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

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120 2.1.6 Mode-locking techniques [Ref. p. 134 Nonlinear reflectivity [%] 100.0 99.8 99.6 99.4 99.2 99.0 R ns R R ns,eff no ISA with ISA R eff 1 10 100 Saturation parameter S= F p / F sat,A 0.1 2 4 6 8 2 4 6 8 2 4 6 8 Fig. 2.1.18. Nonlinear reflectivity as function of saturation parameter S which is equal to F p/F sat,A. F p is the pulse fluence incident on the absorber mirror (i.e. pulse energy density) and F sat,A is the saturation fluence of the absorber mirror. Inverse saturable absorption decreases the reflectivity at higher pulse energies such that a “roll-over” is observed. This decreases the effective modulation depth and increases the effective nonsaturable absorption. However, it improves the Q-switching mode-locking threshold. For F 2 →∞(i.e. without induced nonlinear losses) we retrieve the simpler equation (2.1.77). F 2 is the inverse slope of the induced absorption effect and can be determined from nonlinear SESAM reflectivity measurements (Fig. 2.1.18) [05Gra2, 04Hai]: R ISA (F p )=R (F p ) − F p , (2.1.81) F 2 where F p is the pulse fluence incident on the SESAM (i.e. pulse energy density), R(F p ) the measured nonlinear reflectivity without Inverse Saturable Absorption (ISA) and R ISA (F p ) the measured reflectivity with inverse saturable absorption. The smaller the inverse slope of the roll-over F 2 ,the stronger is the roll-over. The stronger the roll-over, the smaller the maximum modulation depth of the SESAM. 2.1.6.9 External pulse compression SPM generates extra frequency components. The superposition with the other frequency components in the pulse can spectrally broaden the pulse (i.e. for positively chirped pulses assuming n 2 > 0). SPM alone does not modify the pulse width, but with proper dispersion compensation a much shorter pulse can be generated with the extra bandwidth [80Mol]. The positively chirped spectrally broadened pulse then can be compressed with appropriate negative dispersion compensation, where the “blue” spectral components have to be advanced relative to the “red” ones. A careful balance between a nonlinear spectral broadening process and negative dispersion is needed for efficient compression of a pulse. Typically, self-phase modulation in a single-mode fiber with optimized length was used to linearly chirp the pulse, which is then compressed with a grating pair compressor [84Tom]. Ultimately, uncompensated higher-order dispersion and higher-order nonlinearities limit compression schemes. For pulses shorter than 100 fs, compression is typically limited to factors of less than 10. Compression of amplified CPM dye laser pulses with 50 fs duration produced the long-standing world record of 6 fs [87For]. Similar concepts have been used for external pulse compression of 13-fs pulses from a cavity-dumped Ti:sapphire laser [97Bal] and of 20-fs pulses from a Ti:sapphire laser amplifier [97Nis] resulting, in both cases, in approximately 4.5-fs pulses. In the latter case, the use of a noble-gas-filled hollow fiber instead of a normal fiber allows for much higher pulse energies. For example, pulse energies of about 0.5 mJ with 5.2-fs pulses and a peak power of 0.1 TW [97Sar]. More recently, adaptive pulse compression of a super-continuum produced in two cascaded hollow fibers generated 3.8-fs pulses with energies of up to 15 μJ [03Sch]. Further improvements resulted in 3.4-fs pulses but with only 500 nJ pulse energies [03Yam]. The pulse duration was fully characterized by Spectral-Phase Interferometry for Direct Electric-field Reconstruction (SPIDER) (Sect. 2.1.7.3). This is currently the world record in the visible and near-infrared spectral regime. Landolt-Börnstein New Series VIII/1B1
Ref. p. 134] 2.1 Ultrafast solid-state lasers 121 The extra bandwidth obtained with SPM can be extremely large producing a white-light continuum [83For], which can be used as a seed for broadband parametric amplification. Parametric processes can provide amplification with an even broader bandwidth than can typically be achieved in laser amplifiers. Noncollinear phase-matching at a crossing angle of 3.8 ◦ in beta barium borate (BBO) provides more than 150 THz amplification bandwidth [95Gal]. With this type of set-up, parametric amplification has been successfully demonstrated with pulse durations of less than 5 fs [99Shi, 02Zav]. 2.1.7 Pulse characterization 2.1.7.1 Electronic techniques Electronic techniques for pulse-width measurements are typically limited to the picosecond regime. Photodetectors and sampling heads with bandwidths up to 60 GHz are commercially available. This means that the measured pulse duration is limited to about 7 ps. This follows from simple linear system analysis for which the impulse response of a photodetector or a sampling head can be approximated by a Gauss-function. The impulse response for a given system bandwidth B has a FWHM τ FWHM in units of ps: 312 GHz τ FWHM [ps] ≈ B [GHz] . (2.1.82) The impulse response of a measurement system can be determined from the impulse response of each element in the detection chain: τ 2 FWHM = √ τ1 2 + τ 2 2 + τ 3 2 + ..., (2.1.83) where for example τ 1 is the FWHM of the impulse response of the photodetector, τ 2 of the sampling head and so on. Thus, with a 40 GHz sampling head and a 60 GHz photodetector we only measure a impulse response with FWHM of 9.4 ps. 2.1.7.2 Optical autocorrelation Optical autocorrelation techniques with second-harmonic generation of two identical pulses that are delayed with respect to each other are typically used to measure shorter pulses [80Sal, 83Wei]. We distinguish between collinear and non-collinear intensity autocorrelation measurements for which the two pulse beams in the nonlinear crystal are either collinear or non-collinear. In the non-collinear case the second-harmonic signal only depends on the pulse overlap and is given by ∫ I 2ω (Δt) ∝ I (t)I (t − Δt)dt. (2.1.84) The FWHM of the autocorrelation signal I 2ω (Δt) isgivenbyτ Au and determines the FWHM pulse duration τ p of the incoming pulse I (t). However, τ Au depends on the specific pulse shape (Table 2.1.13) and any phase information is lost in this measurement. So normally, transformlimited pulses are assumed. This assumption is only justified as long as the measured spectrum also agrees with the assumption of pulse shape and constant phase (i.e. the time–bandwidth product corresponds to a transform-limited pulse, Table 2.1.13). For passively mode-locked lasers, for Landolt-Börnstein New Series VIII/1B1
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Page 103 and 104: References for 2.1 135 74New 74Sha
Page 105 and 106: References for 2.1 137 87Fan 87For
Page 107 and 108: References for 2.1 139 90Wu Wu, M.C
Page 109 and 110: References for 2.1 141 92Lem Lemoff
Page 111 and 112: References for 2.1 143 94Lin2 94Liu
Page 113 and 114: References for 2.1 145 95Kno Knox,
Page 115 and 116: References for 2.1 147 96Xu1 96Xu2
Page 117 and 118: References for 2.1 149 98Gab Gabel,
Page 119 and 120: References for 2.1 151 99Kub Kubece
Page 121 and 122: References for 2.1 153 00Car Carrig
Page 123 and 124: References for 2.1 155 01Hol Holzwa
Page 125 and 126: References for 2.1 157 02Kra1 02Kra
Page 127 and 128: References for 2.1 159 03Kor 03Kow
Page 129 and 130: References for 2.1 161 04Gra Grange
Page 131 and 132: References for 2.1 163 04Zha2 05Agn
Page 133 and 134: References for 2.1 165 05Sch2 Schla
Page 135: 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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