Numerical investigation of enhanced femtosecond supercontinuum via a weak seed in noble gases.

Numerical simulations are employed to elucidate the physics underlying the enhanced femtosecond supercontinuum generation previously observed during optical filamentation in noble gases and in the presence of a weak seed pulse. Simulations based on the metastable electronic state approach are shown not only to capture the qualitative features of the experiment, but also reveal the relation of the observed enhancement to recent developments in the area of sub-cycle engineering of filaments.

High-dynamic-range cascaded-focus optical limiter.

We report experimental results of using an f/5 , cascaded-focus optical geometry for a high-dynamic-range optical limiter. The device consists of a 2-cm-thick CS(2) cell at the first focus and a reverse saturable-absorber dye in a thin cell (0.1 mm) at the second focus. The strong self-focusing in the CS(2) that is due to the ac Kerr effect and electrostriction keeps the energy at the second cell below its damage threshold. Using lead phthalocyanine in chloroform as the reverse saturable-absorption material, we clamped the maximum output energy below 1muJ for input energies up to 14.5 mJ without damage. We used a frequency-doubled, Q -switched 5-ns (FWHM) Nd:YAG laser operating at a 10-Hz repetition rate. The measured dynamic range of the device is at least 7500.

Investigation of an optical limiting mechanism in multiwalled carbon nanotubes.

We report our investigation of the mechanism that is responsible for the optical limiting behavior in multiwalled carbon nanotubes. We conducted energy-dependent transmission measurements, picosecond time-resolved pump-probe experiment, and nonlinear scattering experiments at 532-nm wavelength on multiwalled carbon nanotube suspension. For comparison, C(60)-toluene solutions and carbon black suspensions were also studied in the same experiments. The similarities that we observed between the multiwalled carbon nanotubes and carbon black suspension suggest that nonlinear scattering, which is known to be responsible for the limiting action in carbon black suspension, should play an important role in the limiting effect in multiwalled carbon nanotubes.

Nonlinear optical beam propagation for optical limiting.

We implement numerical modeling of high-energy laser-pulse propagation through bulk nonlinear optical materials using focused beams. An executable program with a graphical user interface is made available to researchers for modeling the propagation of beams through materials much thicker than the diffraction length (up to 10(3) times longer). Ultrafast nonlinearities of the bound-electronic Kerr effect and two-photon absorption as well as time-dependent excited-state and thermal nonlinearities are taken into account. The hydrodynamic equations describing the rarefaction of the medium that is due to heating are solved to determine thermal index changes for nanosecond laser pulses. We also show how this effect can be simplified in some cases by an approximation that assumes instantaneous expansion (so-called thermal lensing approximation). Comparisons of numerical results with several Z-scan, optical limiting and beam distortion experiments are presented. Possible application to optimization of a passive optical limiter design is discussed.

Optimization of optical limiting devices based on excited-state absorption.

Limiting devices protect sensitive optical elements from laser-induced damage (LID). Passive devices use focusing optics to concentrate the light through a nonlinear optical (NLO) element (or elements) to reduce the limiting threshold. Unfortunately, these NLO elements may themselves undergo LID for high inputs, restricting the useful dynamic range (DR). Recently, efforts at optimizing this DR have focused on distributing the NLO material along the propagation path z of a focused beam, resulting in different portions of the device (in z) exhibiting NLO response at different inputs. For example, nonlinear absorbers closer to the lens, i.e., upstream, protect device elements downstream near the focal plane. This results in an undesirable increase in the threshold, although the lowest threshold is always obtained with the final element at focus. Thus there is a compromise between DR and threshold. This compromise is determined by the material. We concentrate on reverse saturable absorber (RSA) materials (molecules exhibiting larger excited-state than ground-state absorption). We look at both tandem devices and devices in which the concentration of the NLO material is allowed to spatially vary in z. These latter devices require solid-state hosts. The damage threshold of currently available solid-state hosts is too low to allow known RSA materials to reach their maximum absorption, which occurs when all molecules are in their excited state. This is demonstrated by approximate analytical methods as well as by a full numerical solution of the nonlinear wave propagation equation over extremely large distances in z (up to 10(3)Z(0), where Z(0) is the Rayleigh range of the focused beam). The numerical calculations, based on a one-dimensional fast Fourier transform, indicate that proper inclusion of diffraction reduces the effectiveness of reverse saturable absorption for limiting, sometimes by more than a factor of 10. Liquid-based devices have higher damage thresholds (damage occurs to the cuvette wall) and, thus, larger nonlinear absorption. However, RSA material in liquid hosts may suffer from larger thermal lensing.

Measurement of the optical damage threshold in fused quartz.

The damage thresholds of five different types of quartz glass used for the production of spectroscopic cuvettes for liquids were determined with single temporal and spatial mode nanosecond pulses at 532 nm. One of the glasses had a damage threshold of ≃420 J/cm(2), which was more than twice that of the other glasses.

Eclipsing Z-scan measurement of lambda/10(4) wave-front distortion.

We introduce a simple modification to the Z-scan technique that results in a sensitivity enhancement that permits measurement of nonlinearly induced wave-front distortion of =lambda/10(4). This sensitivity was achieved with 10-Hz repetition-rate pulsed laser sources. Sensitivity to nonlinear absorption is also enhanced by a factor of =3. This method permits characterization of nonlinear thin films without the need for waveguiding.

Phase-controlled transistor action by cascading of second-order nonlinearities in KTP.

We demonstrate a 4.6-to-1 modulation depth imposed on the fluence of an intense 1.06-microm picosecond pulse by varying the relative phase of a weak second-harmonic control pulse under near phase-matched conditions. This transistorlike action is based on quadratic nonlinearities in KTP.

Self-focusing and self-defocusing by cascaded second-order effects in KTP.

We monitor the induced phase change produced by a cascaded chi((2)):chi((2)) process in KTP near the phase-matching angle on a picosecond 1.06-microm-wavelength beam using the Z-scan technique. This nonlinear refraction is observed to change sign as the crystal is rotated through the phase-match angle in accordance with theory. This theory predicts the maximum small-signal effective nonlinear refractive index of n(eff)(2) congruent with +/-2 x 10(-14) cm(2)/W (+/-1 x 10(-11) esu) for an angle detuning of +/-5 degrees from phase match for this 1-mm-thick crystal with a measured d(eff) of 3.1 pm/V. For a fixed phase mismatch, this n(eff)(2) scales linearly with length and as d(eff)(2) however, for the maximum n(eff)(2) the nonlinear phase distortion becomes sublinear with irradiance for phase shifts near pi/4.

High-sensitivity, single-beam n(2) measurements.

We present a simple yet highly sensitive single-beam experimental technique for the determination of both the sign and magnitude of n(2). The sample is moved along the z direction of a focused Gaussian beam while the repetitively pulsed laser energy is held fixed. The resultant plot of transmittance through an aperture in the far field yields a dispersion-shaped curve from which n(2) is easily calculated. A transmittance change of 1% corresponds to a phase distortion of approximately lambda/250. We demonstrate this method on several materials using both CO(2) and Nd:YAG laser pulses.

Self-protecting semiconductor optical limiters.

We present a detailed characterization of passive, picosecond optical-power-limiting devices using tightly focused beams in thick semiconductor samples. This study of limiting in ZnSe with 30-psec, 532-nm pulses shows that the resulting internal self-action (two-photon absorption plus free-carrier self-defocusing) protects the bulk material from optical damage. Simple scaling relations were determined from our results that link the limiting energy and the dynamic range to the focusing geometry and sample dimensions. These relations were used to design a monolithic optical limiter, optimized to have maximum dynamic range and minimum limiting energy. This device limits at an input energy of 10 nJ (300 W) and has a dynamic range greater than 10(4).

Effect of linear absorption on self-focusing.

We report the effect of linear absorption on self-focusing. Our experimental results show that power loss due to linear absorption before focus is responsible for the increase in the threshold power for self-focusing and that the critical power is independent of the linear absorption.

Self-defocusing in CdSe induced by charge carriers created by two-photon absorption.

We observe self-defocusing of picosecond, 1.06-microm pulses in CdSe. The effective nonlinear refraction can be 2 orders of magnitude larger than that of CS(2). We obtain good agreement with the theory presented here, which assumes that the self-refraction is caused by charge carriers created by two-photon absorption.

Self-focusing in CS(2) at 10.6 microm.

We have measured the nonlinear refractive index, n(2), of CS(2) at 10.6 microm by observing the onset of whole-beam selffocusing. We find that n(2) is (2.2 +/- 0.7) x 10(-10) esu, which is over an order of magnitude larger than n(2) in the visible.

Energy band-gap dependence of two-photon absorption.

We present measurements of the two-photon absorption coefficients beta(2) of 10 different semiconductors having band-gap energies between 1.4 and 3.7 eV. We find that beta(2) varies as E(g)(-3), as predicted by theory. In addition, the absolute values of beta(2) agree with theory, which includes the effect of nonparabolic bands, the average difference being less than 26%. This agreement permits confident predictions of two-photon absorption coefficients of other materials at other wavelengths.