Saturable output coupler

SOC - Saturable Output Coupler

SOC construction and application

Construction:

The SOC consists of a partial mirror and a saturable absorber.
The single crystalline layers of the mirror and the absorber are grown on an undoped GaAs wafer.

Application:

Using a saturable output coupler (SOC), a self-starting, passively mode-locked diode pumped solid-state laser with a very simple layout can be arranged.
In case of using a SOC instead of a SAM for passive mode-locking the optical pump power can be provided through a dichroitic end mirror of the laser cavity.

Schematic SOC

• Transmittance

Transmittance

The transmittance of the saturable output coupler is mainly governed by the reflectance of the partial reflector and the absorptance of the absorber layer.
The number of film pairs in the quarter-wave stack of the AlAs/GaAs partial reflector (Bragg-mirror) determines the reflectance.
It follows from the energy conservation law T + R + A = 1 (T - transmittance, R -reflectance, A - absorptance), that the transmittance is given by T = 1 - R - A.
The reflectance of the Bragg mirror increases with increasing number of the high and low index film pairs.
An AlAs/GaAs multilayer stack of 10 film pairs has at the design wavelength a reflectance of ~ 96 % and consequently a transmitttance of ~ 4%.

• Absorptance

Absorptance

The absorptance A of the SOC consists of two parts:

saturable absorption A_s
non-saturable absorption A_ns.

The non-saturable part A_ns of the absorption can be caused by macroscopic crystal defects with very short relaxation time. The non-saturable absorption decreases with increasing relaxation time of the excited carriers in the absorber material.
In case of absorbers with a short relaxation time of ~ 1 ps the non-saturable part of the absorption can be A_ns ~ 0.2^.A₀.
The total absorption is the sum of both parts A₁ = A_s + A_ns.

The saturation of the absorption can be described with the following formula:

formula absorption 1

with

A₁ - Sum of saturable and non-saturable absorption
A_s - saturable absorption
A_ns - non-saturable absorption
F - radial dependent pulse fluence
F_sat - saturation fluence of the absorber.

The pulse fluence F depends on the beam radius r for a Gaussian pulse as follows:

formula fluence

with

F(r) radial dependent pulse fluence
F₀ - maximum fluence on the beam axis
r₀ - Gaussian beam radius

Both the fluence and the saturation depend on the beam radius r. To get the effective absorption A for the pulse an averaging over the whole illuminated area on the absorber is needed.

formula fluence

The figure shows the saturation behaviour according to the formulas above for A₁ and the averaged absorption A with a certain value of non-saturable absorption A_ns = 0.2 A₀.
The absorption values A_s and A_ns are normalized on a value A₀ = A_s + A_ns.
The averaging results in a lower saturation simulating an additional virtual non-saturable absorption.

Typical values of a saturable absorber mirror for mode-locking a solid state laser are:
A = 0.02 and F_sat = 70 µJ/cm².

For mode-locking a fiber laser with more gain the absorption of teh SAm must be also larger:
A ~ 0.3, F_sat ~ 50 µJ/cm².

Figure relative absorption

The pule energy results from an integration of the radial dependent fluence as

With the laser repetition rate f the average laser output power P_av can be calculated as P_av = E^.T^.f

• Wavelength dependency

Wavelength dependency

The absorption increases with increasing photon energy, starting at the gap energy of the semiconductor material.
In case of a quantum well structure the absorption increases as a step-like dependency on the photon energy due to the one-dimensional quantisation of free carriers.
Consequently, the reflectance versus wavelength curve of a SOC shows under non-saturated conditions a decreasing reflectance for shorter wavelengths.