Kerr lens mode locking

A. A. Lagatsky, C. T. A. Brown, W. Sibbett, Highly efficient and low threshold diode-pumped, Kerr-lens mode-locked Yb KYW laser, Optics Express 12, 3928 (2004)... 

Abstract. We present a frequency comparison and an absolute frequency measurement of two independent -stabilized frequency-doubled Nd YAG lasers at 532 nm, one set up at the Institute of Laser Physics, Novosibirsk, Russia, the other at the Physikalisch-Technische Bundesanstalt, Braunschweig, Germany. The absolute frequency of the l2-stabilized lasers was determined using a CH4-stabilized He-Ne laser as a reference. This laser had been calibrated prior to the measurement by an atomic cesium fountain clock. The frequency chain linking phase-coherently the two frequencies made use of the frequency comb of a Kerr-lens mode-locked Ti sapphire femtosecond laser where the comb mode separation was controlled by a local cesium atomic clock. A new value for the R.(56)32-0 aio component, recommended by the Comite International des Poids et Mesures (CIPM) for the realization of the metre [1], was obtained with reduced uncertainty. Absolute frequencies of the R(56)32-0 and P(54)32-0 iodine absorp tion lines together with the hyperfine line separations were measured. 

The frequency chain works as follows to the second harmonic of the He-Ne laser at 3.39 jum a NaCl OH color center laser at 1.70 pm is phase locked. To the second harmonic of the color center laser a laser diode at 848 nm is then phase locked. This is accomplished by first locking the laser diode to a selected mode of the frequency comb of a Kerr-lens mode-locked Ti sapphire femtosecond laser (Coherent model Mira 900), frequency-broadened in a standard single-mode silica fiber (Newport FS-F), and then controlling the position of the comb in frequency space [21,11]. At the same time the combs mode separation of 76 MHz is controlled by a local cesium atomic clock [22]. With one mode locked to the 4th harmonic of the CH4 standard and at the same time the pulse repetition rate (i.e. the mode separation) fixed [22], the femtosecond frequency comb provides a dense grid of reference frequencies known with the same fractional precision as the He-Ne S tandard [23,21,11]. With this tool a frequency interval of about 37 THz is bridged to lock a laser diode at 946 nm to the frequency comb, positioned n = 482 285 modes to lower frequencies from the initial mode at 848 nm. 

Fig. 3. Set-up of the frequency chain used to measure the absolute frequency of the two iodine spectrometers. The chain links the 532 nm radiation of the frequency doubled Nd YAG lasers (563 THz) to a methane-stabilized He-Ne laser at 3.39 /rm (88 THz). The two input frequencies of the frequency interval divider stage at 852 nm and 946 nm determine the frequency of the NdtYAG lasers at 1064 nm. The input frequencies are phase-coherently linked to the methane-stabilized He-Ne laser at 3.39 /xm by use of a frequency comb generated with a Kerr-lens mode-locked femtosecond laser...

In passive mode-locking, an additional element in the cavity can be a saturable absorber (e.g., an organic dye), which absorbs and thus attenuates low-intensity modes but transmits strong pulses. Kerr lens mode-locking exploits the optical Kerr63 or DC quadratic electro-optic effect here the refractive index is changed by An = (c/v) K E2, where E is the electric field and K is the Kerr constant. 

The shortest directly produced optical pulses, produced by Kerr-lens mode-locked Ti-sapphire lasers, last around 3.4fs = 3.4 x 10 15s. However, the minimum pulse duration is limited by the period of the carrier frequency (which is about 2.7 fs for Ti S systems). Some advanced techniques (involving high harmonic generation with amplified fs laser pulses) can be used to produce pulses as short as 10 16s for X < 30 nm. 

During the last decade, solid-state lasers captured the market and substituted the complex dye systems more and more (Fig. 1). The breakthrough for solid-state femtosecond oscillators was connected with the development of the Kerr lens mode-locking technique for the Tiisapphire laser [7]. The simple Tiisapphire cavity contains the active medium (Tiisapphire rod) and dispersive elements. Kerr lensing in a Tiisapphire rod develops due to an intensity-dependent refractive index across the spatial beam profile yielding a self-focusing of the laser beam. With an additional aperture in the beam... 

Fig. 2 Kerr lens mode-locking technique for the Ti sapphire laser...

Nearly transform-limited pulses of 100 fs duration are generated from an Ar -laser-pumped Kerr-lens mode locked Ti S oscillator (Coherent Mira 900). Pulses at a repetition rate of 76 MHz and at an average power of about 1 W (10 nJ/pulse, 100 kW peak power) are obtained. The 100 fs pulsewidth is determined by remaining, non-compensated group-velocity dispersion in the oscillator cavity and can be further reduced. 

Tokurakawa M, Shirakawa A, Ueda K-i, Yagi H, Yanagitani T, Kaminskii AA (2007) Diode-pumped sub-100 fs Kerr-lens mode-locked Yb Sc203 ceramic laser. Opt Lett 32 3382-3384... 

Kerr lens mode locking Optical Kerr effect Ti sapphire <10 fs 10-100 nJ... 

Fig. 6.23 Schematic illustration of Kerr lens mode locking inside the laser resonator [679]...

A Kerr-lens mode-locked Ti Sapphire laser with a threshold that is ten times less than in conventional Kerr-lens lasers has been reported by Fujimoto and his group [679]. The schematic diagram of this design with an astigmatically compensated folded cavity is shown in Fig. 6.25. The dispersion of the cavity is compensated by a prism pair and the output coupler has a transmission of I %. The low threshold permits the use of low-power inexpensive pump lasers. 

Fig. 6.25 Schematic diagram of the ultralow-threshold Ti Al203 laser with Kerr-lens mode-locking [680]...

In Table 6.1 the different techniques for the generation of short laser pulses and their typical parameters are compared. It shows that pulse widths below I ps can be achieved with the CPM technique and with Kerr lens mode-locking. In the next section we will discuss how short laser pulses can be further compressed by nonlinear effects in optical fibres. 

Another alternative for the generation of ultrafast pulses is the passive mode locking by fast semiconductor saturable absorbers in front of chirped mirrors (Fig. 6.35) in combination with Kerr lens mode locking [694]. The recovery time of the saturable absorber must be generally faster then the laser pulse width. This is provided by KLM, which may be regarded as artificial saturable absorber that is as fast as the Kerr nonlinearity following the laser intensity. Since the recovery time in a semi-... 

Recently, a new technique has been developed [1323] that allows the direct comparison of widely different reference frequencies and thus considerably simplifies the frequency chain from the cesium clock to optical frequencies by reducing it to a single step. Its basic principle can be understood as follows (Fig. 9.91) The frequency spectrum of a mode-locked continuous laser emitting a regular train of short pulses with repetition rate 1/AT consists of a comb of equally spaced frequency components (the modes of the laser resonator). The spectral width Aw = 2jt/T of this comb spectrum depends on the temporal width T/Ar of the laser pulses (Fourier theorem). Using femtosecond pulses from a Tusapphire Kerr lens mode-locked laser, the comb spectrum extends over more than 30 THz. 

For the first time range, ultrashort laser pulses generated by mode-locked lasers in the femto- to picosecond range (Chap. 6) are needed, whereas for the second class of experiments pulsed lasers in the nanosecond to microsecond range (Q-switched CO2 lasers, excimers, or dye lasers) can be employed. Most experiments performed until now have used pulsed CO2 lasers, chemical lasers, or excimer lasers. For femtosecond pulses Kerr-lens mode-locked Tiisapphire lasers with subsequent amplifier stages are available (see Sect. 6.1). 

Robertson, A., Knappe, R., and Wallenstein, R. (1997). Kerr-lens mode-locked Cr LiS AF femtosecond laser pumped by the dififraetion-limited output of a 672-nm diode-laser master-oscillator power-amplifier system, J. Opt. Soc. Am. B 14, 672. 

Passive mode-locking can be achieved, for example, by using saturable-absorber modulators or a Kerr lens mode-locking modulator. If placed in the resonator, they cause less intense radiation to be damped out, ultimately leaving only a single, intense pulse oscillating back and forth. Here, only Kerr-lens mode locking will be described. 

Kerr lens mode locking optical Ken-effect Ti sapphire < lOfs 1-lOnJ... 

The crucial breakthrough for the realization of ultrafast pulses below lOOfs was the discovery of a fast pulse-forming mechanism in 1991, Kerr lens mode locking (KLM), which can be understood as follows ... 

In Fig. 11.22 the experimental setup for a femtosecond Tiisapphire laser with Kerr lens mode locking is shown, where the amplifying laser medium acts simultaneously as a Kerr lens. The folded resonator is designed in such a way that only the most intense part of the pulse is sufficiently focused by the Kerr lens to always pass for every round-trip through the spatially confined... 

H. A. Haus, J.G. Fujimoto, and E.P. Ippen, Analytic Theory of Additive Pulse and Kerr Lens Mode Locking , IEEE Quant. Electr. 28, 2086 (1992). 

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