Dispersion In Single-mode Fibers Research Articles

Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses

A new method for the coherent characterization of subpicosecond optical pulses after propagation through a nonlinear medium (i.e., with frequency broadening) is described. The phase shift on a single pulse introduced by the nonlinearity can be measured with a high dynamic range. We report as one application of this technique a measurement of the self-phase modulation incurred by an 800-fsec pulse after the pulse propagates along a dispersive single-mode optical fiber.

Chromatic dispersion in single-mode fibers with arbitrary index profiles: a simple method for exact numerical evaluation

An exact numerical method for computation of the chromatic dispersion in single-mode fibers with arbitrary profiles is presented. The method is based on matrix perturbation theory, taking the change in the fiber properties with wavelength as perturbation. This approach requires only one matrix eigenvalue evaluation (as against multiple eigenvalue evaluations in the existing methods) and a few additional simple matrix manipulations, resulting in a considerable reduction of computational effort. >

Chromatic dispersion limitations due to semiconductor laser chirping in conventional and dispersion-shifted single-mode fiber systems

The effect of dynamic linewidth broadening due to frequency chirping in directly modulated single-mode lasers, combined with dispersive single-mode fibers, has been investigated using computer simulation. It has been found that dispersion-shifted fibers have a potential advantage over conventional single-mode fibers for dual-window multigigabit-per-second bidirectional and wavelength-division-multiplexed transmission systems.

Statistical treatment of polarization dispersion in single-mode fiber

Polarization dispersion in single-mode fiber with random polarization mode coupling is given a statistical treatment based on the recently proposed principal-states model. An expression for the ensemble variance of the differential delay time between the principal states of polarization is derived by using coupled-mode theory under the assumption of weak coupling. For long fiber lengths, the variance is shown to have a linear dependence on length while the probability density function for the delay time approaches a Gaussian shape.

Exact relationships between field and dispersion of single-mode fibres in presence of material and linear profile dispersion

Exact explicit relationships relating the Petermann spot size to the propagation constant and its wavelength derivatives are derived including the effect of material and profile dispersion. An explicit expression for the propagation constant in terms of an integral of the spot size over wavelength is obtained.< >

Compensation of nonlinear chirp generated by self-steepening using third order dispersion of a grating pair

The cubic term of a response function of a grating pair can be changed by varying the angle of incidence to the gratings, while the quadratic term is controlled by varying the distance between the gratings. With this cubic term, the self-steepening (optical shock) and third order dispersion in single-mode fibers, which produce a nonlinearly chirped pulse, can be successfully compensated for optical pulse compression.

Measurement of chromatic dispersion in installed single-mode fibre

The measurement of chromatic dispersion in single-mode fibres using a 1300 nm edge-emitting LED, a 1550 nm laser diode, and the phase shift method are described. The approach is insensitive to fibre temperature change throughout the measurement, and may enable dispersion in single-mode fibre optimised for 1300 nm operation to be characterised in the 1550 nm region, as well as in the 1300 nm region. The influence of the edge-emitting LED on the measurement is also considered, in that error can arise through selecting narrow wavelength regions of its output, and matching its wavelength coverage to the fibre zero dispersion region is important for long length characterisation. Measurements on installed SM fibres are discussed.

Propagation constant and waveguide dispersion of single-mode fibers measured from far-field

Wavelength-dependent measurements of the far-field pattern can be evaluated to yield a mode-field radius. It was recently proposed to fit these data to a formula that contained all the parameters necessary to construct an empirical relation for the wavelength dependence of the propagation constant. The authors report on the feasibility of this technique, using actual measurement data. They discuss the calculation of the waveguide dispersion from the measured mode-field radius. In both cases the choice of the empirical fitting function proves to be of great importance. >

High-speed picosecond optical pulse compression from gain-switched 1.3-µm distributed feedback-laser diode (DFB-LD) through highly dispersive single-mode fiber

Picosecond optical pulse compression characteristics of chirped pulses from gain-switched distributed feedback-laser diodes (DFB-LD) transmitting through highly dispersive media are studied theoretically and experimentally. It is clarified theoretically that gain-switched chirped pulses can be compressed to about a 0.7-time bandwidth product by normal dispersion of the dispersive media and that the optimum dispersion value to obtain a minimum compressed pulse is proportional to the square of original pulsewidth. Through a dispersion, shifted single-mode fiber with -48-ps/nm normal dispersion at a 1.3-μm wavelength, gain-switched 30-ps (FWHM) pulses from a directly modulated 1.3-μm DFB-LD at a 4.4-GHz repetition rate have been successfully compressed to 6.4-ps optical pulses with a 0.86-time bandwidth product. Experimental results agree with the theoretical analysis.

Numerical study on combined stimulated Raman scattering and self-phase modulation in optical fibers influenced by walk-off between pump and Stokes pulses

We numerically examine the dynamics of stimulated Raman scattering combined with self-phase modulation for intense 100-psec-long input pulses in a dispersive single-mode optical fiber. Linear dispersion is treated in a first-order approximation by introducing group-velocity mismatch between pump and Stokes pulses. It is shown how this mismatch combined with pump depletion leads to asymmetric distortions of both pulse shapes and frequency chirps. The resulting delay of the Stokes peak is found to reach higher values for lower input pump powers. For sufficiently long fibers the emerging pump pulse has a one-peak structure, in contrast to the two-peak structure in the dispersionless case. The existence of an optimum fiber length to obtain the shortest Stokes pulse for a given input pulse is shown.

Phenomenological approach to polarisation dispersion in long single-mode fibres

We describe a model for polarisation dispersion in single-mode fibres of arbitrary length and configuration that is based on the existence of principal states of polarisation. These are two orthogonal input states of polarisation whose corresponding output states exhibit zero dispersion in their state of polarisation to first order.

Broadening of Intensity-Modulated Pulses in Single-Mode Fibres (Invited Paper)

The main state-of-the-art techniques for the evaluation of chromatic dispersion in single-mode fibres are reviewed, and methods based on nearfield, farfield, and/or spot-size measurements are mentioned. A mathematical development for the estimation of pulse shapes (for arbitrary input pulses) is presented together with an analytical formula for the Gaussian pulse case.

Four-photon mixing and dispersion in single-mode fibers

We show that phase matching for the four-photon mixing process in a single-mode fiber depends only on the propagation constant total dispersion beta(II)(omega). Frequencies omega(s) and omega(a), for the Stokes and anti-Stokes waves must satisfy omega(s) < omega(zd) < omega(a), where omega(zd) is the frequency for which dispersion is zero; beta(II)(omega(zd)) = 0. Variations in the frequency shift Omega(omega(p)) are described for pump frequency omega(p) around omega(zd), i.e., in the region where delicate balances of material and waveguide dispersion effects are used in fiber design. We show that no new waves are created when the pump and zero-dispersion frequencies coincide, i.e., Omega(omega(zd)) = 0. Since the creation of Stokes and anti-Stokes waves is intimately related to the beta(II)(omega) versus omega curve, some interesting results are predicted for advanced design fibers.

Effect of frequency chirping on the performance of optical communication systems

The effect of frequency chirping on the performance of optical communication systems is analyzed theoretically using a simple but realistic model for the chirped pulses emitted by a directly modulated semiconductor laser. The effect of pulse-edge sharpness is investigated by considering the propagation of super-Gaussian chirped pulses in a dispersive single-mode fiber. The results are presented using the parameter values appropriate for a 1.55-μm optical communication system employing conventional silica fibers and are in qualitative agreement with the reported experimental observations.

Single-mode fiber dispersion measurements using optical sampling with a mode-locked laser diode

Pulses from a wavelength-tunable, mode-locked laser diode were measured after 21 km of single-mode fiber propagation by optical sampling with another mode-locked laser diode; a resolution of 0.1 psec/(nm km) is achieved in this chromatic dispersion measurement. In another related experiment, 78-psec-duration pulses from an ordinary, multilongitudinal-mode laser diode are clearly displayed by optical sampling after 36 km of fiber propagation. System bandwidth increases to approximately 500 GHz km as the laser-diode wavelength is temperature tuned through the zero-dispersion region.

Temperature dependence of chromatic dispersion in single mode fibers

This paper describes the temperature dependence of chromatic dispersion in single-mode fibers for a temperature range of -60°- 250°C. Highly accurate dispersion measurements demonstrated a linear relationship (0.025 nm/°C) between the zero dispersion wavelength and temperature for tests conducted below 150°C. Further tests in the high-temperature range showed an increase in this dependence. For both temperature ranges, the results were independent of fiber coating and structure.

Comparison of single-mode fiber dispersion measurement techniques

This paper describes state-of-the-art techniques for characterizing dispersion in single-mode fibers. Special emphasis is placed on achieving high measurement accuracy within the 1.1-1.7 \mu m wavelength region.

Direct measurement of chromatic dispersion in single-mode fibres using streak camera

For the first time the dispersion characteristics in a single-mode fibre in the 1 μm-wavelength region is directly measured using a streak camera with a synchroscan streak tube having an S-1 photocathode.

Single mode operation of 1.5-μm cleaved-coupled-cavity InGaAsP lasers

Single longitudinal mode operation of cleaved-coupled-cavity lasers formed by recleaving of 1.5-μm InGaAsP buried crescent lasers is investigated as a function of bias current, temperature, and modulation frequency. The two-cavity lasers are made to operate in a stable single mode by adjusting the bias levels of the electrically isolated and optically coupled sections. The wavelength stability with temperature results in a change of only 0.48 Å/°C over a range of 14 °C. Single mode operation is preserved under direct modulation at rates as high as 1 Gb/s. The reduction in linewidth and the absence of partition noise makes these lasers useful for optical transmission through highly dispersive single mode fibers.

Accuracy of scalar approximation for single-mode fibers

Total dispersion in single-mode fibers has been computed from the exact numerical solution of scalar and vector wave equations and the accuracy of the scalar approximation has been discussed. It has been shown that for larger values of relative index difference between core and cladding, although the values of total dispersion obtained by the two approaches differ appreciably in the vicinity of zero dispersion, the optimum core radii and the zero dispersion wavelengths obtained by the two methods differ negligibly for all practical purposes.