2.1 Ultrafast solid-state lasers - ETH - the Keller Group

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80 2.1.4 Loss modulation [Ref. p. 134 Table 2.1.5. Saturable absorber quantities, their defining equations and units. Quantity Symbol Defining equation or measurement Unit Saturation fluence F sat,A measurement R (F p,A) orT (F p,A), (Fig. 2.1.9) J/cm 2 Recovery time τ A measurement R (t) orT (t), (Fig. 2.1.8) s Incident beam area A A measurement cm 2 Saturation energy E sat,A E sat,A = A AF sat,A J Saturation intensity I sat,A I sat,A = F sat,A/τ A W/cm 2 Modulation depth ΔR or ΔT measurement R (F p,A) orT (F p,A), (Fig. 2.1.9) Nonsaturable loss ΔR ns or ΔT ns measurement R (F p,A) orT (F p,A), (Fig. 2.1.9) Incident pulse energy E p measurement J Incident pulse fluence F p,A F p,A = E p/A A J/cm 2 Incident intensity I A (t) F p,A = ∫ I A (t)dt W/cm 2 Reflec tivity pump− probe signal 100 fs excitation pulse 4 ps excitation pulse -10 -5 0 5 10 15 20 25 30 Pump−probe delay [ps] Fig. 2.1.8. Typical measured impulse response of a SESAM measured with standard degenerate pumpprobe measurements using two different excitation pulse durations. The saturable was grown at low temperature, which reduced the recovery time to about 20 ps. The short intraband thermalization recovery time results in negligible modulation depth with a 4 ps excitation pulse. Thus, only the slower recovery time due to carrier trapping is important in the picosecond regime. response DR (t) was measured for two different excitation pulse durations using a semiconductor saturable absorber. For excitation with a picosecond pulse the pump-probe trace clearly shows no significant modulation depth with a fast time constant. In the femtosecond pulse regime we normally have to consider more than one absorber recovery time. In this case the slow component normally helps to start the initial pulse formation process. The modulation depth of the fast component then determines the pulse duration at steady state. Further improvements of the saturable absorber normally require some better understanding of the underlying physics of the nonlinearities which can be very interesting and rather complex. A more detailed review about the microscopic properties of ultrafast semiconductor nonlinearities for saturable absorber applications is given in a recent book chapter [00Sie]. Ultrafast semiconductor dynamics in general are discussed in much more detail by [99Sha]. However, the basic knowledge of the macroscopic properties of the absorber and how to measure [04Hai] and adjust them to a certain value is normally sufficient for stable pulse generation. The saturation fluence F sat,A is determined and defined by the measurement of the nonlinear change in reflectivity R (F p,A ) as a function of increased incident pulse fluence (Fig. 2.1.9). The traveling-wave rate equations [89Agr] in the slow absorber approximation give normally a very Landolt-Börnstein New Series VIII/1B1
Ref. p. 134] 2.1 Ultrafast solid-state lasers 81 100 Reflectivity R [%] R ns 95 F sat,A = 18 J/cm 2 Rns= 3.7% R = 4.9% R 0 R ns 90 0 50 100 150 200 250 300 Incident pulse fluence F p,A [ J/cm 2 ] Fig. 2.1.9. Measured nonlinear reflectivity as a function of incident pulse fluence on a typical SESAM. Theoretical fit determines the macroscopic saturable absorber parameters: saturation fluence F sat,A, modulation depth ΔR and nonsaturable loss ΔR ns. good fit and determine the saturation fluence F sat,A , modulation depth ΔR and nonsaturable losses ΔR ns of the absorber [95Bro1, 04Hai]. The modulation depth is typically small (i.e. a few percent to a fraction of a percent!) to prevent Q-switching instabilities in passively mode-locked solid-state lasers [99Hoe1]. Thus it is reasonable to make the following approximation: ΔR =1− e −2q0 ≈ 2q 0 , q 0 ≪ 1 , (2.1.6) where q 0 is the unsaturated amplitude loss coefficient. The saturation of an absorber can be described with the following differential equation [89Agr]: dq (t) dt = − q (t) − q 0 τ A − q (t) P (t) E sat,A , (2.1.7) where q (t) is the saturable amplitude loss coefficient that does not include any nonsaturable losses and P (t) is the time-dependent power incident on the absorber. Note that (2.1.7) may not be precise for high excitations where inverse saturable absorption can start to become important: For example, high excitation many times above the saturation fluence can result in additional effects such as two-photon absorptions, free carrier absorption, thermal and even various damage effects [99Tho], [05Gra2]. Two-photon absorption only starts to become significant in the femtosecond pulse width regime and results in an earlier roll-off of the nonlinear reflectivity at high incident pulse fluences. This is a well-known effect and has been used in power-limiting devices before [86Wal]. In this regime, however, the absorber is operated more closely to the damage threshold which needs to be evaluated separately. Our experience is that damage in semiconductor saturable absorbers typically occurs at around 100 times the saturation fluence of the absorber with longterm degradation observed close to below this damage threshold. Therefore, we normally operate the device a least an order of magnitude below this damage threshold, ideally at an incident pulse fluence of 3 to 5 times the saturation fluence of the absorber. We therefore neglect these very high-fluence effects in the following discussion. They, however, will become important again for suppressing Q-switching instabilities and will be discussed in more detail in Sect. 2.1.6.8. At any time t the reflected (or transmitted) intensity I out (t) from the saturable absorber is given by I out (t) =R (t) I in (t) =e −2q(t) I in (t) (2.1.8) for a given input pulse I in (t). Then the total net reflectivity is given by Landolt-Börnstein New Series VIII/1B1
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References for 2.1 137 87Fan 87For
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References for 2.1 141 92Lem Lemoff
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References for 2.1 143 94Lin2 94Liu
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References for 2.1 145 95Kno Knox,
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References for 2.1 149 98Gab Gabel,
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References for 2.1 151 99Kub Kubece
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References for 2.1 153 00Car Carrig
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References for 2.1 155 01Hol Holzwa
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References for 2.1 157 02Kra1 02Kra
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References for 2.1 159 03Kor 03Kow
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References for 2.1 161 04Gra Grange
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References for 2.1 163 04Zha2 05Agn
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References for 2.1 167 07Li 07Maa 0
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2.1 Ultrafast solid-state lasers - ETH - the Keller Group

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