A gain medium that is pumped to reach an electronic population inversion is able to amplify optical energy. Figure 20.2a illustrates this principle with regard to a semiconductor [4]. The valence and conduction bands serve as the ground and excited state. A positive bias is applied to the semiconductor so that injected electrons flow into the conduction band and populate it, whereas holes are created in the valence band. An incoming photon, if its energy is equal to the energy difference between the two bands, can trigger the transition of an excited electron to the valence band, where it is recombined with a matching hole. In this stimulated transition process, the energy difference is radiated optically, resulting in the emission of a new photon that has identical energy, phase, and propagation direction compared with the original photon. This process, called stimulated emission, is the fundamental mechanism for coherent optical amplification. Other types of gain media, such as gas, dyes, crystals, and glass, are based on the same mechanism, although specifics of the transition levels of electrons and pumping methods are different. Gain saturation, or a decrease of gain due to the depletion of population inversion by strong optical intensity, is an intrinsic characteristic of gain media. In typical laser oscillation at the steady state, gain is saturated substantially to a level where the saturated gain is just enough to compensate for the loss in a laser cavity.

A laser cavity is a resonator that gives phase-coherent optical feedback for regenerative amplification in the gain medium [5]. A variety of optical materials and components can be incorporated into a cavity to control and condition the characteristics of a laser. By its geometrical shape, a laser cavity can be categorized into a linear, ring, or hybrid (such as sigma) type. In a linear cavity, exemplified in Fig. 20.3a, intracavity light passes through a gain medium and a transmissive filter twice in each round trip. A ring cavity is often made unidirectional, ensured by a magneto-optic isolator with a direction-dependent insertion loss. The unidirectional ring cavity offers a distinct advantage that the backward reflected light from intracavity components is de-coupled from the main beam path and as a result, often produces more stable laser oscillation than a linear cavity. This advantage may not be evident, however, in most rapidly swept lasers that are less sensitive to the spurious feedback due to oscillation of multiple longitudinal modes.

Longitudinal cavity modes are a set of frequency components capable of oscillating resonantly in the cavity. Each mode satisfies the resonance condition that the total optical phase accumulated in one roundtrip propagation is equal to an integer multiple of 2π. The frequency difference between two adjacent modes, or the mode spacing f _m , is given by
where τ is the total propagation time of cavity roundtrip and L is the total optical length that includes group refractive indices of the cavity.

The laser output is obtained through an output coupler of the cavity. Large output coupling can extract larger optical energy from the cavity, thus resulting in a higher output power, but may decrease the tuning range due to resulting increased cavity loss. An optimum output coupling ratio can be chosen with some trade-off in performance, ranging from a few percent in low-gain lasers, such as a titanium-sapphire laser, to several tens of percents in high-gain lasers, such as a semiconductor or rare-earth-doped fiber laser.

Wavelength-tunable lasers have developed considerably since the mid-1960s and are now invaluable light sources for numerous scientific and industrial applications. Figure 20.3a represents a schematic of a tunable laser configuration consisting of a broadband gain media, an optical cavity, and a narrowband tunable filter. To illustrate the basic principle of a tunable laser, let us consider an extended-cavity semiconductor lasers, one of the most versatile and commercially successful tunable sources. Figure 20.3b depicts a representative schematic of the laser. One facet of a semiconductor gain chip serves as a partial reflector and output coupler of a laser cavity. Partial reflectance is normally achieved just by cleaving the facet perpendicular to the optic axis, yielding Fresnel reflection by 26–30 % for typical semiconductor materials. Optical reflection at the other facet of the chip is minimized to <0.001 % by anti-reflection dielectric coating (R = 0.1 %) and the curved active waveguide design. At the other end of the cavity, a diffraction grating and a mirror serve as a tunable wavelength selective filter. The angular position of the mirror determines the specific wavelength component that returns to the gain medium via [6]
where p denotes the grating pitch, α is the angle between the grating normal and beam incidence axis, and β is the angle between the grating normal to the diffracted beam as determined by the angular position of the end mirror. The reflected spectrum of the grating filter has a narrowband Gaussian-like profile with a width approximately given by λ/N where N denotes the number of grooves illuminated by the optical beam on the grating.

Figure 20.4a depicts the resulting net-gain profile together with the spectrum of oscillating laser modes. The gain profile has a peak at the wavelength determined by Eq. 20.5. The net roundtrip gain becomes close to one in steady-state laser oscillation. Because of the strong gain discrimination by the filter, only the frequency mode closest to the gain peak is able to oscillate. Single-frequency oscillation offers a very narrow linewidth of <100 kHz and a long coherence length exceeding 10 km, typical of an extended-cavity semiconductor laser.

By rotating the end reflector, the gain peak wavelength can be shifted continuously, and the output spectrum can be swept accordingly [7]. Figure 20.4b illustrates this situation in the case of slow adiabatic tuning where steady-state oscillation is reached at any given time. Here, the cavity length is assumed invariant so that the positions of cavity modes are stationary in the frequency domain. Under this condition, as the gain profile is continuously shifted by tuning, the laser spectrum steps from one mode to another – a process called mode hopping.

In some applications such as high-resolution atomic spectroscopy, truly continuous tuning without mode hopping is desirable. The extended-cavity tunable laser shown in Fig. 20.3b offers a simple way to achieve this feature. The underlying idea is to vary the cavity length in conjunction with tuning, such that the frequency of a cavity mode always coincides with the gain peak frequency. This can be achieved by placing the pivot point of the end mirror exactly at the output facet of the gain chip. Using this geometrical arrangement [8], commercial extended-cavity tunable lasers can produce a mode-hop-free sweep over several tens of nanometers. However, their tuning speeds currently are limited to <1 nm/ms, although the technique can work in principle at an arbitrary sweep speed.