Kerr-lens Mode-locked Laser Research Articles

Mechanism of pulse shaping in femtosecond lasers based on the high-order soliton

The mechanism of pulse shaping in Kerr-lens mode-locking Ti : sapphire lasers is investigated. Considering the balanced interaction between self-phase modulation, introduced by Kerr effect in Ti : sapphire, and group-velocity dispersion provided by prism-pair, pulse-splitting reflected in the intensity autocorrelation trace and pulse-compression display that the pulses outputting from different positions in laser cavity have different durations. We have concluded that the solitonlike pulse shaping that results from the competition between intracavity self-phase modulation within the Ti : S and negative group-velocity dispersion play dominant role in pulse evolution in Kerr-lens mode-locking lasers.

Bifurcation of fundamental Gaussian modes in Kerr-lens mode-locked lasers

We propose that more than one spatial fundamental Gaussian mode may occur in concentric and confocal resonators under persisting nonlinear effect. Extensively studying the influence of the resonator's parameters in a Kerr-lens mode-locked resonator, pitchfork bifurcation results in more symmetrical configurations, and saddle-node bifurcation appears as the symmetry being broken. From the properties of bifurcation, we suggest that the equal-arm and near-confocal resonator is suitable for the emergence of bistability in Kerr-lens mode-locked lasers.

Absolute Optical Frequency Measurement of the CesiumD1Line with a Mode-Locked Laser

We have measured the absolute optical frequency of the cesium ${D}_{1}$ line at 335 THz (895 nm). This frequency provides an important link for a new determination of the fine structure constant $\ensuremath{\alpha}$. The ${D}_{1}$ line has been compared with the fourth harmonic of a methane stabilized He-Ne laser at 88.4 THz ( $3.39\ensuremath{\mu}\mathrm{m}$). To measure the frequency mismatch of 18.39 THz between $4\ifmmode\times\else\texttimes\fi{}88.4\mathrm{THz}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}354\mathrm{THz}$ and the ${D}_{1}$ line a frequency comb spanning around 244 000 modes of a Kerr-lens mode-locked laser was used. We find 1 167 688 (81) kHz for the hyperfine splitting of the ${6P}_{1/2}$ state and 335 116 048 807 (41) kHz for the hyperfine centroid from which we derive ${\ensuremath{\alpha}}^{\ensuremath{-}1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}137.0359924(41)$.

Low-repetition-rate high-peak-power Kerr-lens mode-locked Ti:Al_2O_3 laser with a multiple-pass cavity

We demonstrate a novel, long, multiple-pass cavity (MPC) to obtain low repetition rates and high peak intensities from Kerr-lens mode-locked lasers. We show that the MPC provides a zero effective length by a unity transformation of the q parameter after a given number of transits of the laser beam. Pulse durations of 16.5 fs with 0.7 MW of power at a 15-MHz repetition rate are achieved. This is, to our knowledge, the lowest repetition rate ever achieved directly from a femtosecond laser resonator without use of additional active devices and cavity dumping. The combination of low repetition rates and high peak intensity is extremely useful for femtosecond pump-probe and other nonlinear experiments because it permits the application of high peak intensity without excessive average power.

Dynamical gain saturation in Kerr-lens mode-locked CW solid- state lasers

It is shown that dynamical gain saturation, usually neglected for solid-state lasers, can contribute significantly to the pulse-shaping mechanism in Kerr-lens mode-locked lasers. In particular, in combination with self-phase modulation it can cause red shifts and blue shifts of the laser spectrum. A control of the reciprocal gain and loss saturation rates using these shifts leads to improved mode- locking stability.

Absorber-assisted Kerr-lens mode locking

We study mode locking of a titanium-doped sapphire laser with a slow saturable absorber in the cavity. We show that the presence of the absorber stabilizes the pulsed mode of laser operation over a broader range of cavity mirror position and for a wider aperture. However, the basic principle of operation is unchanged from that of a conventional Kerr-lens mode-locked laser, in that, in all cases, we observed strong space–time focusing of the pulses into the laser crystal. Thus the absorber cannot lead to shortening of the pulse below the limit imposed by the Kerr-lens mode locking.

Thick lens model for self-focusing in Kerr medium

An asymmetric “thick-lens” model for self-focusing in Kerr medium of finite thickness is presented by introducing a complex curvature radius of a Gaussian beam in nonlinear medium and a transfer matrix for the transition from linear to nonlinear medium. With this model the linear ABCD-matrix formalism can be extended to nonlinear optical systems with a clear physical insight. The modulation of the cavity transverse mode of a resonator containing a Kerr medium is characterized by the asymmetry of the “thick lens.” The intracavity small-signal relative spot size variation outside as well as inside the Kerr medium can be calculated efficiently with the “thick-lens”-like matrix formalisms. Criteria for the design and optimization of a Kerr-lens mode-locked laser resonator with a hard or soft aperture are predicted.

Kerr-lens mode-locked laser model: role of space time effects

A spatio-temporal model of a self-mode-locked laser is presented. It uses a full wave-optics approximation of the propagation in the laser resonator and includes dispersion, self-phase modulation, and self-focusing of the intracavity radiation. It is shown that the self-consistent evolution of the pulse toward steady state imposes strong space–time focusing in the crystal, where both the space and time foci are located. This combined focusing is inherent for Kerr-lens mode-locked lasers with linear and ring cavities, and with and without intracavity saturable absorbers. It is considered as a general mechanism for compensation of space–time astigmatism within the nonlinear resonator. The predictions of the model agree very well with the experiment.

Spatiotemporal model of femtosecond pulse generation in Kerr-lens mode-locked solid-state lasers

A spatiotemporal model for the evolution process of the pulse and beam shapes in femtosecond Kerr-lens mode-locked solid-state lasers is presented. For different cavity configurations we comprehensively studied the dependence of the pulse and beam parameters on laser-control parameters such as pump rate, linear phase dispersion up to fourth order, self-phase modulation, and self-amplitude modulation owing to nonlinear resonator transmission. We determine the conditions for the ultimate shortest pulse duration. The influence of third- and fourth-order dispersion results in spectral sidebands, which are phase matched with the peak of the principal spectrum. Excessive fourth-order dispersion yields a steady-state multipulse operating regime with constant peak separation.

Regular, quasi-periodic, and chaotic behavior in continuous-wave solid-state Kerr-lens mode-locked lasers

The nonlinear dynamics of a four-mirror Kerr-lens mode-locked laser is investigated. It is shown that the mode-locking regime contains the windows of nonregular behavior. Theoretical predictions are confirmed by numerical experiments based on the fluctuation model.

Cavity design of a compact Kerr-lens mode-locking laser

The non-astigmatic three-element cavity Ti:sapphire laser is attractive because of its simple and compact stable resonator structure. Analytical equations for Kerr nonlinear pulse-shaping strengths are derived by using the ABCD transfer matrix method. Both hard-aperturing and soft-aperturing for effective Kerr-lens mode-locking are discussed. The dependence of the mode-locking condition on cavity length is also addressed.

Experimental determination of the nonlinear refractive index in an operating Cr:forsterite femtosecond laser

The characteristics of a femtosecond forsterite Kerr-lens mode-locked laser pumped synchronously by an Nd:YAG laser are reported. Transform-limited femtosecond pulses of 60-fs (FWHM) duration with average TEM 00 output powers of 200 mW at 1.25 μm were generated. Experimental studies of power stability and self-starting regime are described and a new experimental method to determine the nonlinear refractive index of the chromium-doped forsterite crystal (which is either the laser rod) is reported. We infer a value of 6 × 10 −16 cm 2/W at 1.25 μm, making possible Kerr-lens mode-locking.

Higher-order phase dispersion in femtosecond Kerr-lens mode-locked solid-state lasers: sideband generation and pulse splitting

The influence of higher-order phase dispersion on the pulse generation in femtosecond Kerr-lens mode-locked lasers for small net group-velocity dispersion is numerically analyzed. Depending on the third- and the fourth-order dispersion, we obtain the formation of spectral sidebands phase matched with the principal spectrum. At a relatively large amount of fourth-order dispersion pulse splitting arises, which leads to a quasi-steady-state multipulse operation regime of the Kerr-lens mode-locked laser.

Compact geometry for diode-pumped Cr:LiSAF femtosecond laser

A novel geometry for dispersion compensation in femtosecond lasers without specific cut of optical parts in a flat/Brewster angle or Gires-Tournots mirrors is demonstrated for attaining a compact diode-pumped Cr:LiSAF femtosecond pulse laser. In this geometry, the laser medium lies between the dispersion-compensation prism pair. This approach enables the laser to operate at variable repetition rates from 163 to 235 MHz keeping the pulsewidth less than 90 fs, where the value of the time-bandwidth product are not larger than 0.34. An 89 fs pulse duration generated at the 235 MHz repetition rate is, to our knowledge, the shortest pulse achieved in an all-solid-state Kerr-lens mode-locked laser operating above the 200 MHz repetition rate.

Kerr-lens mode locking without dispersion compensation

We propose and theoretically investigate a novel operating regime of femtosecond Kerr-lens mode-locked solidstate lasers that avoids group-velocity dispersion compensation by use of a nonresonant semiconductor plate in the focused resonator section that provides an overall negative nonlinear refractive index per round trip. The saturable loss of the laser resonator with an effective self-defocusing nonlinearity is derived from a generalized ABCD matrix formalism, and the correspondingly calculated steady-state pulse parameters show that a Kerrlens mode-locked laser with an overall negative nonlinear refractive index generates stable femtosecond pulses without any dispersion compensation.

Sub-10-fs operation of Kerr-lens mode-locked lasers

We present results of a three-dimensional model of a Kerr-lens mode-locked titanium-doped sapphire laser in the sub-10-fs regime of operation. We find that space-time focusing of the pulse within the laser crystal imposes a limitation on the pulse duration as a function of the crystal length. Thus good compensation of the net group-velocity dispersion of the cavity is not sufficient for successful sub-10-fs operation of the laser. The dependence of the pulse duration on the intracavity dispersion is also presented, which demonstrates that pulses as short as 6 fs can be generated directly from the laser.

Rapid acquisition of in vivo biological images by use of optical coherence tomography

The development of techniques for high-speed image acquisition in optical coherence tomography (OCT) systems is essential for suppressing motion artifacts when one is imaging living systems. We describe a new OCT system for performing micrometer-scale, cross-sectional optical imaging at four images/s. To achieve OCT image-acquisition times of less than 1 s, we use a piezoelectric fiber stretcher to vary the reference arm delay. A Kerr-lens mode-locked chromium-doped forsterite laser is employed as the low-coherence source for the highspeed OCT system. Dynamic, motion-artifact-free in vivo imaging of a beating Xenopus laevis (African frog) heart is demonstrated.

Multidimensional coupling owing to optical nonlinearities I General formulation

A beam propagating in a nonlinear, dispersive medium can experience nonlinear coupling among its parameters in the x, y, and t dimensions. We derive two new computational techniques that account for this coupling. The first technique uses the beam-propagation method to solve three coupled differential equations, and the second uses six coupled second-moment equations. Nonlinear coupling is especially important for the operation of self-mode-locked (Kerr-lens mode-locked) lasers, an example of which is considered in detail in an accompanying paper [ J. Opt. Soc. Am.13, 560 ( 1996)]. The two techniques derived here can be adapted to handle most of the physical effects of importance to self-mode-locked lasers, but we concentrate on the effects of diffraction, second- and third-order dispersion, and Kerr nonlinearity.

Experimental study of a self-starting Kerr-lens mode-locked titanium-doped sapphire laser

We report an experimental investigation of self-starting operation of picosecond and femtosecond Kerr-lens mode-locked Ti:sapphire lasers. Pulses as short as 5 ps duration have been generated from self-starting lasers with no intracavity prisms to optimise group velocity dispersion. Self-starting dispersion-compensated lasers have generated pulses as short as 43 fs duration with mode-locking self-starting within 0.7 ms of the onset of laser action.

Femtosecond forsterite Kerr-lens mode-locked laser pumped synchronously by an Nd3+:YAG laser

A femtosecond laser (pulse duration 30 fs, centre of the emission spectrum at λ = 1260 nm) with a chromium-doped forsterite crystal was developed. This laser operated on the basis of Kerr-lens mode locking. Synchronous pumping with an Nd3+:YAG picosecond laser resulted in forced generation of femtosecond pulses characterised by an enhanced stability of the output power, which was 5–7 times better than the stability of the pump laser. The output radiation of the forsterite laser was converted efficiently to the second harmonic (central wavelength 630 nm) in a thin nonlinear BBO crystal. The average power of the second-harmonic radiation was 15 mW.