulses are derived. The relations can be expressed as a function of the laser's chirp factor C and delay factor τ, the phase of complex degree of temporal coherence is not zero, and the influence of the laser's chirp factor is investigated. Finally, the coherence time-bandwidth product for chirped Gaussian pulses is obtained and can be expressed by τcΔv = 0.664 × (1 + C2)1/2.