Methods of modelocking fiber lasers

It has long been imagined that the unique characteristics of the fiber laser cavity might allow for the development of versatile, compact, efficient sources of coherent light. Particularly in the area of ultrashort pulse production, the fiber geometry provides access to the nonlinear index of the cavity providing additional degrees of freedom for pulse formation mechanisms. The first modelocked fiber laser, reported in 1983, actually used a material saturable absorber to provide the passive loss mechanism necessary for modelocking. The UV radiation from a flashlamp produced transient color centers in the glass matrix which in turn modelocked the laser, producing Q-switched trains of ultrashort pulses (Dzhibladze et al., 1983).

Since that time nearly every method of modelocking that has been used in a bulk laser has been translated into the fiber geometry. In this chapter we will attempt to provide an overview of the more successful attempts and provide the insight necessary to choose the best technique for a given application.

The chapter is organized according to modelocking technique, starting with active modelocking, both amplitude and phase modulation, and then proceeding with the newer techniques of passive modelocking. Of the methods that deal with artificial fast saturable absorbers, this chapter will concentrate on the use of the nonlinear loop mirror (Sagnac interferometer) in the figure eight laser (F8L) configuration (4.2), rather than polarization rotation which will be treated in Chapter 5. Included in this section will be an extensive discussion of the generation and consequences of the sidebands present in the spectra.

Introduction

The hybrid soliton pulse source (HSPS) described in this chapter is being developed at AT&T Bell Laboratories as a possible source for ultra-long distance soliton communication systems. The HSPS integrates a semiconductor laser gain section and a fiber Bragg reflector in a hybrid device, to capitalize on the inherent advantages each possesses. The semiconductor section allows simple and efficient pumping of the device, and the fiber Bragg reflector provides excellent wavelength and optical bandwidth control. Together these components provide a source which is both simple and inexpensive, whilst satisfying the exacting performance requirements for ultra-long distance soliton transmission systems. Practical soliton transmission systems take advantage of the gain from erbium doped fiber amplifiers to provide lossless transmission, coupled with the nonlinearity in optical fibers to balance dispersion and provide dispersionless transmission (see Mollenauer et al., 1986; 1992; 1993; Gordon and Haus, 1986; Gordon and Mollenauer, 1991; Kodama and Hasegawa, 1987; 1992; Haus, 1991; Mecozzi et al., 1991). Current records for soliton transmission, which offer the largest product of bit-rate multiplied by the error free transmission distance, are 20 GBit/s over 13000 km and 10 GBit/s over 20000 km, by Mollenauer et al. (1993). In order for soliton transmission systems to become a reality, a practical source must be produced which can meet the stringent performance characteristics these systems require. The HSPS described in this chapter is a simple and elegant device which meets these requirements.

Introduction

Modelocking was at first demonstrated in the mid-1960s using He-Ne lasers [1], ruby lasers [2], and Nd+ glass lasers [3]. The pulse width was initially quite long, but by the end of the 1970s subpicosecond pulses were generated using passive modelocked dye lasers [4–6]. The colliding pulse modelocking (CPM) of dye lasers in early 1980s [7] made sub-100 femtosecond pulses routinely available, and additive pulse modelocking (APM) of color center lasers pushed the wavelength of the sub-100 femtosecond pulses from the visible to the infrared [8, 9]. Kerr lens modelocking of Ti: sapphire lasers was discovered in 1990 [10–11] and produced the shortest laser pulses [12] directly from the laser cavity without any additional external cavity pulse compression. The advancement of short pulse generation technologies has provided very useful tools for researchers in physics, chemistry, biology, and optical communications. All of those ultrashort laser pulse systems are, however, large and expensive. A compact pulse source such as a modelocked semiconductor laser or fiber laser with comparable specifications to those big laser systems will be attractive because of its simplicity and cost effectiveness. Fiber lasers have limited cavity frequencies, typically below 100 MHz, and this limits their usefulness for many applications such as high bit-rate soliton transmission systems. Our goal with semiconductor modelocked lasers is to integrate the many fiber components into a compact, monolithic source.

Modelocked in-plane semiconductor lasers

Semiconductor lasers were demonstrated in 1962 by four groups almost simultaneously [13–16] only two years after the demonstration of the first laser [17].

Introduction

The generation of ultrafast optical pulses from semiconductor diode lasers is extremely attractive owing to the compact and efficient properties of these devices. Applications of these devices range from photonic switching (Smith, 1984), electro-optic sampling (Valdmanis et al., 1982; Valdmanis et al., 1983), optical computing (Miller, 1987; Miller, 1989), optical clocking (Delfyett et al., 1991), applied nonlinear optics (Miller et al., 1983), and other areas of ultrafast laser technology (Delfyett et al., 1991). There have been many recent advances in ultrafast pulse generation from diode lasers in the past few years, with many researchers concentrating on device fabrication, device physics, theoretical modeling and systems applications.

In the past, picosecond optical pulse generation from diode lasers has been accomplished by modelocking and gain switching techniques (Ho et al., 1978; Ito et al., 1979). Several researchers have used degraded semiconductor lasers, which rely on defects in the semiconductor to provide a mechanism for passive modelocking (Ippen et al., 1980; van der Ziel et al., 1981; Yokoyama et al., 1982). The pulses produced from these systems ranged from a few picoseconds to just under a picosecond. The drawback with utilizing degraded diodes is that the lifetime of these devices is limited, typically several hours. Proton implanted multiple quantum well structures (MQW) have been used to passively modelock semiconductor lasers, producing pulses of 1.6 ps in duration which were then compressed to 0.83 ps (Silberberg et al., 1984; Smith et al., 1985; Silberberg and Smith, 1986).

Since the development of the first diode lasers and the recent proliferation of fiber amplifiers, the dream of researchers for a compact, efficient, turn-key source of ultrashort pulses has come closer to reality. A number of candidates for this ultimate source have been proposed and researched and a large body of information has been produced. To date there has not been a compilation of this valuable information in one place. It is the intent of this work to present the state of the art in the development of these sources. It is the added intention to provide a basis for the future research of others attempting to enter this still very active field.

In 1983, when the technique of electro-optic sampling was developed, the dream was that the sampler could be combined with a compact ultrashort pulse source to produce a subpicosecond resolution oscilloscope. This technology has languished due to the missing source. In 1988 the development of high efficiency low temperature GaAs photoconductive switches has produced similar high promise, but there is still no suitable low cost compact ultrashort pulse source. It is hoped that this book will show that much progress has been made since the early 80s and the groundwork has been laid for a new class of instrumentation, where a laser is included for optical processing and may not ever leave the instrument.

Introduction

Compact and lightweight picosecond semiconductor laser sources are needed for high bit-rate time-division multiplexed communication systems (Andrekson et al., 1992), 100 Gbit/s transmission systems (Kawanishi et al., 1993), ultra-long distance soliton fiber transmission (Mollenauer et al., 1991; 1992; Nakazawa et al., 1991), picosecond optical logic gates (Nelson et al., 1991), electro-optic sampling systems (Valdmanis and Mourou, 1986), and opto-electronic generation of millimeter and sub-millimeter waves (Scott et al., 1992). Though there has been substantial progress in the area of ultrashort optical pulse generation using dye or solid state gain media (Ippen et al., 1989; Krausz et al., 1992), semiconductor optical sources are preferred for the above applications because of the following advantages. First, the repetition frequency of interest is usually above 1 GHz, thus substantially shorter cavity length is needed. Second, semiconductor lasers can be electrically pumped, eliminating the need of another pumping laser. Third, the power consumption is very low, typically of the order of 100 mW. No air or water cooling is required. They are also very energy efficient. Typical external quantum efficiencies of semiconductor lasers are between 30% and 90%.

More importantly, the semiconductor gain medium can be integrated with many other optical components using integrated optics techniques. In fact, the whole modelocked laser can be integrated monolithically on a single piece of semiconductor, completely eliminating optical alignment process. This is the main topic of this chapter.

There are two commonly used methods to generate short optical pulses using semiconductor lasers: gain switching (Downey et al., 1987; Lau, 1988a) and modelocking (van der Ziel, 1985).

Introduction

The development of commercially available laser diodes (LDs) has revolutionised solid state lasers so much so that today the term solid state lasers normally implies laser diode pumping. The change started in the mid 1980s with the commercial release of GaAs LD arrays capable of generating between 50 mW and 250 mW around 800 nm and capable of optically pumping Nd doped laser hosts. Subsequently, the range of available wavelengths and the power levels from LDs has increased dramatically, particularly around 980 nm, 800 nm and 670 nm, so that almost every possible dopant and host combination is capable of being LD pumped. In parallel with the improving technology for the pump sources, a new understanding of techniques for modelocking solid state lasers, that allowed the pulse durations directly from the laser to approach the limit set by the gain bandwidth of the laser, has dramatically changed the pulse duration expectations from solid state lasers. Consequently the design of a modern modelocked solid state laser is quite different from previous designs. It is the purpose of this chapter to summarise the developments that have been made over the past five to ten years in developing compact modelocked sources based on LD pumped solid state lasers.

Laser diode pumping

Pumping using LDs has been a major factor in allowing the phrases compact or miniature to be applied to LD pumped solid state lasers (LDPSSLs). This claim will be justified by quoting typical values for various parameters that should be achievable.

Introduction

Single-mode fibers typically contain two eigenmodes with the same light intensity distribution, but with orthogonal polarization states. In perfectly isotropic fibers these modes are degenerate and have the same propagation constants. Hence isotropic fibers are polarization maintaining, i.e. the output polarization state is the same as the input polarization state. However, this statement is not generally valid in the presence of nonlinearities. Though an isotropic fiber is still polarization maintaining for linearly and circularly polarized light independent of the light intensity, an elliptical polarization state will rotate as a function of power.

The phenomenon of ellipse rotation was already well known in the 1960s and was commonly used to measure the refractive index of isotropic materials with Kerr-type nonlinearities (Maker and Terhune, 1965). By incorporating suitable polarization optics, ellipse rotation can also be used as an ultrafast saturable absorber for passive modelocking, as first realized by Dahlström (1972). However in this work stable CW modelocking was not obtained due to the low available power levels. The first application of nonlinear polarization evolution in optical fibers dates back to Stolen et al. (1982), who used a highly-birefringent fiber for shortening and cleaning the pulses from a separate external ultra-short pulse source. Nonlinear polarization evolution for the general case of low birefringence fibers was first analyzed by Winful (1985), who also predicted the phenomenon of polarization instability when high intensity light is launched close to the fast axis of the fiber.

Introduction

We will now study the properties of fluctuating electromagnetic fields, paying attention mainly to the optical region of the electromagnetic spectrum. It seems hardly necessary to stress that every electromagnetic field found in nature has some fluctuations associated with it. Even though these fluctuations are, as a rule, much too rapid to be observed directly, one can deduce their existence from suitable experiments that provide information about correlations between the fluctuations at two or more space-time points.

The simplest manifestations of correlations in optical fields are the well-known interference effects that arise when two light beams that originate from the same source are superposed. With the availability of modern light detectors and electronic circuitry of very short resolving time, other types of correlations in optical fields began to be studied in more recent times. These investigations, as well as the development of lasers and other novel types of light sources, led to a systematic classification of optical correlation phenomena and the complete statistical description of optical fields. The area of optics concerned with such questions is now generally known as optical coherence theory.

The first investigations of coherence phenomena are due to Verdet (1865, 1869) and von Laue (1907a, b). Some early investigations of Stokes (1852) and Michelson (1890, 1891a, b, c, 1892, 1920) although not explicitly mentioning coherence – because this concept is of a much later origin – have also contributed to the clarification and development of this subject.

Introduction

We have now prepared the way for a quantum treatment of problems that are of interest in optics. We have examined some basic properties of the quantized field and have explored the coherent-state representation and some of its virtues. Until now our discussions have been essentially formal; we have not concerned ourselves with what is actually measured in the laboratory, nor with questions concerning the interactions of the quantized field with other systems.

In the following sections we shall turn our attention to some of the quantum field theoretic quantities that are of particular interest in quantum optics and are of significance in the measurement of the field. Our discussions in this chapter will still be somewhat formal, in that we shall not yet come to grips with the problem of the interaction of the field with the apparatus. That problem will be tackled in Chapter 14. For the moment we shall continue to oversimplify and treat the field as a free field. However, within the idealized context of the free field we shall examine some of the questions encountered in measurements in quantum optics. We shall see that normally ordered correlations play a dominant role and examine some of their properties. Anti-normally ordered correlations will be seen to arise in much less common and less useful measurements of the field. We shall also examine the sense in which a photon may be said to be localized in a measurement in which a photoelectric emission is registered.

Introduction to statistical ensembles

The concept of a random or stochastic process or function represents a generalization of the idea of a set of random variables x1, x2, …, when the set is no longer countable and the variables form a continuum. We therefore introduce a continuous parameter t, such as time, that labels the variates. We call x(t) a random process or a random function of t if x does not depend on t in a deterministic way. Random processes are encountered in many fields of science, whenever fluctuations are present. Examples of a real random process x(t) are the fluctuating voltage across an electrical resistor, and the coordinates of a particle under-going Brownian motion. We shall see shortly that the optical field generated by any realistic light source must also be treated as a random function of position and time. Of course the parameter t may also stand for some quantity other than time, but for simplicity we shall take it to represent time. In our applications x(t) will frequently represent a Cartesian component of the electric or magnetic field vector in a light beam. To begin with we shall take x(t) to be real, but complex random processes will also be encountered.

The ensemble average

As x does not depend on t deterministically, we can only describe its values statistically, by some probability distribution or probability density.

Introduction

We have already encountered situations in which light of one frequency falling on an atomic system gives rise to light of different frequencies (cf. Section 15.6). The atom may here be considered to play the role of a (noisy) nonlinear transducer for the incident field. Even stronger nonlinear effects arise when one is dealing with a large number of atoms, or a nonlinear medium. Under these circumstances it is sometimes permissible to ignore the atomic structure and to treat the medium as a continuum, as in Maxwell's electromagnetic theory. The subject of the interaction of the incident field with the nonlinear medium is usually known as nonlinear optics.

The subject had its beginnings in an experiment in which a strong beam of red light (wavelength 6943 Å) from a ruby laser was allowed to fall on a quartz crystal, and a faint beam of blue light at a wavelength of 3472 Å, the first harmonic of the red, was produced (Franken, Hill, Peters and Weinreich, 1961). The development of the subject of nonlinear optics into a mature field is due largely to the work of Bloembergen and his collaborators. In the following we shall consider only a few simple illustrative examples of phenomena in nonlinear optics. More topics and more detail can be found in the books by Bloembergen and others (Bloembergen, 1965; Yariv, 1967, Chap. 21; Shen, 1984; Schubert and Wilhelmi, 1986; Butcher and Cotter, 1990; Boyd, 1992).