Laser threshold

The laser threshold is the pump excitation level at which the gain medium provides enough optical gain to overcome cavity losses, enabling self-sustaining stimulated emission. Below threshold, the device operates as an LED (incoherent spontaneous emission); above threshold, it operates as a laser (coherent stimulated emission).

Threshold condition. For oscillation to be self-sustaining, the round-trip gain must equal or exceed round-trip losses:

$$\Gamma g_\text{th} \;=\; \alpha_i + \alpha_m,$$

where $\Gamma g_\text{th}$ is the threshold modal gain, $\alpha_i$ is the internal optical loss (scattering, free-carrier absorption), and $\alpha_m$ is the mirror loss:

$$\alpha_m \;=\; \frac{1}{2L} \ln\!\left( \frac{1}{R_1 R_2} \right).$$

The threshold inversion or carrier density required to achieve this gain depends on the gain medium's differential gain coefficient.

Threshold current and current density. For semiconductor lasers, the threshold is specified as a current $I_\text{th}$ or current density $J_\text{th} = I_\text{th} / (W \cdot L)$, where $W$ and $L$ are the active region width and length.

Laser type	Threshold current	Threshold current density
Fabry-Perot 1310 nm DFB	5 – 20 mA	0.5 – 2 kA/cm²
1550 nm DFB	8 – 25 mA	0.8 – 2.5 kA/cm²
980 nm pump diode	30 – 100 mA	0.5 – 2 kA/cm²
VCSEL 850 nm	0.5 – 2 mA	5 – 20 kA/cm²
GaN-based blue laser	30 – 80 mA	5 – 15 kA/cm²
Quantum cascade laser	0.5 – 5 A	1 – 5 kA/cm²
Mid-IR interband cascade	100 mA – 1 A	1 – 3 kA/cm²

Threshold pump power. For optically-pumped solid-state lasers:

Laser	Threshold pump power
Nd:YAG (Q-switched)	1 – 100 mW (CW)
Yb:fiber	5 – 100 mW
Er:fiber	1 – 10 mW
Ti:sapphire	1 – 5 W (typically)
Cr:LiSAF	100 mW – 1 W
HeNe	5 – 20 W input electrical (small fraction reaches gain)

LIV curve behavior. A laser's LIV curve (light output vs current, with voltage on a second axis) shows characteristic features:

• Below threshold: small, sublinear light output proportional to spontaneous emission
• At threshold: sharp inflection, sometimes called the "knee" of the LIV curve
• Above threshold: linear region with slope $\eta_d$ (differential quantum efficiency) of typically 0.2 – 0.8 W/A
• Roll-off at high current: thermal effects, gain saturation, or auger recombination bend the curve down

The threshold current is conventionally defined by extrapolating the linear region back to the zero-output axis.

Threshold scaling with cavity parameters.

• Cavity length: $J_\text{th}$ generally decreases with longer cavity (less mirror loss per unit length) but power consumption increases with length
• Mirror reflectivity: increasing $R_1 R_2$ decreases mirror loss and threshold, but also reduces output efficiency
• Width of active region: $I_\text{th} \propto W$ (proportional), all else equal
• Number of quantum wells: changes both gain and loss; optimum is typically 3 – 6 wells

Temperature dependence. Threshold current generally rises with temperature:

$$I_\text{th}(T) \;=\; I_\text{th}(T_0) \exp\!\left( \frac{T - T_0}{T_0^{\text{char}}} \right),$$

where $T_0^{\text{char}}$ is the characteristic temperature. Typical values:

Material system	$T_0^\text{char}$
GaAs (850 nm)	150 – 250 K
InGaAsP (1310 / 1550 nm)	50 – 80 K
AlGaInAs (1310 / 1550 nm, strained)	80 – 150 K
GaN (visible)	100 – 200 K
InGaAs/GaAs strained (980 nm)	200 – 400 K
QCL	100 – 200 K

Higher $T_0$ means lower temperature sensitivity. The poor $T_0$ of InGaAsP at 1550 nm is a primary reason DFB lasers need TECs for stable operation.

Threshold dependence on threshold quantities.

Parameter	Effect on $I_\text{th}$
Cavity length	Generally weakly negative correlation, but $I_\text{th}/L$ has a minimum
Width	Roughly proportional
Number of wells	Optimum typically 3 – 6
Mirror reflectivity	Higher $R$ → lower threshold
Temperature	Exponential increase via $T_0$
Strain	Compressive strain often reduces threshold
Doping in cladding	Higher doping → lower series resistance but higher absorption

Sub-threshold and supra-threshold regimes.

Below threshold, the laser emits "amplified spontaneous emission" (ASE) — broad-spectrum incoherent light. The spectrum is roughly the spontaneous-emission profile of the active region. Above threshold, the spectrum collapses to the single (or few) lasing modes; the linewidth narrows dramatically.

At threshold, the laser shows critical-point-like behavior: the photon number per cavity mode transitions from $\sim 1$ (spontaneous) to $\sim 10^5$ (stimulated), with a kink in the LIV curve.

Threshold definitions and disputes. Different threshold definitions exist:

• Linear extrapolation: extrapolate the lasing-regime linear slope back to zero output; intersection with current axis is $I_\text{th}$
• First-derivative maximum: $I_\text{th}$ is the current where $dP/dI$ is maximum
• Second-derivative: $I_\text{th}$ is where $d^2P/dI^2$ is maximum (the "kink")
• Linewidth criterion: $I_\text{th}$ is where the linewidth first narrows to its lasing value

For most semiconductor lasers, these definitions agree within a few percent. For very low-threshold or highly-nonideal lasers, they can differ significantly.

Why threshold matters.

• Power efficiency: power consumed below threshold (= $I_\text{th} V$) is "wasted" — only above-threshold current contributes to laser output. Threshold sets the minimum power budget.
• Modulation: pre-biasing the laser slightly above threshold reduces turn-on delay; pre-biasing below threshold reduces noise
• Reliability: high threshold often correlates with higher operating current → worse reliability
• Tunability: lasers operate stably only at currents above threshold

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 17 (semiconductor lasers); Coldren, Corzine & Mašanović, Diode Lasers and PICs (2nd ed., 2012), Ch. 5 — comprehensive treatment of threshold for semiconductor lasers; Siegman, Lasers (University Science Books, 1986), Ch. 13 for the general laser-physics treatment.