Introduction

In chapter 3 we derived a Hamiltonian to describe the electronic motion in a diatomic molecule, starting from first principles. In our case, the first principles were the Dirac equation for a single particle, and the Breit equation for two interacting particles. We pointed out that even at this level our treatment was a compromise because it did not include quantum electrodynamics explicitly. Nevertheless we concluded the chapter with a rather complete and complicated Hamiltonian, and added yet more complications in chapter 4 with the inclusion of nuclear spin effects. In the next chapter, chapter 7, we will show how terms in the ‘true’ Hamiltonian may be reduced to ‘effective’ Hamiltonians designed to handle the particular cases which arise in spectroscopy. We will make extensive use of angular momentum theory, described in chapter 5, to describe the electronic and nuclear dynamics in diatomic molecules, and the interactions with applied magnetic and electric fields. The experimental study of these dynamical effects is dealt with at length in chapters 8 to 11. We will be classifying these studies according to molecular electronic states, and demonstrating how the high-resolution spectroscopic methods described probe the structural details of these electronic states. That, indeed, is one of the main purposes of spectroscopy.

Before we proceed to these details we must describe some aspects of the theory of the electronic and vibrational states of diatomic molecules.

The Dirac equation

The analysis of molecular spectra requires the choice of an effective Hamiltonian, an appropriate basis set, and calculation of the eigenvalues and eigenvectors. The effective Hamiltonian will contain molecular parameters whose values are to be determined from the spectral analysis. The theory underlying these parameters requires detailed consideration of the fundamental electronic Hamiltonian, and the effects of applied magnetic or electrostatic fields. The additional complications arising from the presence of nuclear spins are often extremely important in high-resolution spectra, and we shall describe the theory underlying nuclear spin hyperfine interactions in chapter 4. The construction of effective Hamiltonians will then be described in chapter 7.

In this section we outline the steps which lead to a wave equation for the electron satisfying the requirements of the special theory of relativity. This equation was first proposed by Dirac, and investigation of its eigenvalues and eigenfunctions, particularly in the presence of an electromagnetic field, leads naturally to the property of electron spin and its associated magnetic moment. Our procedure is to start from classical mechanics, and then to convert the equations to quantum mechanical form; we obtain a relativistically-correct second-order wave equation known as the Klein–Gordon equation. Dirac's wave equation is linear in the momentum operator and is so constructed that its eigenvalues and eigenfunctions are also solutions of the Klein–Gordon equation.

INTRODUCTION

In the last chapter, we examined resonator-enhanced blue-green light generation, in which a nonlinear crystal is placed inside an optical resonator so that the high circulating intensity increases the efficiency of SHG or SFG. We considered some implementations of this approach in which light from a diode-pumped solid-state laser is coupled into such a resonator, and we saw that it becomes necessary to lock the laser frequency to a resonant frequency of the enhancement cavity. Looking at such a system, we might well ask, “Since the solid-state laser itself consists of a cavity which is resonant at the infrared wavelength, why not place the nonlinear crystal inside that cavity instead of inside a separate one?” Inclusion of the nonlinear crystal within the resonator of an infrared laser is the basic idea behind intracavity SHG and SFG, which is the subject of this chapter.

Although generation of green light by intracavity frequency doubling of neodymium lasers has been pursued since the mid-1960s (Smith et al., 1965, Geusic et al., 1968), the current wave of interest in this field was ignited in the mid-1980s by the development of high-power, high-brightness diode lasers capable of efficiently pumping solid-state lasers and the demonstration that milliwatt levels of green light could be generated by placing a nonlinear crystal within the cavity of a diode-pumped Nd3+ laser (Baer and Keirstead, 1985, Fan et al., 1986).

A SHORT HISTORICAL OVERVIEW

For years after its invention in 1961, the laser was described as a remarkable tool in search of an application. However, by the late 1970s and early 1980s, a variety of applications had emerged that were limited in their implementation by lack of a suitable laser. The common thread running through these applications was the need for a powerful, compact, rugged, inexpensive source of light in the blue-green portion of the spectrum. The details varied greatly, depending on the application: some required tunability, some a fixed wavelength; some required a miniscule amount of optical power, others a great deal; some required continuous-wave (cw) oscillation, others rapid modulation.

In many of these applications, gas lasers – such as argon-ion or helium-cadmium lasers – were initially used to provide blue-green light, and in some cases were incorporated into commercial products; however, they could not satisfy the requirements of every application. The lasing wavelengths available from these lasers are fixed by the atomic transitions of the gas species, and some applications required a laser wavelength that is simply not available from an argon-ion or helium–cadmium laser. Other applications required a degree of tunability that is unavailable from a gas laser. In many of them, the limited lifetime, mechanical fragility, and relatively large size of gas lasers was a problem.

At about the same time, new options for generation of blue-green radiation began to appear, due to developments in other areas of laser science and technology.

Since the mid-1980s, the development of practical, powerful sources of coherent visible light has received intense interest and concentrated activity. This interest and activity was fueled by twin circumstances: the realization of powerful, efficient infrared laser diodes and the emergence of numerous applications that required compact visible sources. The availability of these infrared lasers affected the development of visible sources in two ways: It stimulated the investigation of techniques for efficiently converting the infrared output of these lasers to the visible portion of the spectrum and it encouraged the hope that the fabrication techniques themselves might be adapted to make similar devices working at shorter wavelengths.

Within the visible spectrum the blue-green wavelength region has demanded – and received – special attention. The demonstration of powerful red diode lasers followed relatively soon after the development of their infrared counterparts – in contrast, the extension to shorter blue-green wavelengths has required decades of wrestling with the idiosyncrasies of wide-bandgap materials systems. The first blue-green diode lasers were not successfully demonstrated until 1991, and it has only been within the past year or two that long-lived devices with output powers of tens of milliwatts have been achieved.

As this field emerged and began to grow, it quickly became evident that it would necessarily be a very multi-disciplinary one. On one hand, a variety of approaches were being pursued in order to generate blue-green light. The three main ones – nonlinear frequency conversion, upconversion lasers, blue-green semiconductor lasers – are the focus of this book.

INTRODUCTION

In the preceding chapter, we considered single-pass SHG and SFG. There, we saw that efficient frequency upconversion from infrared to blue-green wavelengths is generally possible only when the power at the fundamental wavelength is several watts. The approach to achieving such powers that we considered in Chapter 3 was a very direct and “brute force” one: build a more powerful laser. We examined several approaches that have been used for increasing the infrared power available for the nonlinear interaction, including:

• using a power amplifier to boost the output of a master oscillator;

• using high-power diode lasers that have poor spectral and spatial characteristics for pumping solid-state lasers which then act as sources for frequency-doubling;

• using pulsed, rather than cw, operation in order to achieve higher peak powers.

While these brute force approaches have the advantage of being conceptually straightforward, it has only been since about 1995 that they have succeeded in producing blue-green powers sufficient for some of the applications described in Chapter 1. In addition, these approaches suffer from a number of practical disadvantages. The powerful lasers required for efficient single-pass conversion tend to be complicated and expensive, and since they generate high powers they require substantial electrical power and thermal management. Furthermore, although pulsed configurations have succeeded in producing large average blue-green powers, the power generated by cw operation has been too low for many applications.

BACKGROUND

VCSELs have gained importance in recent years for applications where beam quality, prospects for high-density arrays, and inherent compatibility with planar processing are particularly important. In the case of resonant-cavity LEDs (RCLEDs), the quasi-beam-like directionality in the spontaneous emission and possible enhancements to the radiative recombination rates likewise have spurred active research. VCSEL technologies that rely on III–V semiconductor heterostructures have now risen to a dominant position within the semiconductor laser industry, supplying high-performance components that play an increasingly vital role in optical communications technology. Both GaAs- and phosphide-based QW VCSELs are making significant headway in penetrating into the 1.3–1.5µm wavelength region, following spectacular device successes in the roughly 650–900 nm range in the 1990s.

To date, the shortest wavelength VCSELs that have been implemented have reached the short end of the red (∼630 nm). There are a number of reasons, both fundamental and practical, that make the development of blue and green VCSELs and RCLEDs in the wide-gap semiconductors challenging. In terms of the technological approaches and prospects for short-wavelength VCSELs and RCLEDs, this chapter is speculative in tone, given the early stages of research. At this writing, it is unclear what combination of epitaxial growth and device design/processing schemes might result in a technologically viable VCSEL, for instance. On the other hand, there are ample fundamental physical reasons that suggest that microcavity emitters based on wide-gap semiconductors, and the nitrides in particular, have special properties that offer unique opportunities both in terms of the basic physics and device performance.

We began in Chapter 1 by discussing applications that required compact blue-green lasers; hence, it seems only fitting to end by examining the extent to which these requirements have been fulfilled. In this final chapter, then, we attempt to gather up some of the diverse topics that this book has treated and establish the current state of the art in the application of compact blue-green lasers.

The preceding chapters have covered three principal approaches to creating compact blue-green lasers. In the first approach, blue-green light is generated through nonlinear frequency conversion of infrared semiconductor diode lasers or diode-pumped solid-state lasers. We saw that since these nonlinear processes tend to be rather weak, the desire for efficient generation of blue-green light has stimulated the development of high-power infrared lasers as well as the invention of a host of device configurations intended to boost the nonlinear conversion efficiency. These configurations include resonator-enhancement schemes, intracavity SHG, and waveguide implementations.

An alternative approach – the “upconversion laser” – directly excites a blue-green laser transition by combining the energy of two or more lower-energy pump photons through excited state absorption or cooperative energy transfer processes. Upconversion lasers using both bulk and fiber-optic media have been demonstrated.

Finally, we examined semiconductor diode lasers that are pumped by electrical injection and directly produce blue-green photons. Two main materials systems have been used to fabricate these devices: GaN and ZnSe.

The organizing idea of the previous chapters is that nonlinear, nonresonant, properties of insulating materials can be exploited to convert long-wavelength coherent radiation into short-wavelength radiation. As was discussed at length, this compels the device designer to simultaneously satisfy two demanding operational constraints: (1) Optical intensities at a first-harmonic frequency must be sufficiently high that the electromagnetic response of dielectric media is pushed into the nonlinear regime. (2) A travelling wave thus generated at the second-harmonic frequency must propagate at the same phase velocity as the fundamental wave lest the second harmonic switch roles from receiver to donor of optical power in the device. However, nonlinear frequency generation hardly requires that the operative interactions take place off resonance. Photon adding functions can be accomplished equally well with the aid of resonant optical processes in insulating materials, in turn wholly eliminating the two challenging constraints just named. We are, of course, referring to upconversion lasers. In this chapter and the next, we present this second approach to the nonlinear generation of short visible wavelengths and discuss what different operational challenges arise in creating a practical upconversion device.

INTRODUCTION TO UPCONVERSION LASERS AND RARE-EARTH OPTICAL PHYSICS

Upconversion lasers function just as ordinary lasers do, at least insofar as the mechanism by which their output beams are generated: A population inversion is created between two widely separated states thus making possible optical gain and laser oscillation in whatever media play host to the atoms, ions, or molecules possessing those states. The difference comes in the pumping mechanism.

The science of upconversion laser development can lay claim to many critical achievements on the path to a practical device. Among these are broad spectral coverage, room-temperature operation, single-wavelength pumping, and all-solid-state design. Arguable remaining milestones to overtake are high power, low cost, and easy manufacture. In this chapter we present a discussion of the origins and development of this subject with an eye toward conferring on researchers, who are new to the field, a comprehensive grasp of the published literature on upconversion laser experiments. After an account of the early history of upconversion laser research, we divide the topic into parts: the first comprises work involving bulk laser gain media – exclusively rare-earth-doped crystals – whereas the second comprises work on optical fiber gain media – primarily doped fluorozirconate glasses. Following a similar organization, nearly all the publications discussed in this chapter are reprinted under one cover in the anthology by Gosnell (2000). The chapter concludes with a brief discussion of potential directions for future research.

HISTORICAL INTRODUCTION

The notion of multi-photon upconversion in the solid state was first discussed by Bloembergen (1959) in the context of microwave and infrared quantum counters. The idea, depicted in Figure 8.1, is to exploit the photon counting capabilities of photomultiplier tubes sensitive only in the visible and near-infrared spectral range to detect upconversion emission. As seen in the figure, a single low-energy “signal” photon is converted to a single high-energy output photon when an upconverting pump photon supplied by an external source is simultaneously absorbed by the system. Transparent host materials doped with rare-earth and transition-metal ions were specifically named as potential detectors.

OVERVIEW OF BLUE AND GREEN DIODE LASER DEVICE ISSUES

In this chapter we focus chiefly on the device science and engineering features of the violet edge-emitting InGaN MQW diode lasers. The extraordinary progress made with these devices since 1999, spearheaded by Nakamura and coworkers, seems to assure them an important place in future optoelectronics technology (Nakamura, 1999). By 2001, approximately half a dozen research groups reported achieving lifetimes of hundreds to a thousand hours for cw room-temperature operation, although the extrapolated lifetime of 15 000 hours at Nichia remained unequalled. Among the other groups we mention those at the laboratories of Sony, Toyoda Gosei, NEC, and Sharp in Japan, Samsung in Korea, and Xerox PARC, Cree Lighting, and Agilent Technologies in the USA.

A number of the core issues that intertwine the design, performance, and the physics of operation of the nitride lasers will be discussed in this chapter. We will focus on representative heterostructures that encompass the requirements of joint electronic and optical confinement, comment on some fabrication techniques, and highlight continuing challenges. The last include questions concerning the high threshold current density and the continued efforts to create artificial substrate templates for reducing the misfit (threading) dislocation density for improved device performance and lifetime. At a more fundamental level, there is evidence that the InGaN alloy which forms the optically-active QW medium has characteristic compositional disorder that impacts the gain spectrum of the laser. This feature, which increases in seriousness with the indium concentration, may restrict the operation of the devices at practical threshold current densities to the violet, leaving the longer blue and green regions to await future developments, perhaps involving complementary material approaches.

INTRODUCTION

Blue-green light can be generated by using nonlinear crystals to “upconvert” the infrared wavelengths produced by high-power semiconductor diode lasers. In secondharmonic generation (SHG), a single infrared laser with frequency ω1 is passed through a nonlinear crystal and blue-green light emerges with frequency 2ω1. In sum-frequency generation (SFG), two infrared lasers with frequencies ω1 and ω2 are combined in the crystal; the generated blue-green beam then has frequency ω1 + ω2. These “second-order” nonlinear effects are relatively weak, yet it is still possible to use them to generate blue-green radiation at power levels suitable for the applications described in Chapter 1. In fact, of the three basic approaches to blue-green light generation discussed in this book, nonlinear frequency upconversion has so far been the most extensively developed and the most prolific in spawning commercial blue-green laser products.

The inherent weakness of these nonlinear effects has forced researchers and laser engineers to explore a variety of techniques for enhancing the efficiency of these interactions. In Chapters 3–6, we will discuss these different approaches, which include such things as intracavity frequency-doubling, resonant enhancement, and guided-wave interactions. However, all of these different embodiments exploit the same basic nonlinear interactions, and this chapter is devoted to explaining the essential nature of those processes. In it, we will give a qualitative explanation of the physical process underlying SHG and SFG, we will present some of the basic equations necessary for understanding and designing blue-green lasers based on these effects, we will discuss techniques for providing “phasematching”, which we will see is a crucial requirement for efficient generation of blue-green light, and we will examine some of the nonlinear materials that can be used for frequency conversion of near-infrared light.