There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Optical nonlinearities in the context of lightwave systems limitations are described. The nature and severity of system degradation due to stimulated Raman scattering, carrier-induced phase noise, stimulated Brillouin scattering, and four-photon mixing are discussed. The system power limitations are plotted as a function of a number of wavelength-multiplexed channels. Methods for scaling these results with changes in system parameters are presented. >

Limitations on lightwave communications imposed by optical-fiber nonlinearities

This paper reviews the developments of a distributed strain and temperature sensing technique that uses Brillouin scattering in single-mode optical fibers. This technique is based on strain- and temperature-induced changes in the Brillouin frequency shift. Several approaches for measuring the weak Brillouin line are compared. >

Development of a distributed sensing technique using Brillouin scattering

We present a detailed overview of stimulated Brillouin scattering (SBS) in
 single-mode optical fibers. The review is divided into two parts. In the first part,
 we discuss the fundamentals of SBS. A particular emphasis is given to analytical
 calculation of the backreflected power and SBS threshold (SBST) in optical fibers
 with various index profiles. For this, we consider acousto-optic interaction in the
 guiding geometry and derive the modal overlap integral, which describes the
 dependence of the Brillouin gain on the refractive index profile of the optical
 fiber. We analyze Stokes backreflected power initiated by thermal phonons, compare
 values of the SBST calculated from different approximations, and discuss the SBST
 dependence on the fiber length. We also review an analytical approach to calculate
 the gain of Brillouin fiber amplifiers (BFAs) in the regime of pump depletion. In the
 high-gain regime, fiber loss is a nonnegligible effect and needs to be accounted for
 along with the pump depletion. We provide an accurate analytic expression for the BFA
 gain and show results of experimental validation. Finally, we review methods to
 suppress SBS including index-controlled acoustic guiding or segmented fiber links.
 The second part of the review deals with recent advances in fiber-optic applications
 where SBS is a relevant effect. In particular, we discuss the impact of SBS on the
 radio-over-fiber technology, enhancement of the SBS efficiency in Raman-pumped
 fibers, slow light due to SBS and SBS-based optical delay lines, Brillouin
 fiber-optic sensors, and SBS mitigation in high-power fiber lasers, as well as SBS in
 multimode and microstructured fibers. A detailed derivation of evolutional equations
 in the guided wave geometry as well as key physical relations are given in
 appendices.

Stimulated Brillouin scattering in optical fibers

Brillouin frequency shift in a single-mode optical fiber has been measured as a function of tensile strain. The strain coefficient of normalized Brillouin frequency shift C identical to (dv/sub B//d epsilon )/v/sub B/ is found to be 4.4 for silica fibers. This result shows the potential of Brillouin spectroscopy to evaluate tensile strain in the fiber with the strain resolution of about 2*10/sup -4/. The origin of the large strain coefficient is discussed. >

Tensile strain dependence of Brillouin frequency shift in silica optical fibers

Several resonance peaks owing to an interaction between light-wave and guided modes of longitudinal acoustic waves are observed in the Brillouin gain spectra for a single-mode fiber with a GeO2-doped core and pure silica cladding. Brillouin gain spectra measurements are carried out at 1286- and 1550-nm wavelengths. Longitudinal acoustic modes guided in the GeO2-doped core region are identified by applying the analysis of leaky modes in a fiber acoustic waveguide.

Identification of longitudinal acoustic modes guided in the core region of a single-mode optical fiber by Brillouin gain spectra measurements.

Transmission limitations due to stimulated Brillouin scattering and four-wave mixing processes are investigated for optical frequency division multiplexing (FDM) systems. The applicability of the dispersion-shifted (DS) and nondispersion-shifted (NDS) fibers is discussed, taking account of channel frequency separation, total channel numbers, input signal power, transmission length, and receiver sensitivity degradation. Experimental results on Brillouin gain spectra and the wave generation efficiency in four-wave mixing processes are also presented to discuss the applicability of the two types of single-node fiber. It was found that NDS fibers operated at a wavelength of 1550 nm can be widely deployed in multichannel systems both for the long-haul and information distribution transmissions, if the signal waveform distortion due to fiber chromatic dispersion is precluded. The delay equalizer will be useful for a high-speed system employing bit rates over 10 Gb/s and repeaterless spans over 300 km. For such an application, DS fiber is preferable. Concerning information distribution network applications, the NDS fiber should be more attractive as a transmission medium for FDM system applications. >

Transmission limitations due to fiber nonlinearities in optical FDM systems

Brillouin-gain profiles are measured for fused-silica core and GeO2-doped core fibres at wavelengths of 1286nm and 1550nm. The intrinsic Brillouin linewidth is found to vary as the square of optical frequency, as predicted for bulk fusedsilica. However, the experimentally evaluated Brillouin linewidths at both wavelengths are broader by a factor of 2.5 than those predicted for the bulk glass.

Wavelength dependence of Brillouin-gain spectra for single-mode optical fibres

The effect of pump or Stokes field polarization-state changes on Brillouin gain is investigated in standard (non-polarization-maintaining) single-mode fibers with a modal birefringence of ~10−7. The Brillouin gain change due to polarization azimuth variation of the input pump or Stokes field reaches ±31% of the average gain expected for a completely scrambled polarization state. This polarization effect on the Brillouin gain may lead to cross-talk fluctuation in bidirectional coherent transmission systems and to degradation of Brillouin amplifier performance.

Brillouin gain variation due to a polarization-state change of the pump or Stokes fields in standard single-mode fibers.

This paper presents a method for adjusting a free space optics (FSO) system that links two single-mode optical fibers using collimators with a symmetrical configuration. It operates as if the two optical fibers were seamlessly connected without the need for any photoelectric devices. Collimator focusing, as well as axis alignment, is critical for low-loss transmission. A simultaneous optimization requires a task of six degrees of freedom (DOFs) in total. The assisted focus adjustment proposed here is performed for an FSO system to match a specified link span using an optomechatronic system in advance of its installation. Thus, the six-DOF task is mitigated, leaving an axis alignment task only. Then, the tuned FSO system can be combined with an existent misalignment compensation mechanism for beam acquisition/tracking at the installation site if necessary.

Yuji Azuma

Papers

Identification of longitudinal acoustic modes guided in the core region of a single-mode optical fiber by Brillouin gain spectra measurements.

Transmission limitations due to fiber nonlinearities in optical FDM systems

Wavelength dependence of Brillouin-gain spectra for single-mode optical fibres

Brillouin gain variation due to a polarization-state change of the pump or Stokes fields in standard single-mode fibers.

Assisted Focus Adjustment for Free Space Optics System Coupling Single-Mode Optical Fibers