Introduction

Fiber OPAs have a number of features that are potentially attractive for optical communication systems. In particular there is the prospect of using amplifiers with several hundred nanometers of gain bandwidth for the construction of wavelength-division multiplexing (WDM) systems with tens of terabits per second of capacity. However, before this potential can be realized a number of effects that can degrade the signal-to-noise ratio (SNR) must be addressed. Specifically these effects are: cross-gain modulation, mediated via pump depletion; four-wave mixing (FWM) between signals or between signals and a pump; cross-phase modulation (XPM) between signals. The physical origin of these effects is simple: efficient OPA operation generally requires that all the waves of interest be close to the zero-dispersion wavelength (ZDW) of the fiber, and this in turn implies that a number of other unwanted nonlinear interactions will also be well phase matched and so may generate large undesired effects. This origin indicates that these effects are fundamental in nature and may therefore be difficult to suppress.

Because of the importance of this issue, these effects have been investigated in depth by several research groups [1–12]. It has been found, through simulations and experimentally, that some of these effects can indeed be quite large under certain circumstances, to the point where they bring into question the viability of using fiber OPAs in WDM communication systems.

Introduction

During recent years much research has been performed with the aim of developing fiber Raman amplifiers. Some work was done on discrete Raman amplifiers, but now it appears that the best way to utilize Raman gain is in distributed amplification, i.e. the amplification of communication signals along transmission fibers rather than in discrete amplifiers located between such fibers. Some system manufacturers have developed long-haul systems based on distributed Raman amplification (DRA). Such systems, however, generally require high pump powers, sometimes in excess of 1 W, and this raises concerns about safety and reliability.

Concerning fiber OPAs, to date most efforts have concentrated on discrete devices, i.e. subsystems that could eventually be used as a substitute for other discrete optical amplifiers, such as erbium-doped fiber amplifiers (EDFAs) [1, 2]. Raman and parametric fiber amplification are related third-order nonlinear phenomena, which occur in common silica fibers in the presence of strong optical pumps. Whether a particular amplification mechanism is best suited for discrete or distributed amplification depends on a number of parameters, such as the gain bandwidth, the required pump power, the noise characteristics, etc.

Distributed parametric amplification (DPA) has previously been investigated as a detrimental effect, because strong carriers can further amplify in transmission fibers the amplified spontaneous emission (ASE) generated by the discrete EDFAs used to amplify signals between fiber spans. This has been done for one-pump [3–19] and two-pump [20] parametric amplification.

Introduction

The potential for fiber OPAs and OPOs is based on some characteristic features that are not present in other types of optical amplifiers and oscillators. Specifically, the features that can be exploited are: (i) the availability of gain at essentially arbitrary wavelengths, limited only by the availability of the necessary pumps and of fibers with suitable nonlinearity, loss, and dispersion; (ii) the availability of an idler; (iii) the nearly instantaneous response of the gain to pump power variations; (iv) the all-fiber structure, which is capable of withstanding high powers.

In this chapter we will discuss the main applications that can be envisioned and describe the experiments that have been performed in some areas. For OPAs, the main areas of applications that have been envisioned so far are in optical communication and high-power wavelength conversion. We now discuss each of these areas in some depth.

OPAs in optical communication

This is the most advanced area, in part because of the availability of convenient fibers and pumps, developed for conventional communication systems. These have been exploited in recent years to demonstrate several applications of OPAs, naturally at wavelengths of interest for optical communication.

Amplification

The realization that fiber OPAs could exhibit gain bandwidths as large as or larger than those of erbium-doped fiber amplifiers (EDFAs), by the use of commercially available fibers and the watt-level pump powers that are now considered reasonable, sparked interest in their possible use in communication systems.

Introduction

In previous chapters we studied wave propagation in fiber OPAs from a classical standpoint, i.e. starting from Maxwell's equations. That approach provides only a partial view of the rich nature of the electromagnetic field, namely its wave nature. However, a complete description of the electromagnetic field requires quantum mechanics. This quantum description of the electromagnetic field (called quantum electrodynamics, or QED) predicts fluctuations in measurable quantities due to the Heisenberg uncertainty principle and sets ultimate limits on the performance of devices such as optical amplifiers. A remarkable result of this theory is that the statistics and thus the noise performance of a system are affected by the quantum statistics of the source and by the physical measurement that is made. Thus a different analysis is needed depending on whether homodyne, heterodyne, or direct detection (where the field simply impinges on a photodiode) is used. Direct detection reveals the particle nature of the electromagnetic field. More specifically, energy arrives in discrete units, called photons, each of which may create an electron–hole pair in a semiconductor photodetector. In particular, the number of photons in an optical pulse can be thought of as a random variable having a mean and a variance. By deriving the mean and variance of the photocurrent that would be present if one performed direct detection of ideal laser light at the input of an optical amplifier and then a similar measurement at its exit, one can quantify the degradation of the signal-to-noise ratio (SNR) caused by the amplifier.

The Rowland grating

This is a grating ruled on a concave spherical mirror, in consequence of which it has a self-focusing property and needs no other optical component to produce a spectrum from a point or short line source. It is the invention of H. A. Rowland of Johns Hopkins University who gave an account of it in 1883. The rulings are the intersections of the sphere with a set of parallel, equi-spaced planes, so that the interval between rulings is not constant on the surface of the sphere, and the device, although it is a spherical mirror, has a definite optic axis.

The focusing property is as follows:

The grating is ruled on a spherical mirror of radius R. There is a circle, the Rowland circle, touching the sphere at its vertex perpendicular to the rulings and of radius R/2. The elementary theory of the grating states that monochromatic light from any point on this circle is diffracted according to the grating equation, and is subsequently focused at another point on the Rowland circle.

The theorem is not exact. There is no point focus but an approximation to the proof can be given by elementary geometry. In Fig. 9.1 the grating is displaced by an infinitesimal amount along the optic axis and intersects the Rowland circle at points x, x′. Suppose the grating constant at x is a.

The problem of photometry with silver halide emulsions is that of finding the relation between density and exposure. Density is defined as minus the logarithm of the transmission ratio, i.e. of the fraction of incident light transmitted through the emulsion to the detector (on the assumption that the response of the detector is linear). Exposure is defined as the product of incident intensity during the photographic exposure and the duration of the exposure, and it is assumed, justifiably, that the density depends only on the product.

The method of the common calibration curve is to take several photographs of the same spectrum under identical circumstances, but with different neutral-density filters, the filter densities ascending for example in factors of 2. The densities of a particular spectrum line, measured from the different exposures, will give a set of points on the calibration curve. A different spectrum line can then be interpolated on this initial line and the different exposures of this second line provide further points which extrapolate the curve at one end or the other. By continuing in this fashion with other spectrum lines, the curve can be continued, always by interpolating new initial material, gradually extending the curve in both directions as far as necessary and well beyond the linear portion.