Saturable Absorber Mirror - SAM information

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How does a SAM™ work ?

Contents

1. Aim of SAM
2. Parameters
3. Absorption A
4. Modulation depth ΔR
5. Relaxation time t
6. Saturation fluence
7. Reflection and absorption bandwidth

1. Aim of SAM

Passive mode-locking techniques for the generation of ultra-short pulse trains are preferred over active techniques due to the ease of incorporation of passive devices into various laser cavities.
SAM scheme A passive mode-locking device, the saturable absorber mirror (SAM), can be used to mode-lock a wide range of laser cavities. Pulses result from the phase-locking (via the loss mechanism of the saturable absorber) of the multiple lasing modes supported in continuous-wave laser operation.
The absorber becomes saturated at high intensities, thus allowing the majority of the cavity energy to pass through the absorber to the mirror, where it is reflected back into the laser cavity. At low intensities, the absorber is not saturated, and absorbs all incident energy, effectively removing it from the laser cavity resulting of suppression of possible Q-switched mode-locking. Moreover, due to the absorption of the pulse front side the pulse width is slightly decreased during reflection.

2. Parameters

A SAM consists of a Bragg-mirror on a semiconductor wafer like GaAs, covered by an absorber layer and a more or less sophisticated top film system, determining the absorption.
Although semiconductor saturable absorber mirrors have been employed for mode-locking in a wide variety of laser cavities, the SAM has to be designed for each specific application. The differing loss, gain spectrum, internal cavity power, etc, of each laser necessitates slightly different absorber characteristics.

The most important parameters of a SAM are:

absorption A
modulation depth ΔR
relaxation time t
saturation fluence F_sat
reflection and absorption bandwidth.

3. Absorption

A SAM is a nonlinear optical device. Therefore the absorption A depends on the pulse fluence F_P. If the pulse duration τ_p is shorter than the relaxation time τ of the absorber material, the time dependent absorption is given by

with

eq. (1)

A(t)

time dependent absorption

A₀

small signal absorption (saturable absorption)

time dependent light intensity (measured in W/m²)

F(t)

time dependent fluence

F_sat

saturation fluence

The effective absorption A of a pulse is the result of an averaging over the fluence F(t) of a pulse:

eq. (2)

F_P

pulse fluence

The small signal absorption A₀ is proportional to the square of the electric field strength of the standing wave at the position of the absorber layer. Therefore the saturable absorption of the SAM can be adjusted by the design. A typical value for the saturation fluence F_sat is 50 µJ/cm².

4. Modulation depth ΔR

The modulation depth ΔR is smaller than the absorption A₀ because of non-saturable losses A_ns: ΔR = A₀ -A_ns. The main reason for the non-saturable losses are the crystal defects, which are needed for the fast relaxation of the excited carriers. The modulation depth increases with increasing relaxation time t.

Typical values for ΔR are

fast absorber with t ~ 500 fs: ΔR ~ 0.5 A₀; A_ns ~ 0.5 A₀
slow absorber with t ~ 10 ps: ΔR ~ 0.7 A₀; A_ns ~ 0.3 A₀

The pulse fluence dependent reflection R(F_p) of a saturable absorber mirror is governed by the effective absorption according to eq.(2). For high pulse fluences F_P the two photon absorption decreases the reflection and therefore also the effective moulation depth. This effect depends on the two-photon absorption parameter F_TPA, which is material dependent.

eq. (3)

5. Relaxation time

The saturable absorber layer consists of a semiconductor material with a direct band gap slightly lower than the photon energy. During the absorption electron-hole pairs are created in the film. The relaxation time t of the carriers has to be a little bit longer than the pulse duration. In this case the back side of the pulse is still free of absorption, but during the hole period between two consecutive pulses the absorber is non saturated and prevents Q-switched mode-locking of the laser.
Because the relaxation time due to the spontaneous photon emission in a direct semiconductor is about 1 ns, some precautions has to be done to shorten it drastically.

Two technologies are used to introduce lattice defects in the absorber layer for fast non-radiative relaxation of the carriers:

low-temperature molecular beam epitaxy (LT-MBE)
ion implantation.

The parameters to adjust the relaxation time in both technologies are the growth temperature in case of LT-MBE and the ion dose in case of implantation. Typical values of the relaxation time t of SAMs are between 500 fs and 10 ps.

Because of the different relaxation processes in most cases the relaxation of the excited carriers cannot be described by a single time constant. As is shown in the pump-probe measurement of a slow SAM below, the real relaxation can be characterized by two time constants.

6. Saturation fluence F_sat

The saturation fluence depends on the semiconductor material parameters and on the optical design of the SAM. To prevent the SAM from unwanted degradation and destruction due to high pulse fluences, the saturation fluence must be low.
To decrease the saturation fluence, the thickness of the semiconductor absorber layer is reduced below ~ 10 nm. In this case a quantization of the electron energy and the momentum in the direction perpendicular to the absorber layer takes place and as a consequence the density of states decreases below the value of a compact semiconductor. Therefore the absorber layers in a SAM are thin quantum wells with a smaller band gap than the barriers on both sides. If a larger absorption value of the SAM is needed, the number of the quantum wells is increased instead of using a single thick absorber layer.
The electric field intensity in front of the Bragg mirror of a SAM is a periodic function with nodes and antinodes. The absorbing quantum wells are positioned in the antinodes to get a low saturation fluence. Together with the Fresnel reflectance at the semiconductor-air boundary the Bragg mirror builds a Fabry-Perot like resonator, which contains the quantum wells. The optical thickness of the semiconductor material between the reflectors determines the cavity to be resonant or anti-resonant. The saturation fluence of a resonant SAM is lower than that of an anti-resonant SAM because of the field enhancement inside the cavity.

7. Reflection and absorption bandwidth

7.1 Time-bandwidth product (TBWP)

From Heisenberg's uncertainty principle for the conjugated variables pulse width Dt and photon energy E = h^. nthe TBWP of a laser pulse is limited to about D t^.Dn >1/(2p).

h = 6.626 ^.10^-34Js is Planck's constant
n the pulse mean frequency and
Dn the pulse bandwidth

An accurate calculation shows, that the minimum TBWP for a Gaussian pulse is Dt^. Dn = 0.44 (pulse duration in seconds x pulse bandwidth in Hertz > 0.44).

The minimum TBWP for a Sech²pulse is Dt^.Dn = 0.32 .

Most people do not work with frequency n but prefer wavelength l. Using the relation c=l^.n the frequency interval Dn is related to the wavelength interval Dl by Dn = - c^. Dl/l².
c = 2.988 ^. 10⁸ m/s is the speed of light in the vacuum.

Numerical values for the minimum bandwidth Dn as a function of pulse duration Dt

Pulse duration Dt	Gaussian bandwidth Dn	Sech² bandwidth Dn	Gaussian bandwidth Dn Sech² bandwidth Dn
5 fs	88 THz	64 THz
10 fs	44 THz	32 THz
20 fs	22.THz	16 THz
50 fs	8.8 THz	6.4 THz
100 fs	4.4 THz	3.2 THz
200 fs	2.2 THz	1.6 THz
500 fs	880 GHz	640 GHz
1 ps	440 GHz	320 GHz
2 ps	220 GHz	160 GHz
5 ps	88 GHz	64 GHz
10 ps	44 GHz	32 GHz
20 ps	22 GHz	16 GHz

Numerical values for the minimum bandwidth in nm as a function of pulse duration Dt

Pulse duration Dt	Gaussian bandwidth (nm)				Sech² bandwidth (nm)
Pulse duration Dt	@ 800 nm	@ 1200 nm	@ 1600 nm	@ 2000 nm	@ 800 nm	@ 1200 nm	@ 1600 nm	@ 2000 nm
5 fs	188 nm	424 nm	752 nm	1180 nm	137 nm	308 nm	547 nm	858 nm
10 fs	94 nm	212 nm	377 nm	590 nm	68 nm	154 nm	274 nm	429 nm
20 fs	47 nm	106 nm	188 nm	295 nm	34 nm	77 nm	137 nm	214 nm
50 fs	19 nm	42 nm	75 nm	118 nm	13 nm	31 nm	55 nm	86 nm
100 fs	9.4 nm	21 nm	38 nm	59 nm	6.8 nm	15 nm	27 nm	43 nm
200 fs	4.7 nm	10.6 nm	18.8 nm	29.5 nm	3.4 nm	7.7 nm	13.7 nm	21.4 nm
500 fs	1.9 nm	4.2 nm	7.5 nm	11.8 nm	1.4 nm	3.1 nm	5.5 nm	8.6 nm
1 ps	0.94 nm	2.12 nm	3.77 nm	5.90 nm	0.69 nm	1.54 nm	2.74 nm	4.29 nm
2 ps	0.47 nm	1.06 nm	1.88 nm	2.95 nm	0.34 nm	0.77 nm	1.37 nm	2.14 nm

7.2 Reflection bandwidth

The reflection bandwidth of the SAM has to be larger than the pulse bandwidth. In case of a SAM with an underlying Bragg-mirror the reflection bandwidth is determined by the ratio of the refractive indices n_H/n_L of the layers in the thin film stack. More about Bragg-mirrors ...

The relative spectral width w = Dl/l of the high reflectance zone of a conventional semiconductor AlAs/GaAs thin film stack is about 0.1. Therefore the width of the high reflection zone of an AlAs/GaAs Bragg-mirror with a center wavelength of 1000 nm is about 100 nm. From the tables above this results in a minimum pulse duration of about 20 fs. For shorter pulses other mirror types, for instance dielectric or metallic mirrors has to be used.

7.3 Absorption bandwidth

An ideal SAM has a constant saturable absorption for all wavelengths of the pulse spectrum. Because of the wavelength dependence of the absorption in a semiconductor material above the band gap, the absorption increases with decreasing wavelength. In case of a resonant SAM this dependency may be changed by the standing waves inside the cavity in such a way, that the maximum absorption is at the resonance wavelength of the SAM.