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

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90 2.1.4 Loss modulation [Ref. p. 134 and passively mode-locked miniature lasers (Fig. 2.1.7b) where a short laser crystal defines a simple monolithic cavity. The SESAM attached directly to the laser crystal then formed one end-mirror of this laser cavity. As the laser cannot be pumped through the SESAM, the laser output needs to be separated from the collinear pump by a dichroic mirror. These examples suggest that there is need for a device that combines the nonlinear properties of the SESAM with an output coupler. This has been demonstrated before for a passively mode-locked fiber laser [96Sha] and later also for solid-state lasers [01Spu1]. 2.1.4.4 Effective saturable absorbers using the Kerr effect 2.1.4.4.1 Transverse and longitudinal Kerr effect The extremely rapid response and the broad bandwidth of the Kerr nonlinearity are very attractive for a mode-locking process. For high intensities, the polarization inside a dielectric medium does not proportionally follow the electric field anymore. This gives rise to an index change proportional to intensity. Off-resonance, this nonlinear optical effect is extremely fast, with estimated response times in the few-femtosecond range. The transverse and longitudinal effects resulting from the intensity dependence are shown schematically in Fig. 2.1.13. The transverse Kerr effect retards the central and most intense part of a plane wave front and thus acts as a focusing lens, referred to as the Kerr lens. Along the axis of propagation, the longitudinal Kerr effect retards the center of an optical pulse, producing a red shift of the leading part of the pulse, and a blue shift in the trailing part. Consequently, the longitudinal Kerr effect has been named Self-Phase Modulation (SPM). Longitudinal Kerr effect: self phase modulation (SPM) n( z)= n2I ( z) Transverse Kerr effect: Kerr lens n( xy , ) = n2I( xy , ) Fig. 2.1.13. The Kerr effect gives rise to an increase of the refractive index with intensity, causing a retardation of the most intense parts of a pulse (i.e. for n 2 > 0). In its longitudinal form, the Kerr effect causes Self-Phase Modulation (SPM) and in its transverse form, a nonlinear lens is formed in the central part of the beam profiles (i.e. Kerr lens). 2.1.4.4.2 Nonlinear coupled cavity The longitudinal Kerr effect can also be used to produce the same effect as a fast saturable absorber. To do this, the phase nonlinearity provided by the longitudinal Kerr effect has to be converted into an effective amplitude nonlinearity. The earliest mode-locking schemes based only on SPM used a coupled cavity to convert SPM into SAM. In the soliton laser [84Mol], pulses compressed by SPM and anomalous dispersion in the coupled cavity are directly coupled back into the main laser cavity. This provides more gain for the center of the pulse. Pulses as short as 19 fs have been Landolt-Börnstein New Series VIII/1B1
Ref. p. 134] 2.1 Ultrafast solid-state lasers 91 demonstrated with color-center lasers [87Mit]. Later, the SPM-to-SAM conversion with a coupled cavity was demonstrated even when the pulses inside the coupled cavity were broadened due to positive group velocity dispersion [89Kea]. In this case, no compressed pulse was fed back into the main cavity. An effective SAM was obtained because SPM inside the coupled cavity generates a phase modulation on the pulse that adds constructively at the peak of the pulse in the main cavity and destructively in the wings, thus shortening the pulse duration inside the main cavity. This was also later referred to as Additive Pulse Mode-locking (APM) [89Ipp]. Although very powerful in principle, these coupled-cavity schemes have the severe disadvantage that the auxiliary cavity has to be stabilized interferometrically. An alternative method for converting the reactive Kerr nonlinearity into an effective saturable absorber was discovered in 1991: Kerr-Lens Mode-locking (KLM) [91Spe]. 2.1.4.4.3 Kerr lens The discovery of Kerr-lens mode-locking has been a breakthrough in ultrashort pulse generation [91Spe]. Initially the mode-locking mechanism was not understood and was somewhat of a mystery. But within a short time after the initial discovery it became clear that the transverse Kerr effect provides a fast saturable absorber. In KLM, the transverse Kerr effect produces a Kerr lens (Fig. 2.1.13) that focuses the high-intensity part of the beam more strongly than the low-intensity part. Thus, combined with an intracavity aperture the Kerr lens produces less loss for high intensity and forms an effective fast saturable absorber [91Kel, 91Sal1, 91Neg] (Fig. 2.1.14). A similar modelocking effect can be obtained without a hard aperture when the Kerr lens produces an increased Incident beam Δn = n 2 I (r,t ) Nonlinear medium Kerr lens Aperture Intense pulse Low−intensity light Loss Saturated gain Pulse Time t Fig. 2.1.14. Kerr-Lens Mode-locking (KLM) is obtained due to the Kerr lens at an intracavity focus in the gain medium or in another material, where the refractive index is increased with increased intensity Δn = n 2I(r, t), where n 2 is the nonlinear refractive index and I(r, t) the radial- and time-dependent intensity of a short-pulsed laser beam. In combination with a hard aperture inside the cavity, the cavity design is made such that the Kerr lens reduces the laser mode area for high intensities at the aperture and therefore forms an effective fast saturable absorber. In most cases, however, soft-aperture KLM is used where the reduced mode area in the gain medium improves for a short time the overlap with the (strongly focused) pump beam and therefore the effective gain. A significant change in mode size is only achieved by operating the laser cavity near one of the stability limits of the cavity. Landolt-Börnstein New Series VIII/1B1
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2.1 Ultrafast solid-state lasers - ETH - the Keller Group

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