Laser Diodes

A laser diode is a forward-biased p-n junction that produces highly coherent, monochromatic, and directional light through the process of stimulated emission. Unlike LEDs which produce spontaneous emission, laser diodes rely on optical feedback from a Fabry-Perot cavity to achieve lasing. They are the primary light sources in optical fiber communication, optical storage, and laser printing systems.

Core Concept of Stimulated Emission and Lasing

The fundamental distinction between LED emission and laser emission is the nature of the photon generation process. In spontaneous emission (as in LEDs), an excited electron randomly falls to a lower energy state and emits a photon at a random phase and direction. In stimulated emission, an incoming photon triggers an excited electron to drop to a lower state, emitting a second photon that is perfectly coherent with (same phase, frequency, and direction as) the original photon. This is the quantum mechanical process that makes laser emission possible.

For stimulated emission to dominate over absorption, the semiconductor must achieve population inversion. In a conventional p-n junction, thermal equilibrium means more electrons occupy lower energy states than upper states, so photons are more likely to be absorbed than to stimulate emission. Population inversion is achieved by injecting a sufficient density of electrons and holes into the active region through forward biasing, such that the quasi-Fermi levels for electrons and holes are separated by more than the photon energy: E_Fn - E_Fp > hf.

The optical cavity provides the positive feedback necessary to build up coherent light from the stimulated emission process. In a Fabry-Perot laser diode, the two end facets of the semiconductor chip are cleaved along crystal planes, forming partial mirrors due to the refractive index contrast between the semiconductor (~3.5) and air (~1.0). The cleaved facets reflect approximately 30% of the light back into the cavity, allowing photons to make multiple passes and trigger more stimulated emission before partially exiting as the output beam.

Mathematical Expression and Threshold Condition

The threshold current density J_th is the minimum injection current per unit area required to achieve lasing. Below threshold, the device operates as an LED with broad spontaneous emission. Above threshold, the optical gain provided by stimulated emission exactly compensates the optical losses in the cavity (internal absorption losses and mirror transmission losses). The threshold condition is: g_th = alpha_i + (1/2L) * ln(1/R_1*R_2), where g_th is threshold gain, alpha_i is internal loss, L is cavity length, and R_1, R_2 are mirror reflectivities.

The output power versus injection current relationship shows a sharp threshold behavior. Below I_th, the output power increases very slowly (spontaneous emission). Above I_th, the output power increases linearly with current with a slope called the slope efficiency or differential quantum efficiency, given by eta_d = dP/dI * q / (h*f). Typical slope efficiencies for GaAs laser diodes are 0.3 to 0.8 W/A.

The laser output wavelength is determined by two conditions. First, the semiconductor band gap sets the approximate photon energy. Second, the cavity longitudinal modes condition requires that the cavity length L must contain an integer number of half-wavelengths: 2*n_r*L = m*lambda, where n_r is the refractive index and m is an integer. Only wavelengths satisfying both the gain spectrum and the mode condition lase, resulting in one or a few discrete longitudinal modes at the output.

Practical Understanding of Laser Diode Performance

Modern laser diodes use a double heterostructure (DH) design where the active region has a smaller band gap than the surrounding cladding layers. This serves two purposes simultaneously. First, the band gap discontinuity confines both electrons and holes inside the narrow active region, maintaining a high carrier density with lower threshold current. Second, the lower refractive index of the wider band gap cladding layers creates a waveguide that confines the optical mode to the active region, increasing the interaction between photons and carriers for higher gain.

Temperature severely affects laser diode performance. The threshold current increases exponentially with temperature as I_th(T) = I_0 * exp(T/T_0), where T_0 is the characteristic temperature (typically 50 to 150 K for GaAs-based lasers). This means that as temperature increases, more current is needed just to reach threshold, reducing efficiency. In high-power applications, thermoelectric coolers are commonly used to stabilize laser diode temperature.

Given:
Cavity length L = 300 um = 300 x 10^-6 m
Refractive index n_r = 3.6
Center wavelength lambda = 850 nm = 850 x 10^-9 m

Why this formula applies:
The Fabry-Perot mode condition 2*n_r*L = m*lambda determines
which longitudinal modes exist inside the laser cavity.

Formula:
m = 2 * n_r * L / lambda
Mode spacing: delta_lambda = lambda^2 / (2 * n_r * L)

Substitution:
m = 2 * 3.6 * 300e-6 / 850e-9
m = 2160e-6 / 850e-9
delta_lambda = (850e-9)^2 / (2 * 3.6 * 300e-6)

Calculation:
m = 2541 (integer mode number)
delta_lambda = 722.5e-18 / 2.16e-3
delta_lambda = 3.34e-13 m

Final Answer:
Mode number m = 2541
Longitudinal mode spacing = 0.334 nm

Exam Tip: In GATE problems on laser diodes, threshold current questions often use I_th = I_0 * exp(T/T_0). A common trap is applying this formula to threshold current density rather than threshold current, which gives wrong units. Also, do not confuse slope efficiency (W/A) with overall wall-plug efficiency (output power / input electrical power).

• Below threshold current I_th: spontaneous emission dominates, broad incoherent output similar to an LED with low efficiency.
• Above I_th: stimulated emission dominates. Each photon triggers additional identical photons, building up a coherent beam within the cavity.
• The Fabry-Perot cavity (cleaved facets) provides optical feedback by partially reflecting photons back into the active region on each pass.
• Population inversion condition: the quasi-Fermi level separation E_Fn - E_Fp must exceed the photon energy hf, achieved by sufficient forward bias injection current.
• Double heterostructure design confines carriers and optical mode to the thin active region, drastically reducing threshold current compared to homojunction designs.

Quick Revision

• Laser diode operates by stimulated emission: one photon triggers emission of a second coherent (same phase, frequency, direction) photon.
• Population inversion required: E_Fn - E_Fp > hf, achieved by forward bias injection above threshold.
• Threshold condition: g_th = alpha_i + (1/2L)*ln(1/R1*R2). Above I_th, output power rises linearly with slope efficiency eta_d.
• Fabry-Perot cavity: cavity length L, mode condition 2*n_r*L = m*lambda. Mode spacing delta_lambda = lambda^2 / (2*n_r*L).
• Double heterostructure: wider band gap cladding confines carriers (band gap discontinuity) and light (refractive index waveguide) into the active region.
• Threshold current temperature dependence: I_th(T) = I_0 * exp(T/T_0). Higher temperature -> higher threshold current -> reduced efficiency.
• GATE trap: Do not confuse slope efficiency (dP/dI) with overall efficiency. The L-I curve linearity above threshold is a key exam feature.