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

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110 2.1.6 Mode-locking techniques [Ref. p. 134 This analytical result can explain the much shorter 7–12 ps pulses in actively mode-locked diode-pumped Nd:YAG [89Mak1] and Nd:YLF [89Mak2, 90Kel1, 90Wei, 90Juh] lasers because the laser mode area in those diode-pumped lasers is very small which results in significant SPM pulse shortening (2.1.54). For example, our experiments with an actively mode-locked diode-pumped Nd:YLF laser [95Bra2] are very well explained with (2.1.54). In this case the lasing wavelength is 1.047 μm, the gain bandwidth is Δλ g =1.3 nm, the pulse repetition rate is 250 MHz, the output coupler is 2.5 %, the average output power is 620 mW, the mode radius inside the 5 mm long Nd:YLF crystal is 127 μm × 87 μm and the loss modulation of the acousto-optic mode-locker is about 20 %. We then obtain a FWHM pulse duration of 17.8 ps (2.1.54) which agrees well with the experimentally observed pulse duration of 17 ps. Without SPM we would predict a pulse duration of 33 ps (2.1.49). Equation (2.1.54) would predict that more SPM continues to reduce the pulse duration. However, too much SPM will ultimately drive the laser unstable. This has been shown by the numerical simulations of Haus and Silberberg [86Hau] which predict that pulse shortening in an actively modelocked system is limited by roughly a factor of 2 in the case of SPM only. They also showed that the addition of negative GVD can undo the chirp introduced by SPM, and therefore both effects together may lead to stable pulse shortening by a factor of 2.5. However, experimental results with fiber lasers and solid-state lasers indicate that soliton shaping in the negative GVD regime can lead to pulse stabilization and considerable more pulse shortening. We have extended the analysis of Haus and Silberberg by investigating the possible reduction in pulse width of an actively mode-locked laser as a result of soliton-like pulse formation, i.e., the presence of SPM and an excessive amount of negative GVD [95Kae2]. We show, by means of soliton perturbation theory, that beyond a critical amount of negative GVD a soliton-like pulse is formed and kept stable by an active mode-locker. If the bandwidth of the gain is large enough, the width of this solitary pulse can be much less than the width of a Gaussian pulse generated by the active mode-locker and gain dispersion alone. We established analytically that the pulse shortening possible by addition of SPM and GVD does not have a firm limit of 2.5. Numerical simulations and experiments with a regeneratively actively mode-locked Nd:glass laser [94Kop2] confirm these analytical results. The pulse-width reduction achievable depends on the amount of negative GVD available. For an actively mode-locked Nd:glass laser a pulse shortening up to a factor of 6 may result, until instabilities arise. 2.1.6.4 Passive mode-locking with a slow saturable absorber and dynamic gain saturation Dynamic gain saturation can strongly support pulse formation in passive mode-locking and has allowed pulses with duration much shorter than the absorber recovery time. Dynamic gain saturation means that the gain undergoes a fast pulse-induced saturation that recovers between consecutive pulses. This technique has been used to produce sub-100-fs pulses with dye lasers and dye saturable absorbers even though the absorber recovery time was in the nanosecond regime. Dynamic gain saturation can only help if the following conditions are fulfilled (Fig. 2.1.5a): 1. The loss needs to be larger than the gain before the pulse: q 0 >g 0 , (2.1.56) where q 0 is the unsaturated loss coefficient (2.1.6) and g 0 is the small signal gain coefficient in the laser. 2. The absorber needs to saturate faster than the gain. From (2.1.14) (i.e. slow saturable absorber and gain) then follows that Landolt-Börnstein New Series VIII/1B1
Ref. p. 134] 2.1 Ultrafast solid-state lasers 111 Table 2.1.12. Femtosecond Rhodamin 6G dye laser with its saturable absorber DODCI at a wavelength of 620 nm. σ L gain and σ A absorber cross-section, τ L upper-state lifetime, τ A absorber recovery time. Dye material Cross-section Time Rhodamin 6G σ L =1.36 × 10 −16 cm 2 τ L =4ns DODCI σ A =0.52 × 10 −16 cm 2 τ A =2.2 ns Photoisomer ˜σ A =1.08 × 10 −16 cm 2 ˜τ L =1ns E sat,A
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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
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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 2.1 165 05Sch2 Schla
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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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