QDT enables us to characterize series of autoionizing states in a consistent way and to describe how they are manifested in optical spectra. We shall first consider the simple case of a single channel of autoionizing states degenerate with a continuum. Of particular interest is the relation of the spectral density of the autoionizing states to how they are manifested in optical spectra from the ground state and from bound Rydberg states using isolated core excitation. We then consider the case in which there are two interacting series of autoionizing states, converging to two different limits, coupled to the same continuum.

First we consider the two channel problem shown in Fig. 21.1. Our present interest is in the region above limit 1, i.e. the autoionizing states of channel 2. Later we shall consider the similarity of the interactions above and below the limit. A typical quantum defect surface obtained from Eq. (20.12) or (20.40) for all energies below the second limit is shown in Fig. 21.2. The surface of Fig. 21.2 may be obtained with either of two sets of parameters, δ1 = 0.56, δ2 = 0.53, and R′l2 = 0.305, R′11 = R′22 = 0 or μ1 = 0.4, μ2 = 0.6, and U11 = U22 = cosθ and U12 = – U21 = sinθ, with θ = 0.6 rad. To conform to the usual convention, in Fig. 21.2 the vi axis is inverted.

In the first two chapters we have seen that the Na atom, for example, differs from the H atom because the valence electron orbits about a finite sized Na+ core, not the point charge of the proton. As a result of the finite size of the Na+ core the Rydberg electron can both penetrate and polarize it. The most obvious manifestation of these two phenomena occurs in the lowest ℓ states, which are substantially depressed in energy below the hydrogenic levels by core penetration. Core penetration is a short range phenomenon which is well described by quantum defect theory, as outlined in Chapter 2.

In the higher ℓ states the Rydberg electron is classically excluded from the core by the centrifugal potential ℓ(ℓ + 1)/2r2, and, as a result, core penetration does not occur in high ℓ states, but core polarization does. Since it is not a short range effect, it cannot be described in terms of a phase shift in the wave function due to a small r deviation from the coulomb potential. However, the polarization energies of each series of nℓ states exhibit an n–3 dependence, so the series can be assigned a quantum defect. Unlike the low ℓ states, in which the valence electron penetrates the core, measurements of the Δℓ intervals of a few high ℓ states enable us to describe all the quantum defects of the high ℓ states in terms of the polarizability of the ion core.

Perturbed Rydberg series

One of the most intensively studied manifestations of channel interaction in the bound states is the perturbation of the regularity of the Rydberg series, which is evident if one simply measures the energies of the atomic states. Although measurements of Rydberg energy levels by classical absorption spectroscopy show the perturbations in the series which are optically accessible from the ground state, the tunable laser has made it possible to study series which are not connected to the ground state by electric dipole transitions as well. One of the approaches which has been used widely is that used by Armstrong et al. As shown in Fig. 22.1, a heat pipe oven contains Ba vapor at a pressure of ∼1 Torr. Three pulsed tunable dye laser beams pass through the oven. Two are fixed in frequency, to excite the Ba atoms from the ground 6s21So state to the 3P1 state and then to the 6s7s 3S1 state. The third laser is scanned in frequency over the 6s7s 3S1 → 6snp transitions. The Ba atoms excited to the 6snp states are ionized either by collisional ionization or by the absorption of another photon. The ions produced migrate towards a negatively biased electrode inside the heat pipe. The electrode has a space charge cloud of electrons near it which limits the emission current.

The autoionizing two electron states we have considered so far are those which can be represented sensibly by an independent electron picture. For example, an autoionizing Ba 6pnd state is predominantly 6pnd with only small admixtures of other states, and the departures from the independent electron picture can usually be described using perturbation theory or with a small number of interacting channels. In all these cases one of the electrons spends most of its time far from the core, in a coulomb potential, and the deviation of the potential from a coulomb potential occurs only within a small zone around the origin.

In contrast, in highly correlated states the noncoulomb potential seen by the outer electron is not confined to a small region. In most of its orbit the electron does not experience a coulomb potential, and an independent electron description based on nℓn′ℓ′ states becomes nearly useless. There are two ways in which this situation can arise. The first, and most obvious, is that the inner electron's wavefunction becomes nearly as large as that of the outer electron. If we assign the two electrons the quantum numbers niℓi and noℓo, this requirement is met when ni approaches no, which leads to what might be called radial correlation. The sizes of the two electron's orbits are related. The second way the potential seen by the outer electron can have a long range noncoulomb part is if the presence of the outer electron polarizes the inner electron states.

Introduction

One method by which the rate of information transmission can be increased is by the use of multiple, independently addressable sources to form parallel data channels. In the optical domain, this may be implemented by semiconductor diode lasers, which can be fabricated into monolithic arrays of emitters. The purpose of this chapter is to describe the development of linear arrays of index-guided diode lasers, and indicate directions in which the technology may proceed. Note that all the discussions in this chapter will be confined to semiconductor diode lasers in which the light propagates parallel to the epitaxial planes.

A few words are in order to explain the motivations that have driven the development of individually addressed diode laser arrays. Early work included the fabrication of both AlGaAs and InGaAsP devices for parallel data transmission through bundles of optical fibers, and arrays of lasers have often been considered in optical printing or optical data processing applications. The application that has been most responsible for the development of these devices, however, is optical data storage. This discussion will focus on the use of multielement arrays in optical recording systems, as a very useful example that has driven diode laser array technology towards certain performance capabilities.

Diode laser arrays have been studied for the last 15 years. Initially the interest was in creating phase-locked arrays of high coherent powers delivered in narrow, diffraction-limited beams for applications such as free-space optical communications. Around 1983 interest arose in spatially incoherent arrays as efficient pumps for solid-state lasers. This remains nowadays the most widespread use of diode laser arrays. In recent years there has been a demand for individually addressable one-dimensional and two-dimensional arrays to be used in parallel optical-signal processing, optical interconnects, and multichannel optical recording. We have attempted in this book to cover the development and features of all types of arrays demonstrated to date. The first five chapters treat various aspects of coherent arrays: lasers, amplifiers, external-cavity control, modeling and operational dynamics. Chapters 6–8 are dedicated primarily to spatially incoherent arrays. High-power capability, reliability, packaging and pumping schemes are discussed as they relate to the major application: solid-state-laser pumping. Individually addressable arrays of both the surface-emitting type (i.e. vertical-cavity surface emitters) and edgeemitting type are treated in Chapters 9 and 10, respectively.

Coherent arrays have proved a particularly challenging task. For the first ten years of research (1978–1988) the best that could be achieved was 50–100 mW in a diffraction-limited beam; that is, pretty much the same power as from a single-element device.

Introduction

Semiconductor optical sources exhibit several distinct advantages relative to other solid-state and gas laser systems including compact size, high efficiency, high reliability, robustness and manufacturability. As a result, many of the rapidly growing commercial and consumer markets, including telecommunications, printing and optical data storage, have only been realized through the introduction of semiconductor lasers. The next generation of high-performance electronics will require higher-power semiconductor lasers; but as recently as 1992, commercially available high-power (greater than 200 mW cw) semiconductor lasers did not operate in a single spatial mode and therefore did not radiate in a single diffraction-limited lobe. However, the latest advances in the design and fabrication of semiconductor lasers have resulted in the development of high-power diffraction-limited laser sources.

The architectures that have been studied for high-power diffraction-limited semiconductor lasers can be divided into three categories: oscillators, injection-locked oscillators, and master oscillator power amplifiers (MOPAs). The highest-power diffraction-limited operation from oscillators has been demonstrated from antiguided laser arrays. These devices have demonstrated up to 0.5 W cw and 1.5 to 2.0 W pulsed in a diffraction-limited radiation pattern. Disadvantages of antiguide oscillators are their multi-longitudinal-mode spectra and multi-lobed far-field patterns. Another promising oscillator configuration is the broad-area ring oscillator, which has demonstrated single-frequency operation to greater than 1 W pulsed, and diffraction-limited single-lobed operation to approximately 0.5 W pulsed.