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> Energy band gap > GaAs  Al_{x}Ga_{1x}As  In_{x}Ga_{1x}As  
> Refractive index > GaAs  AlAs  Al_{x}Ga_{1x}As  In_{x}Ga_{1x}As  
> Devices > Bragg mirror  SAM  RSAM  SA  SANOS  SOC  Microchip laser  PCA  
RSAM  Resonant Saturable Absorber Mirror 

>  Contents  
>  How does a RSAM work?  
The resonant saturable absorber mirror (RSAM) is a similar device as a
saturable absorber
mirror (SAM), but has a larger saturable absorption, a smaller bandwidth and a lower
saturation fluence. The RSAM is designed as a resonant Gires–Tournois interferometer
with absorber layers positioned at the antinodes of the optical field inside the
resonator cavity. 

>  RSAM applications  
The main applications for RSAMs are:


>  Resonance wavelength  
Influence of the angle of incidence  
The resonance wavelength l of the Gires–Tournois interferometer depends on the angle of incidence j and is given by  
eq.(1)  
with  
l  resonance wavelength of the interferometer  
n  refractive index of the absorbing spacer layer  
d  thickness of the absorbing spacer layer  
m  order of the resonance; m = 1, 2, 3, ....  
j  angle of incidence on the RSAM  
In case of a perpendicular beam incidence the first order resonance wavelength is simply l = 2nd.  
Resonance wavelength l of a RSAM with l(0) = 1064 nm and n = 3.1 after eq. (1) 

Resonance wavelength for parallel polarized light at different angles of incidence  
Resonance wavelength for perpendicular polarized light at different angles of incidence  
Influence of the temperature  
There is also a temperature influence on the resonance wavelength l. The temperature dependency of the optical thickness nd of the absorbing spacer layer, which governs the resonance wavelength l, is mainly determined by the refractive index. The influence of the thermal expansion of the layer thickness is negligible.  
The change of the resonance wavelength l with the temperature can be calculated by  
eq.(2)  
with  
l (T)  resonance wavelength at temperature T  
l (T_{0})  resonance wavelength at reference temperature T_{0}  
1/n*dn/dT  ~ 7.5x10^{5}K^{1}, temperature coefficient of the refractive index  
T_{0}  reference temperature  
T  working temperature  
Resonance wavelength l of a RSAM with
l(0) = 1064 nm after eq. (2) 

>  Bandwidth  
The bandwidth Dl of the interferometer resonance dip is gouverned by the round trip loss l of the wave inside the cavity and can be estimated in case of small losses l << 1 by  
Dl = l (1  r_{f} + A)/(m π) = ll/(m π)  
with  
Dl  bandwidth FWHM (full width at half maximum)  
l  resonance wavelength of the interferometer  
(r_{f})^{2} = R_{f}  reflectance of the front mirror (back mirror reflectance R_{b} = 1)  
A  single pass absorptance of the spacer layer  
m  order of the resonance; m = 1, 2, 3, ....  
l  round trip loss: 1  r_{f} + A  
Dl for RSAM at l = 1064 nm 

RSAM, impedance matched at l = 1064 nm with front mirror reflection
r_{f} = 0.97, unsaturated absorption of A = 1.5% and resonance order m = 4 


>  Saturation intensity  
The RSAM is a strong nonlinear optical device. The absorptance A of the absorber layer
and the reflectance R of the RSAM depend on the incoming light intensity I. Due to the
resonance condition of the Gires–Tournois interferometer at the working wavelength the
effective saturation intensity I_{sat,eff} of the device shifts by a factor of
about (p/F)^{2}
(F  finesse of the Gires–Tournois interferometer) to lower values in relation to the
intrinsic material value I_{sat}, which is valid for nonresonant saturable absorber mirrors
(SAM). The absorptance A of a RSAM with a not too small finesse F > 10 can be estimated by 

eq.(3)  
with  
A  absorptance  
A_{0}  small signal absorptance (saturable absorption)  
I  light intensity (measured in W/m^{2})  
I_{sat}  intrinsic material saturation intensity  
F  finesse of the RSAM  
The effective saturation fluence F_{sat,eff} of a RSAM can be estimated using the relaxation time t and the effective saturation intensity I_{sat,eff}  
eq.(4)  
with  
F_{sat,eff}  effective saturation fluence of the RSAM  
I_{sat,eff}  effective saturation intensity of the RSAM  
t  relaxation time of the absorber material  
With typical values for a nonresonant SAM


>  Intensity dependent reflectance  
RSAM at l = 1064 nm with front mirror reflection
r_{f} = 0.97, unsaturated absorption of A = 1.5% and resonance order m = 4 


>  Relaxation time  
The saturable absorber layer consists of a semiconductor material with a direct
band gap, which is slightly smaller than the photon energy. During the absorption
electronhole pairs are created in the film. The relaxation time
t of the carriers is very short due to fast nonradiative
relaxation channels introduced by lowtemperature growth of the absorber layer. 
Recovery of the absorption A_{0} with a relaxation time t = 10 ps 

A(t) = A_{0}[1  exp(t/t )]  
with  
A(t)  time dependent absorption  
A_{0}  small signal saturable absorption  
t  time  
t  relaxation time  