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Showing papers in "IEEE Journal of Quantum Electronics in 1983"


Journal ArticleDOI
TL;DR: In this paper, Abraham and Casperson used the BR = y + p P (3a j ) to express the BR in terms of BR + p p + 3a j.
Abstract: Manuscript received April 14, 1983; revised June 24, 1983. N. B. Abraham is with the Department of Physics, BrynMawr College, Bryn Mawr, PA 19010. P. Mandel is with the Service de Chimie Physique 11, Universite Libre de Bruselles, Brussels, Belgium. L. W. Casperson is with the Department of Electrical Engineering and Applied Science: University of California, Los Angeles, CA 90024. Editor’s Note: A similar correction by Dr. F. Holigner and Prof. Dr. H. Weber of the Universitat Kaiserslautern was received on May 4, 1983. tions can be expressed as BR = y + p P (3a j

371 citations


Journal ArticleDOI
Charles H. Henry1
TL;DR: In this paper, it was shown that the additional phase changes also give rise to line shape structure in the form of additional peaks separated from the main peak by multiples of the relaxation oscillation frequency.
Abstract: Spontaneous emission alters the phase and amplitude of the laser field. The amplitude changes induce relaxation oscillations, which cause additional phase changes while restoring the field amplitude to the steady state value. It was previously shown that the additional phase changes greatly enhance the linewidth. We show here that the additional phase changes also give rise to line shape structure in the form of additional peaks separated from the main peak by multiples of the relaxation oscillation frequency. The calculated mean square phase change and power spectrum are in good agreement with published observations.

302 citations


Journal ArticleDOI
TL;DR: In this paper, the authors compared the performance of cyclotron autoresonance masers (CARM's) and ubitrons at mm and sbmm waves.
Abstract: FEL's based on the stimulated undulator radiation (ubitrons) are compared with those based on the stimulated cyclotron radiation [cyclotron autoresonance masers (CARM's)]. If the high-current accelerators are used as electron injectors, then from the viewpoint of simplicity of oscillatory electron energy pumping, criticality with respect to electron velocity dispersion, and efficiency, CARM's seem to be more effective than ubitrons at mm and sbmm waves. For such HF generators, resonators based on selective Bragg reflection of electromagnetic waves in corrugated metallic tubes are most atractive. CARM's of this type yield 6 MW at a 4 mm wavelength and 10 MW at a 2 mm wavelength in the single-mode regime.

279 citations


Journal ArticleDOI
TL;DR: In this article, a model of semiconductor laser noise is presented which includes the carrier density as a dynamical variable and carrier density dependence of the refractive index, and the role of carrier noise in determining the field spectrum linewidth.
Abstract: A model of semiconductor laser noise is presented which includes the carrier density as a dynamical variable and the carrier density dependence of the refractive index. The Van der Pol laser noise model is shown to he a special case of this treatment. Expressions are calculated for all laser spectra and compared with their Van der Pol counterparts. The power fluctuations spectrum and the frequency fluctuations spectrum exhibit a resonance corresponding to the relaxation resonance and the field spectrum contains fine structure, similar to sidebands which result from harmonic frequency modulation of a carrier signal. The role of carrier noise in determining the field spectrum linewidth is also considered.

245 citations


Journal ArticleDOI
D. H. Auston1
TL;DR: In this paper, the response of high-speed photoconductors to picosecond optical pulses is analyzed by representing them as time-varying circuit elements in transmission lines, and the results provide a basis for estimating the limiting speed of response of this approach to very high speed electronic measurements.
Abstract: The response of high-speed photoconductors to picosecond optical pulses is analyzed by representing them as time-varying circuit elements in transmission lines. Expressions are derived for transmitted and reflected waves for photoconductors used both as pulse generators and sampling gates. These results are then used to determine the correlated response of pairs of photoconductors in different transmission line networks. The results provide a basis for estimating the limiting speed of response of this approach to very high-speed electronic measurements.

241 citations


Journal ArticleDOI
TL;DR: In this paper, a circuit modeling technique for directly modulated narrow-stripe semiconductor lasers with strong carrier confinement and index guiding is described, and diffusion damping of the modulation response, due to a nonuniform electron density distribution in the active layer, can be accounted for in terms of an equivalent optical gain saturation.
Abstract: This paper describes a circuit modeling technique for directly modulated narrow-stripe semiconductor lasers with strong carrier confinement and index guiding It is shown that diffusion damping of the modulation response, due to a nonuniform electron density distribution in the active layer, can be accounted for in terms of an equivalent optical gain saturation Based on this equivalence, a small-signal ac circuit model of a narrow-stripe laser is derived The model can be used to determine the intensity modulation and frequency modulation response characteristics of a packaged device

222 citations


Journal ArticleDOI
TL;DR: In this article, the carrier-induced index change has been measured for a large number of broad-area AlGaAs and 1.3 μm InGaAsP diode lasers.
Abstract: The carrier-induced index change has been measured for a large number of broad-area AlGaAs and 1.3 μm InGaAsP diode lasers. The observed index change with injected carrier density is -(1.2 \pm 0.2) \times 10^{-20} cm3for AlGaAs lasers and -(2.8 \pm 0.6) \times 10^{20} cm3for 1.3 μm lasers. The index change at threshold varies from -0.03 to -0.06 for AlGaAs lasers and from -0.04 to -0.10 for InGaAsP lasers. This variation is correlated with the carrier density at threshold, which depends on active layer thickness and doping level. For the first time, the observed index change is compared to the carrier density found from differential carrier lifetime measurements. This accurate determination of the carrier density represents a significant improvement over previous studies.

211 citations


Journal ArticleDOI
TL;DR: In this paper, second-order optical nonlinearities associated with intra-subband transitions in Al x Ga 1-x AS heterostructure exhibiting the quantum size effect are considered and shown to be large under conditions of degenerate doping and nonsymmetric compositional grading.
Abstract: Second-order optical nonlinearities associated with intra-subband transitions in Al x Ga 1-x AS heterostructure exhibiting the quantum size effect are considered and shown to be large under conditions of degenerate doping and nonsymmetric compositional grading. Nonlinearities of between 10-100 times larger than in bulk GaAs seem feasible.

194 citations


Journal ArticleDOI
TL;DR: In this article, a lithium tantalate traveling wave Pockels cell was employed in conjunction with a high repetition rate subpicosecond laser system for the characterization of electrical transients.
Abstract: We report on the recent advances of an electrooptic sampling technique for the characterization of electrical transients that has now achieved an unprecedented temporal resolution of less than 1 ps. Voltage sensitivity is on the order of 50 μV. A lithium tantalate traveling wave Pockels cell is employed in conjunction with a high repetition rate subpicosecond laser system.

184 citations


Journal ArticleDOI
TL;DR: In this paper, two theoretical approaches are employed: one is based on the quantum mechanical Langevin equation, and the other on the density matrix equation, which are derived from three different formulations, that is, the rate equation, Fokker-Planck equation and van der Pol equation, that are derived by using the Kane function interpolated to Halperin-Lax bandtail and the Stern improved matrix element.
Abstract: AM and FM quantum noise properties of semiconductor lasers have been studied theoretically. Theoretical formulations for the AM noise spectrum, photon number probability density, FM noise spectrum, instantaneous frequency probability density, and power spectrum are presented here as functions of semiconductor laser material, structural, and pumping parameters. Two theoretical approaches are employed: one is based on the quantum mechanical Langevin equation, and the other on the density matrix equation. Starting from the quantum mechanical Langevin equation, three different formulations, that is, the rate equation, Fokker-Planck equation, and van der Pol equation, are derived. The parameters which represent stimulated emission, spontaneous emission, and refractive-index dispersion are obtained by using the Kane function interpolated to Halperin-Lax bandtail and the Stern's improved matrix element. The above four different theoretical formulations are related to each other, and the applicability for each method is discussed.

174 citations


Journal ArticleDOI
TL;DR: In this paper, a new ultrafast optical waveguide gate based on a nonlinear optical interaction in a waveguide interferometer is presented. Butler et al. used a modified Mach-Zehnder Interferometer, 2 cm long, fabricated in a LiNbO 3 substrate.
Abstract: We present a new ultrafast optical waveguide gate based on a nonlinear optical interaction in a waveguide interferometer. A train of signal pulses is gated by control pulses which change the refractive index in only one arm of the interferometer. The principle of operation is demonstrated using a modified Mach-Zehnder interferometer, 2 cm long, fabricated in a LiNbO 3 substrate. The experiments were performed with a near-infrared dye laser which produced 5 ps pulses at \lambda = 840 nm. A maximum modulation on the order of 10-3was obtained for a peak control power of 2 W. Experimentally, we determined the appropriate nonlinear coefficient of LiNbO 3 to be n_{2} = 3 \times 10^{-9} (MW/cm2)-1. As possible applications of the structure we describe an all-optical inverter, an XOR gate, and an AND gate. We conclude with a brief description of a random number generator encoder and decoder based on a few all-optical logic gates.

Journal ArticleDOI
TL;DR: In this article, the stimulated emission cross section for the 2F 5/2 → 2F 7/2 transition of Yb3+ has been determined from absorption and emission measurements of 41 different oxide, fluoride, and oxyfluoride glasses at 293 K.
Abstract: The stimulated emission cross section for the2F 5/2 →2F 7/2 transition of Yb3+has been determined from absorption and emission measurements of 41 different oxide, fluoride, and oxyfluoride glasses at 293 K. The effective peak cross sections for transitions to Stark levels above the ground state range from approximately 0.3 to 0.8 pm2. The largest values occur in borate and phosphate glasses; the smallest values occur in silicate and low-refractive-index fluoride glasses. Radiative lifetimes calculated from integrated absorption spectra are also reported and range from 0.6 to 2.7 ms. Systematic variations in cross sections with changes in modifier ions can be used to tailor stimulated emission cross sections and fluorescence lifetimes.

Journal ArticleDOI
TL;DR: In this paper, the effects of both phase velocity and group velocity mismatch between fundamental and second harmonic fields are analyzed for optical pulse width measurements. And an expression for the time average second harmonic energy, which except for special cases differs from the intensity autocorrelation function, is derived.
Abstract: The use of second harmonic generation as a technique for optical pulse width measurements is analyzed to determine the effects of both phase velocity and group velocity mismatch between fundamental and second harmonic fields. An expression for the time average second harmonic energy, which except for special cases differs from the intensity autocorrelation function, is derived. For Type I phase matching, the measurement yields an apparent correlation width which can be either shorter or longer than the actual intensity correlation width, depending on the specific pulse shape. When the group velocity mismatch is nonzero, the measurement becomes sensitive to the phase matching condition. Two special pulse shapes for which the measurement is independent of group and phase velocity mismatch are the Gaussian and the single-sided exponential.

Journal ArticleDOI
Dietrich Marcuse1
TL;DR: In this article, the authors proposed a model based on numerical solutions of traveling-wave equations, where the noise output of the laser amplifier is treated by traveling-Wave power equations, but the light signal is described by travelingwave equations for its amplitude.
Abstract: Laser amplifiers can be used in two ways: as preamplifiers to enhance the sensitivity and improve the noise performance of detectors and, in a pulsed mode of operation, as modulators to boost and stabilize the output of an injection laser oscillator. Most mathematical models of injection lasers are based on time-dependent rate equations that ignore the spatial dependence of the electron and photon densities. The model discussed here is based on numerical solutions of traveling-wave equations. The noise output of the laser amplifier is treated by traveling-wave power equations, but the light signal is described by traveling-wave equations for its amplitude. The parameters responsible for spontaneous and stimulated emission are being related to each other by the requirement that the amplifier achieve optimal noise performance in the absence of internal losses and without gain saturation. The most important results obtained from this computer model of a laser amplifier are as follows. 1) The theory contains a heuristic electron injection efficiency parameter. To agree with experimental observations this parameter must be kept small and its value must decrease with increasing current. 2) Cavity amplifiers saturate more readily than amplifiers without feedback. 3) Because of internal loss mechanisms the amplifier supplies more noise than is required by quantum theory, but its noise performance is still surprisingly good. In particular, the optical signal-to-noise ratio prior to detection is insensitive to gain saturation by strong signals. It remains approximately 4 dB below the theoretical maximum value for weak to moderately strong input signals and drops dramatically only when the amplifier is almost completely saturated.


Journal ArticleDOI
TL;DR: In this paper, the authors measured the intervalence band absorption spectra of In 0.53 Ga 0.47 As, InP, and GaAs and showed that the measured spectra are broader, have less temperature dependence, and have 2× less peak intensity than theoretical curves predicted by an elementary k\cdotp band model.
Abstract: Measurements of intervalence band absorption spectra were made in p-type In 0.53 Ga 0.47 As, InP, and GaAs. The measured spectra are broader, have less temperature dependence, and have 2× less peak intensity than theoretical curves predicted by an elementary k\cdotp band model. For p = 10^{18} cm-3, all three crystals have absorption coefficients of about 13 cm-1at 1.3 μm and 25 cm-1at 1.6 μm. These values of absorption should also be applicable as estimates of intervalence band absorption in quaternary laser material. Because of the low strength and weak temperature dependence of the intervalence band absorption, it should have only a minor effect on the temperature dependence of laser threshold. For example, using our absorption data, we calculate that intervalence band absorption will reduce the experimental temperature parameter T 0 of 1.3 μm quaternary lasers from 194 to 179 K.

Journal ArticleDOI
TL;DR: In this article, the authors show that phase-noise spectrum is found to present a sharp peak at the same peak frequency of intensity noise spectrum, a fact which is proven to be responsible for the appearance of satellite peaks in the emission line shape.
Abstract: Experimental results concerning the study of phase noise in single-mode semiconductor lasers are reported, which show a strict connection between phase and intensity noise. In particular, phase-noise spectrum is found to present a sharp peak at the same peak frequency of intensity-noise spectrum, a fact which is proven to be responsible for the appearance of satellite peaks in the emission line shape. Direct measurements of the line shape, performed by means of a Fabry-Perot interferometer, are in agreement with the line shape evaluated by using phase-noise spectrum measurements.

Journal ArticleDOI
TL;DR: The importance of photoelastic effect in controlling polarization in optical fibers is discussed in this article, where measurements of the stress-optic coefficient, its dispersion, and temperature dependence are reported using a fiber measurement method.
Abstract: The importance of the photoelastic effect in controlling polarization in optical fibers is discussed. Measurements of the stress-optic coefficient, its dispersion, and temperature dependence are reported using a fiber measurement method. The results compare closely to data obtained for bulk silica by an extrapolation technique. It is shown that the dispersion of the stress-optic coefficient can have a significant effect on the performance of birefringent fibers and of fiber birefringent devices. Furthermore, the temperature dependence is sufficiently large to be troublesome in fiber sensors.

Journal ArticleDOI
TL;DR: In this paper, four different theoretical formulations for AM and FM quantum noise properties in semiconductor lasers are compared with each other for AlGaAs lasers, based on van der Pol, Fokker-Planck, rate, and photon density matrix equations.
Abstract: Four different theoretical formulations for AM and FM quantum noise properties in semiconductor lasers are compared with each other for AlGaAs lasers. These formulations are based on van der Pol, Fokker-Planck, rate, and photon density matrix equations. Experimental results with AM noise spectra, FM noise spectra, and spectral linewidths for four different types of AlGaAs lasers are also delineated and compared with the theoretical predictions. The spontaneous emission coefficient β and population inversion parameter n sp , which are basic parameters for determining the quantum noise properties of semiconductor lasers, were calculated by the density of states with Kane function interpolated to Halperin-Lax bandtail and the Stern's improved matrix element. Experimental AM and FM quantum noise properties show good agreement with the theoretical predictions derived through use of estimated β and n sp values.

Journal ArticleDOI
TL;DR: In this paper, the energy requirements for short-pulse writing and erasing are greater than or equal to those obtained for typical CW lasers in all cases investigated, including BaTiO 3, Bi 12 SiO 20, and LiNbO 3.
Abstract: Solutions are obtained for the refractive index grating in a photorefractive material in which the writing or erasing beams are short-pulse (less than tens of nanoseconds), high-irradiance (greater than kW/cm2) lasers. The response of the photorefractive material is modeled using the continuity equation for the charge carriers, a rate equation for the ions, a current equation, and Poisson's equation for the space charge field. Two cases are discussed in detail: 1) the time for recombination of carriers with ions is much less than the pulse length of the laser; and 2) the recombination, drift, and diffusion times are all much longer than the pulse length. The energy requirements for short-pulse writing and erasing are greater than or equal to those obtained for typical CW lasers in all cases investigated. Application to previous observations in BaTiO 3 , Bi 12 SiO 20 , and LiNbO 3 is discussed.

Journal ArticleDOI
TL;DR: In this article, the steady state behavior of the external cavity operated laser has been analyzed, taking into account multiple reflections, and the effect of optical feedback is included in the phase and gain conditions by a factor which is shown to have a simple geometrical representation.
Abstract: The steady state behavior of the external cavity operated laser has been analyzed, taking into account multiple reflections. The effect of optical feedback is included in the phase- and gain-conditions by a factor which is shown to have a simple geometrical representation. From this representation it is easily seen how the laser frequency spectrum and the threshold gain depend on external parameters such as distance to the reflection point and the amount of optical feedback. Furthermore, by inserting a variable attenuator in the external cavity and measuring the threshold current versus transmittance we have simultaneously determined the photon lifetime and the absolute amount of optical feedback. For the laser considered we found the photon lifetime \tau_{p} = 1.55 ps.

Journal ArticleDOI
TL;DR: In this paper, a method for measuring the modal reflectivity of the antireflection coating applied to a laser diode is described and demonstrated based on measurements of the Fabry-Perot modulation depth of the resulting superluminescent diode output spectrum at the threshold current of the original laser.
Abstract: A method for measuring the modal reflectivity of the antireflection coating applied to a laser diode is described and demonstrated. It is based on measurements of the Fabry-Perot modulation depth of the resulting superluminescent diode (SLD) output spectrum at the threshold current of the original laser. A modal reflectivity of less than 2 \times 10^{-4} has been obtained.

Journal ArticleDOI
TL;DR: In this paper, the performance of a single-photon avalanche photodiode particularly suitable for the detection of fast and ultra-weak light pulses is described, and the advantages of this device over other available detectors are discussed.
Abstract: The performance of a new single-photon avalanche photodiode particularly suitable for the detection of fast and ultraweak light pulses is described. The advantages of this device over other available detectors are discussed. The electronic circuitry developed allows the measurement of fluorescence decays with a time resolution of 70 ps FWHM (full-width at half-maximum) and a data acquisition rate of up to 50 kHz.

Journal ArticleDOI
TL;DR: In this paper, a comparative theoretical study of the transient grating coherent effects in resonant picosecond excitation-probe experiments is presented, in which signal contributions from concentration and orientational gratings are distinguished and their temporal natures discussed.
Abstract: A comparative theoretical study of the transient grating coherent effects in resonant picosecond excitation-probe experiments is presented. Signals in both the probe and conjugate directions are discussed. The effects of recombination, nonradiative scattering, and spatial and orientational diffusion are included. The analysis is applied to both a molecular and a semiconductor model. Signal contributions from concentration and orientational gratings are distinguished and their temporal natures discussed. From the solid-state point of view, we show that state-filling, and in particular, anisotropic state-filling, can be identified from the configurational and time dependence of the detected signal, and thereby establish a theoretical explanation for our recent observations in germanium.

Journal ArticleDOI
TL;DR: In this article, the authors analyzed the oscillating transverse and longitudinal modes in semiconductor injection lasers using the density matrix formalism and derived the optimal range to obtain stable fundamental transverse mode operation with respect to several guiding factors.
Abstract: Mechanisms which determine the oscillating transverse and longitudinal modes in semiconductor injection lasers are discussed in this paper. The analysis is based on the semiclassical method in which the optical field is represented by Maxwell equations and the lasing phenomenon is analyzed quantum mechanically using the density matrix formalism. Guided modes are classified by the relation between refractive index and gain-loss differences at the boundaries of the active region as normal guided mode (index guiding), active-guided mode (gain guiding), and leaky mode (anti-index guiding). The guiding loss and cutoff conditions are given for these modes. The optimum range to obtain stable fundamental transverse mode operation is discussed with respect to several guiding factors, such as width of active region, the refractive index difference, and gain-loss differences at the boundaries of the active region. Longitudinal mode behavior is discussed in terms of electron transition mechanism in semiconductor crystals. The relaxation effect of the electron wave is introduced in this model. Profiles of the saturated gain and the spatial diffusion of the electron are related to this relaxation effect. Mode competition phenomena are analyzed, and a strong gain suppression among the longitudinal modes is shown to be as an intrinsic property of semiconductor lasers. The possibility of obtaining single longitudinal mode operation is postulated. Physical influences for stable single longitudinal mode operation are discussed in terms of transverse mode control (or stripe structure), spontaneous emission, threshold current level, impurity concentration in the active region, and direct modulation. Some experimental results are also given to support these analyses.

Journal ArticleDOI
TL;DR: In this paper, a two-photon resonant sum and difference frequency mixing (SDF) was used to generate coherent tunable VUV radiation of narrow spectral width by pulsed dye laser radiation in Hg vapor.
Abstract: Coherent tunable VUV radiation of narrow spectral width is generated by two-photon resonant sum and difference frequency mixing (\omega_{vuv}^{\pm} = 2\omega_{uv} \pm \omega_{D}) of pulsed dye laser radiation in Hg vapor. The UV frequency ω uv is tuned to the two-photon resonances 61S 0 - 71S 0 ( \lambda_{uv} = 3127.6 A), 61S 0 -61D 2 ( \lambda_{uv} = 2802.9 A), and 61S 0 - 71D 2 ( \lambda_{uv} = 2594.5 A). A second dye laser produces tunable radiation at ω D ( \lambda_{D} = 4200-6700 A). At input powers of 1-2 MW, the different conversion schemes generate VUV light pulses of typically 0.5-3 kW in spectral regions between 1090 and 1960 A. The experimental results provide information on the wavelength dependence of the generated VUV output, on the conversion efficiency, the phase-matching conditions, and on conversion limiting saturation phenomena. Besides the resonant frequency conversion, nonresonant frequency tripling and mixing is investigated at \lambda_{vuv} = 1800-1880 A in the vicinity of the resonance transition 61S 0 -61P 1 ( \lambda = 1849.5 A).

Journal ArticleDOI
TL;DR: In this paper, a condition for the single-mode operation of a rapidly modulated DBR laser, called a "dynamic-singlemode laser," and the dynamic spectral width were theoretically presented.
Abstract: The theoretical bases and the experimental results of the dynamic behavior of 1.5-1.6 \mu m GaInAsP/InP dynamic-single-mode (DSM) lasers with distributed Bragg reflector (DBR) are given. A condition for the single-mode operation of a rapidly modulated DBR laser, called a "dynamic-single-mode laser," and the dynamic spectral width were theoretically presented. Experimentally, buried-heterostructure distributed-Bragg-reflector integrated-twin-guide (BH-DBR-ITG) and buried-heterostructure butt-jointed-built-in distributed-Bragg-reflector (BH-BJB-DBR) lasers emitting at the wavelength of 1.5-1.6 \mu m were directly modulated up to 3 GHz, and the stable single-mode operations were obtained in both types of lasers. The dynamic spectral width at the worst modulation condition was measured to be 0.27 nm, which was about \frac{1}{35} times smaller than that of conventional lasers.

Journal ArticleDOI
TL;DR: In this article, the authors describe use of colliding pulse mode locking to generate pulses of 65 fs duration and pulse compression to reduce those pulse durations to 30 fs, and amplify femtosecond pulses to gigawatt powers.
Abstract: Recent advances in generation, amplification, compression, and frequency broadening of femtosecond optical pulses are reviewed. We describe use of colliding pulse mode locking to generate pulses of 65 fs duration and pulse compression to reduce those pulse durations to 30 fs. Amplification of femtosecond pulses to gigawatt powers and frequency broadening to obtain white light continuum pulses while retaining femtosecond pulse durations are also examined.

Journal ArticleDOI
TL;DR: In this article, the authors used self-focusing in CS 2 and other liquids to make a power-limiting device having a picosecond response time, which can produce phase aberrations and laser-induced breakdown, which in turn limit the transmitted power.
Abstract: Optical self-action in CS 2 and other liquids was used to make a power-limiting device having a picosecond response time. This device uses self-focusing in liquids to produce phase aberrations and laser-induced breakdown, which in turn limit the transmitted power. This device has near-unity transmission for input power below P c , which is on the order of the critical power for self-focusing, and limits the transmitted power to a nearly constant value for input power greater than P c . The onset of nonlinear transmission was adjusted by mixing various liquids to adjust the nonlinear refractive index. Experimental results using linearly and circularly polarized 40 ps (FWHM) pulses at 1.06 μm are presented.

Journal ArticleDOI
Nick Doran1, Keith J. Blow
TL;DR: In this article, the effects of loss on the propagation of soliton solutions of the nonlinear Schrodinger equation were investigated in the context of long-distance communications and some conclusions about the application of solitons in long distance communications were drawn.
Abstract: In this paper we have calculated the effects of loss on the propagation of soliton solutions of the nonlinear Schrodinger equation. Since we are interested in the application of these results to optical communications, it is necessary to go beyond perturbative results. This is due to the fact that propagation distances in optical fibers are significantly greater than the decay length of the energy in the pulses. Some conclusions are drawn about the application of solitons in long-distance communications.