Optical properties of a SESAM

3.2.1 Static reflectivity

The static reflectivity of a SESAM is mainly determined by the static reflectivity of the Bragg mirror. The Bragg mirror consists of a material with a high refractive index n_H and a material with low refractive index n_L. Typical materials for semiconductor Bragg mirrors for near infrared are AlAs/GaAs layer systems.

The reflectivity of the Bragg mirror is based on multilayer interference. Due to the difference of the refractive indexes of the Bragg mirror materials the incoming electro-magnetic wave is partially transmitted and partially reflected on each interface. The reflected waves interfere constructively for a quarter wave layer structure where the single layers have a thickness of d = λ(4n)⁻¹, where n is the refractive index of the layer material and λ the laser wavelength [Dem04]. Hence, by means of multilayer interference the Bragg mirror is a device with a reflectivity close to 100 % for appro-priate wavelengths. The wavelength range where the waves are best reflected is called stopband. The reflectivity of the stopband increases with the amount of layers build-ing the Bragg mirror. Increasbuild-ing the ratio n_H/n_L of the refractive indexes leads to a broadening of the stopband [She95b]. A formalism to calculate the reflectivity spectra of a multilayer system can be found in [Bor86, She95b]. A formalism based on transfer matrix method is briefly introduced in Section 4.4.2.

Fig. 3.2 shows a typical static reflectivity spectrum of a SESAM. The spectrum clearly exhibits the stopband in the region of 1000-1100 nm. The dip within the stopband at approximately 1090 nm results from excitonic absorption of the quantum well. The oscillations outside the stopband region are due to multilayer interference.

3.2.2 Nonlinear reflectivity

As already mentioned the reflectivity of a SESAM depends on the incoming light in-tensity. Due to the absorber the reflectivity is lower for small intensities and increases with increasing intensity due to the absorber’s bleaching. This leads to a nonlinear reflectivity curve as it is plotted in Fig. 3.3. Based on this curve crucial parameters for SESAM characterization are stressed and will be explained in the following. The labels of the characterizing parameters are taken from [Hai04].

In Fig. 3.3 the reflectivity of a SESAM versus incoming fluence is plotted where fluence F_P = E_P/A is the pulse energy E_P per area A. When nonlinear effects such as two-photon absorption and free-carrier absorption are neglected the reflectivity in-creases and saturates at a given value (blue curve in Fig. 3.3). Taking into account nonlinear effects at high fluences (see Section 3.3.2) the reflectivity exhibits a roll-over and decreases again, as the red curve in Fig. 3.3 shows it [Hai04].

The maximum change of reflectivity is called modulation depth ∆R_mod and is deter-mined by the difference between the linear reflectivity of a nonsaturated SESAM R_lin and a fully saturated SESAMR_ns: ∆R_mod =R_ns−R_lin.

3.2 Optical properties of a SESAM

10⁰ 10¹ 10² 10³ 10⁴

95 96 97 98 99 100

Reflectivity (%)

Fluence (µJ/cm²)

∆ R

∆ R eff mod

∆ R R ns

ns

Rlin

Fsat

Figure 3.3: Typical nonlinear reflectivity curves of a SESAM. The important charac-terizing parameters are explained in detail in the text. The blue curve is calculated according to Eq. (3.1). In the calculation of the red curve nonlinear effects such as two photon absorption and free carrier absorption are taken into account leading to the roll-over at high fluence values. This curve is calculated according to Eq. (3.2).

Both calculations are based on the following input parameters: R_lin=95.9 %,R_ns=99.0

%,F_sat=50 µJ/cm², andF₂=500 000µJ/cm² for the red curve.

However, due to the roll-over the maximum reflectivity decreases leading to a re-duced modulation depth, which we call effective modulation depth ∆R_eff which is given by the difference of the maximum reflectivity and the linear reflectivity:

∆R_eff=Maximum(Reflectivity)−R_lin=Maximum(R(F_P)−R_lin)=Maximum(∆R).

∆R_ns are the nonsaturable losses and are determined by ∆R_ns = 100%−R_ns.

Reasons for nonsaturable losses are scattering losses at defect states and the surface of the SESAM, losses due to two-photon absorption and free-carrier absorption, and the reflectivity of the Bragg mirror that is just close to 100 % [Kel99].

The saturation fluenceF_sat characterizes the beginning of the saturation of the absorp-tion. F_sat is the fluence value where the reflectivity reaches approximately 1/e≈ 37%

of the modulation depth: R(F_sat) =R_lin+ 1/e·∆R_mod. Hence, the saturation fluence characterizes the steepness of the nonlinear reflectivity curve.

The measure of the reduction of the reflectivity for high fluence values due to nonlinear effects is the roll-over parameter F₂. Analogous to F_sat the parameter F₂ corresponds to a fluence value, in particular a reflectivity curve with a strong roll-over has a small F₂-parameter, whereas a large F₂-parameter indicates that the roll-over occurs at high fluence values.

As it is published in [Hai04] the nonlinear reflectivity curve of a SESAM is based on these parameters and can be calculated according to

R(F_P) =R_ns ln

h

1 +Rlin/Rns

exp(FP/Fsat)−1 i

FP/Fsat

(3.1) with F_P as the pulse fluence.

In Equation (3.1) nonlinear effects are not taken into account. However, since in a laser cavity fluence values of a hundredµJ/cm²or even mJ/cm² can be reached, these fluence values are high enough to induce effects of induced absorption within the SESAM (see Section 3.3.2) that reduce the reflectivity. Hence, Equation (3.1) has to be modified and the reflectivity is given in [Hai04]:

R(F_P) =R_ns lnh

1 +R_lin/R_ns

exp(F_P/F_sat)−1i

F_P/F_sat exp(−F_P/F₂). (3.2) The reflectivity curves in Fig. 3.3 are based on Equations (3.1) and (3.2).

The roll-over parameter F₂ is a crucial parameter of SESAMs for high-power lasers, since it describes the reduction of the modulation depth. This has a negative impact for high-power lasers where the SESAM should exhibit the full modulation depth even at very high fluence values. Therefore, a large F₂-parameter is required. Different methods to influenceF₂ and other SESAM parameters will be stressed in Section 3.4.