Output coupler

The output coupler is the cavity mirror through which the useful laser output power exits the resonator. Of the two (or more) mirrors in a laser cavity, one is typically a highly-reflective (HR) end mirror and one is a partially-transmitting "output coupler" (OC) that allows a controlled fraction of the intracavity power to leave the cavity as the laser beam. The choice of OC reflectivity is one of the primary design parameters for any laser.

The OC reflectivity tradeoff. The output coupler reflectivity $R_\text{OC}$ controls:

• Threshold gain $g_\text{th} = \alpha_i + (1/2L) \ln(1/R_\text{HR} R_\text{OC})$ — lower $R_\text{OC}$ means higher mirror loss and higher threshold
• Output coupling efficiency $\eta_c = \alpha_m / (\alpha_i + \alpha_m)$ — higher mirror loss means more of the intracavity power exits usefully
• Intracavity power — for a given output power, low-$R_\text{OC}$ requires less intracavity power; high-$R_\text{OC}$ requires more
• Slope efficiency $\eta_d = \eta_i \cdot \alpha_m / (\alpha_i + \alpha_m)$ — output per unit pump above threshold

The optimum OC reflectivity balances these. For typical solid-state lasers, optimum $R_\text{OC}$ falls in the range 5 – 30%; for high-gain media (semiconductor), 30 – 50%; for low-gain media (HeNe), 99% or higher.

Standard output coupler reflectivities.

Laser type	OC reflectivity	Mirror loss $\alpha_m$
Cleaved-facet diode laser	30% (uncoated InP/GaAs facet)	~40 cm⁻¹ for 300 μm cavity
AR-coated diode laser	1 – 10%	High loss; usually combined with external cavity
Yb:fiber laser (CW kilowatt)	4 – 20%	depends on length
Nd:YAG CW oscillator	5 – 50%	depends on rod length, gain
Q-switched Nd:YAG	30 – 70%	high mirror loss for high Q-switched power
Ti:sapphire CW	1 – 15%	depending on intracavity loss
HeNe (red)	99 – 99.5%	extremely low loss, low-gain medium
Excimer laser	4 – 10%	low because of short pulse, single-pass-like operation
External cavity tunable laser	4 – 30% (back mirror)	grating provides wavelength selection
VCSEL	$> 99\%$	tens of DBR pairs needed

Optimum OC formula. For a 4-level CW laser, the OC reflectivity that maximizes output power for a given pump $P_\text{pump}$ is approximately:

$$T_\text{OC}^\text{opt} \;\approx\; \sqrt{\alpha_i \cdot 2 g_0 L} - \alpha_i \cdot 2 L,$$

where $g_0$ is the small-signal gain coefficient and $\alpha_i$ is the intrinsic loss. The optimum increases with available gain and decreases with intrinsic loss.

For Nd:YAG with $g_0 L \approx 0.1$ and $\alpha_i \cdot 2L \approx 0.01$: $T_\text{OC}^\text{opt} \approx 0.04$, i.e., 4% OC (96% reflectivity).

This formula is the Rigrod equation in disguise — the canonical CW laser power extraction analysis.

Output coupler in semiconductor diode lasers. Most edge-emitting Fabry-Perot diodes use uncoated cleaved facets as both mirrors:

• Facet reflectivity from Fresnel: $R = ((n-1)/(n+1))^2 = ((3.5-1)/(3.5+1))^2 = 30\%$
• Both facets identical; emission from both ends (about half of intracavity power exits each direction)
• Convenient: no coating step required; high yield

For specialized applications, one facet is coated:

Coating combination	Use
HR back (95+%) + 30% front	Boosts output from front, slightly raises threshold
HR back (95+%) + AR front (~ 1%)	External-cavity diode laser configuration
70% back + 30% front	Asymmetric output for fiber coupling
HR back + HR front	High-finesse cavity for narrow linewidth

For DFB lasers, the grating provides the dominant feedback; facet reflectivities are typically AR-coated to suppress unwanted Fabry-Perot resonances.

OC for VCSELs. Vertical-cavity surface-emitting lasers use distributed Bragg reflectors (DBRs) for both mirrors. Because the gain region is very short (10 nm to a few hundred nm), the mirror reflectivities must be extremely high:

• Top DBR (output side): 99 – 99.9% (typically 20 – 25 quarter-wave pairs)
• Bottom DBR: > 99.9% (30 – 40 pairs)
• Slight asymmetry forces output from the top side

The high-reflectivity requirement means VCSEL DBRs must use high-index-contrast materials (typically GaAs/AlAs for 850 nm; harder to achieve for 1310/1550 nm, which requires more pairs or wafer-bonded DBRs).

OC in fiber lasers. Fiber lasers use one of:

• Cleaved fiber end + external mirror: simple, often used for prototypes
• Fiber Bragg grating (FBG): written into the fiber itself; partial reflectivity selectable
• Loop mirror (Sagnac): 50:50 coupler with a fiber loop
• Multimode pump combiner + signal output: integrated output and pump injection

Fiber Bragg gratings provide wavelength-specific output coupling with very narrow bandwidth — essentially functioning as the OC and wavelength selector simultaneously.

OC heating and damage. The output coupler is the cavity mirror with the highest transmitted power; it can be subject to thermal lensing, coating damage, or in extreme cases facet melting:

Power level	Considerations
< 1 W	Standard dielectric coatings fine
1 – 100 W CW	Ion-assisted-deposition coatings, good thermal contact
0.1 – 10 kW CW	Special coating designs, water-cooled mounts
Pulsed (high peak)	Coating damage threshold dominates; up to 50 J/cm² for 10 ns
Ultra-high pulsed	Cleaved fiber endfaces with end-cap fusion

Variable output coupling. Some applications need adjustable OC reflectivity:

• Variable-reflectivity grating couplers: tunable for output power control
• Polarization-controlled OC: birefringent OC + polarization rotator gives effective variable reflectivity
• Acousto-optic modulator inside cavity: cavity-dumping for high-energy pulses; like adjustable instantaneous OC

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 14 (laser oscillators); Siegman, Lasers (University Science Books, 1986), Ch. 12 (Rigrod analysis, optimum coupling); Coldren, Corzine & Mašanović, Diode Lasers and PICs (2nd ed., 2012), Ch. 3 (semiconductor laser mirrors); Koechner, Solid-State Laser Engineering (6th ed., 2006) for solid-state laser OC design.