To achieve lasing in any system, a number of requirements must be fulfilled. Each of these basic principles will be revisited later in the specific case of the quantum cascade laser.

There are three basic photon-carrier processes involved in the operation of the laser. Figure 1 depicts these in a simple two level system. An incident photon with an energy larger than that of the energy gap between the two levels has a high probability of being absorbed and exciting a carrier. This is stimulated absorption, Figure 1(a). Carriers will reside in this excited state for some finite time before decaying to a state lower in energy. In doing so, a photon is emitted with an energy equal to that of the energy gap. This is spontaneous emission, Figure 1(b). The principle photon creation process in the laser is stimulated emission (Figure 1(c)) where an incident photon stimulates the aforementioned decay to produce a further photon. Importantly, the new photon has the same energy and phase as the one that stimulated it. These photons then continue to further stimulated emission, resulting in gain in the system and an amplification of the photon count, hence the term LASER - Light Amplification by Stimulated Emission of Radiation.

(a) Stimulated absorption.

(b) Spontaneous emission.

(c) Stimulated emission.

Figure 1: Basic carrier-photon processes in a laser.

In a system in thermal equilibrium, the rate at which these three processes occur is determined by ρ_ν - the energy density of the incident photons, N₁ or N₂ - the carrier population of the initial level, and the Einstein coefficients for the particular transition, A and B.

In order for lasing to take place, stimulated emission is required to dominate over the other processes. To ensure this holds for spontaneous emission the photon energy density must be large or the A coefficient small (corresponding to a long lifetime of the upper level), i.e. N₂ ρ_ν B₂₁ / N₂ A₂₁ >> 1. In a perfect system, B₁₂ = B₂₁ so that emission between a pair of levels will be reabsorbed by the same levels. Thus, to ensure absorption is outperformed, the population of the upper level must be greater than that of the lower, i.e. N₂ / N₁ >> 1, a population inversion¹.

Boltzmann theory states the population of a level decreases exponentially with increasing energy (Figure 2(a)). Therefore, a population inversion cannot exist in a system in thermal equilibrium and some mechanism is required to force a non-equilibrium distribution and drive the inversion. That mechanism is pumping or selective excitation. A number of methods exist, depending on the type of laser. In this work on the semiconductor laser the pumping is electrical. By applying an electric field, the upper level is populated by aligning it to some reservoir of carriers. Other methods include optical pumping, most common in solid state and dye lasers and atomic/molecular collisions, found in gas discharge lasers.

In practice at least two different energy separations are required so that complete reabsorption does not take place. The simplest is the three level system, shown in Figure 2(b). Pumping takes place from the ground state, E₀ to the excited state E₂. To increase the pumping efficiency, this excited state can be broad since it is not directly involved in a radiative process. By a fast decay to the long lifetime (metastable) state E₁, a population inversion can be formed with the lasing transition to the ground state. To maintain the population inversion, the pumping must be rapid to ensure a small population in the ground state. This requirement can be relaxed somewhat in the four level scheme, Figure 2(c) where the ground state and lower laser level are no longer coincident. This allows the ground state to have a naturally large population. In much the same way as the three level system, pumping occurs from E₀ to a broad E₃ with a fast non-radiative transition to a metastable E₂, building its population. The population inversion between the lasing levels E₂ and E₁ is sustained by a short lifetime E₁ and can be further aided by minimising the natural population of E₁ by engineering E₁ - E₀ to be much larger than the thermal energy of the system. Most lasers are four level, although both schemes apply to the QCL.

(a) Boltzmann distribution.

(b) Three level system.

(c) Four level system.

Figure 2: Energy-population distribution for equilibrium and non-equilibrium (laser) systems.

For spontaneous emission to build, then stimulated emission to be sustained, the radiation must be confined to the optically active region of the device for photon gain to take place. This is achieved by forming a resonant cavity containing the gain medium with two high reflectivity mirrors at either end of the direction of propagation. Due to diffraction effects within the cavity, a degree of confinement is also required in directions other than the longitudinal. This constitutes a waveguide and is usually formed by a reduction of the refractive index or the addition of reflective layers around the gain medium such that the optical mode is confined to a layer of higher refractive index.

There are a number of sources of optical loss in the system, the total of which must be exceeded by the gain for lasing to take place. As already mentioned, reabsorption can take place between the levels of the lasing transition, but it can also occur between any other pair of levels that share the same energy separation. Also, any radiation leaving the gain medium constitutes a loss, including the output of the laser itself. This largely consists of radiation leaking from the gain medium by poor waveguiding, absorption and scattering by the mirrors and inhomogeneous scattering in the gain medium itself.

• ¹Lasers principles and applications
  J Wilson, J F B Hawkes