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Picosecond and nanosecond pulsed laser studies of nonlinear absorption and nonlinear refraction in solutions of metallophthalocyanines and metallonaphthalocyanines are presented. The role of excited state absorption and dynamics in the singlet and triplet manifolds and the implications for passive optical limiters is discussed. Performance of optical limiters based on metallomacrocylic dyes is presented as are results on hybrid optical limiters employing a tandem combination of dye solution and a semiconductor slab.

We calculate the spectrum of three-photon absorption (3PA) in zinc blende semiconductors using Kane's four-band model. We apply this to ZnSe and measure the 3PA spectrum using femtosecond pulses, obtaining excellent agreement. The spectrum shows the apparent onset of 3PA from the split-off band and also shows quantum interference between the several possible evolution pathways when exciting carriers from valence to conduction band.

Narrow bandgap semiconductors exhibit very large optical nonlinearities in the infrared owing to large two-photon absorption that scales as the inverse cube of the bandgap energy and the large losses and refraction from two-photon generated free carriers. Except for extremely short pulses, the free-carrier effects dominate the nonlinear losses and nonlinear refraction. Here we develop a method for the calculation of the free-electron refraction cross section in InSb. We also calculate the Auger recombination coefficient in InSb and find it to be in good agreement with existing experimental data. In all the calculations we rely on Fermi-Dirac statistics and use a four-band k⋅p theory for band structure calculations. Experiments on the transmission of submicrosecond CO2 laser pulses through InSb produce results consistent with the calculated parameters.

We generate a high-spectral-irradiance, high-quality continuum by weakly focusing femtosecond pulses in Kr gas. We use this continuum as a source for rapid Z-scan measurements of the degenerate nonlinear absorption spectrum and the associated dispersion of the nonlinear refraction in optical materials throughout the visible. We measure the degenerate two-photon absorption spectra and the dispersion of the nonlinear refractive index, n2, of two well-characterized semiconductors (ZnSe and ZnS) as reference samples for our method, along with dilute solutions of organic materials. The latter materials demonstrate application of the technique to samples with lower nonlinearities.

We present measurements of nonlinear absorption and refraction in semiconductors used in the realization of optical limiters. We show that nonlinear refraction at 532 nm in ZnSe is caused by a negative third order electronic Kerr effect in addition to the two-photon-absorption (2PA) induced carrier refraction. We have used time-resolved beam distortion, picosecond time-resolved degenerate four-wave mixing and our recently developed Z-scan technique to determine the sign and magnitude of the 2PA coefficient, the bound electronic nonlinearity, n2 and the refractive index change per free carrier.

Nonlinear refractive index and two-photon absorption measurements on semiconductors show that the bound electronic nonlinearity can be calculated from two-photon absorption dispersion via a simple Kramers- Kronig analysis. This analysis shows n2 changing from positive to negative as the photon energy approaches the band-gap energy, consistent with observations. Additionally, this simple calculation, which assumes two parabolic bands, gives good agreement with measured values of n2 in wide-gap dielectrics that are 2 to 3 orders of magnitude smaller than in semiconductors.

We describe a sensitive technique for measuring nonlinear refraction in a variety of materials that offers simplicity, sensitivity and speed. The transmittance of a sample is measured through a finite aperture in the far-field as the sample is moved along the propagation path (z) of a focused Gaussian beam. The sign and magnitude of the nonlinearity is easily deduced from such a transmittance curve (Z-scan). Employing this technique a sensitivity of better than λ/300 wavefront distortion is achieved in n2 measurements of BaF2 using picosecond frequency doubled Nd:YAG laser pulses.

We have performed picosecond Degenerate Four-Wave Mixing (DFWM) experiments and beam distortion experiments, including using the newly developed Z-scan technique,[1] to accurately measure the bound electronic nonlinear refractive index n2 in a variety of materials at 1.06 and 0.53 μm. In semiconductors where two-photon absorption (2PA) is allowed, we find that n2 decreases from its maximum value near the 2PA (2ħω≃Eg) edge to zero as the wavelength is increased, changing to negative nearer the fundamental absorption edge. In order to measure n2, we experimentally separated the effects of 2PA excited carrier refraction (coefficient σ) from the electronic Kerr effect induced refraction. Using DFWM this is accomplished by observing that the carrier effect lasts for hundreds of picoseconds and varies as the fifth power of the incident irradiance I, while the χ(3) effect follows the temporal variation of the pulse and varies as I3. Such a signal is shown in Fig. 1.

We performed a detailed experimental investigation and quantum-chemical analysis of two-photon absorption (2PA) spectra of a series of symmetrical cationic polymethines and neutral squaraines having similar structures. Degenerate 2PA spectra of these molecules are taken by using two-photon fluorescence spectroscopy and the Z-scan technique. All measurements are made with 150 fs laser pulses of 1 kHz repetition rate in the tuning range of 520-2100 nm(0.6-2.4 eV). Comparing 2PA spectra of polymethines and squaraines, we find that we can access considerably larger 2PA cross sections (≥8600×10−50 cm4s/photon) in the squaraines owing to narrower linear absorption spectra and an increase in the density of unoccupied molecular orbitals introduced by the squaraine acceptor group in the conjugated chain.

We performed a comprehensive experimental investigation of two-photon absorption (2PA) spectra of a series of 12 symmetrical and asymmetrical cationic polymethine dyes, including complete one-and two-photon excitation anisotropy measurements. Quantum-chemical calculations were performed with the goal of understanding the nature of 2PA bands and of uncovering structure-property relations. We found that there are 2PA bands in the spectral region between the first absorption band and that for twice its energy. A weakly allowed 2PA band within the short-wavelength shoulder of the first absorption band was observed owing to the effects of vibrational and charge distribution symmetry breaking. The nature of the strongest 2PA band is connected to the electron transition from the molecular orbital localized at the benzene rings of the terminal groups to the lowest unoccupied molecular orbital (LUMO). Structure-property relations revealed that the 2PA cross section tends to be enhanced by either an increase in the length of the polymethine chromophore or an increase in the donor strengths in the terminal groups.

The linear and nonlinear optical properties of a series of polymethine molecules are investigated to study the effects of molecular structure and the host environment on overall nonlinear absorption performance. The linear characterization includes measuring the solvatochromic shifts between absorption and fluorescence peaks and studying the excited-state orientational diffusion kinetics. The nonlinear characterization involves measuring the excited-state absorption spectra with a femtosecond white-light-continuum pump-probe technique and performing Z scans and nonlinear transmission measurements from the picosecond to the nanosecond time regimes. The results of these experiments allow us to develop an energy-level structure for the polymethines, which accurately predicts nonlinear absorption properties from the picosecond to the nanosecond time regimes. From this model we are able to identify the key molecular parameters for improved nonlinear absorption.

We report measurements of frequency degenerate and nondegenerate two-photon absorption (2PA) spectra of CdTe quantum dots, QDs, in glass matrices and compare them with 2PA in bulk CdTe. We find that the 2PA is strongly dependent on the size of the QDs becoming smaller with decreasing size, even when normalizing to the volume of the dots. We adapt a simple degenerate 2PA model, based on the effective mass approximation, to nondegenerate 2PA, and this model correctly describes the experimental data for 2-photon energies up to ~ 1.4Eg. This suggests that, once the spectrum for one size of quantum dot is known, the model can be used for predicting the degenerate and nondegenerate 2PA spectra of different sized QDs of the same semiconductor.

We theoretically and experimentally study absorption of picosecond laser pulses in materials described by a four-level system that exhibit reverse saturable absorption (RSA). Using an approximate solution to the rate equations, we derive, analyze, and verify, numerically and experimentally, a single dynamical equation for the spatial evolution of the pulse fluence that includes both the rate equations and the propagation equation. This analytical approach considerably simplifies the study of optical limiting with picosecond pulses and helps to predict the behavior of the nonlinear transmittance, the level of output signal clamping, and a possible turnover from RSA to saturable absorption that restricts the performance of optical limiters based on RSA. The results obtained can also be used to characterize RSA materials by the pump–probe technique.

We develop an analytical approach to the dynamics of band populations of reverse saturable absorbers modeled by the three-level approximation of the five-level rate equations. We find high-accuracy approximate solutions to these rate equations, taking into account the temporal shape of the incident laser pulse for different regimes of excitation. The results obtained are confirmed by direct numerical integration of the rate equations and are verified by solution of the full system of the rate and the propagation equations. The validity ranges of the approximations are determined. We also prove that for input pulses that are much longer than the lifetime of the first excited state the ground-state depletion obeys the same functional dependence on the input fluence as in the case of rectangular input pulses. The dynamics of the excited states, however, explicitly depends on the pulse shape. We quantitatively estimate the effect of various parameters on the nonlinear absorption coefficient and discuss implementation of the approach by a beam propagation method to reduce the computational time.

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.

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.

We present the results of modeling of nanosecond pulse propagation in optically absorbing liquid media. Acoustic and electromagnetic wave equations must be solved simultaneously to model refractive index changes due to thermal expansion and/or electrostriction, which are highly transient phenomena on a nanosecond time scale. Although we consider situations with cylindrical symmetry and where the paraxial approximation is valid, this is still a computation-intensive problem, as beam propagation through optically thick media must be modeled. We compare the full solution of the acoustic wave equation with the approximation of instantaneous expansion (steady-state solution) and hence determine the regimes of validity of this approximation. We also find that the refractive index change obtained from the photo-acoustic equation overshoots its steady-state value once the ratio between the pulsewidth and the acoustic transit time exceeds a factor of unity.

We describe a series of experiments on acetonitrile solutions of an inorganic cluster molecule Mo2Ag4S8(PPh3)4 and compare them with data on a suspension of carbon particles in liquid (dilute ink). The optical-limiting behavior is measured by single-picosecond 532-nm pulses and nanosecond-long trains of these picosecond pulses. Nonlinear loss measurements are also performed with pulse trains at 1064 nm. Both materials show reduced transmittance for increasing fluence (energy per unit area). We also perform picosecond time-resolved pump–probe measurements at 532 nm, and we find that the observed pump–probe behavior is identical for the metal-cluster solution and the carbon-black suspension. We believe that the nonlinear mechanisms are the same for the two materials. Our previous studies of carbon-black suspension indicate that the primary nonlinear losses are due to scattering and absorption by microplasmas formed after thermionic emission from heated carbon black augmented by scattering from subsequently created bubbles. The conclusion of a similar limiting mechanism for the two materials is confirmed by time-resolved shadowgraphic images taken on both samples; however, a definitive conclusion concerning the role of microplasmas versus bubbles in either material is still under investigation.

We investigate nonlinear optical absorption of a series of polymethine dyes in liquid solution and in a solid poly(urethane acrylate) elastopolymer host. Depending on the ratio between the absorption cross section from the ground to the first excited state (σ01) and from the first to the higher excited states (σ12) and on the pump wavelength, they demonstrate absorption that either increases or decreases with increasing incident energy density. Our interest is directed at studying the optical limiting behavior of the dyes for sensor protection applications, which requires that σ12 be greater than σ01. We performed a detailed investigation of the dynamics of these processes, using Z-scan and pump–probe techniques at the single wavelength of 532 nm. We obtained σ12/σ01≈80 for one of the dyes, which is significantly higher than any previously reported value of which we are aware. The linear absorption remained significant, a requirement for good optical limiting. However, at high incident energy density for most of the dyes the increasing absorption converted to a bleaching effect with repeated irradiation. This effect was reversed after several seconds in liquid solutions and several minutes in the polymer host, possibly because of replenishment of the dye by diffusion in both media.

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.

We report two-photon absorption in CuCl and its polarization dependence to give all three χ(3) tensor elements at 532 nm. We also report bound electronic n2 and free-carrier refraction in CuCl. The values obtained are each approximately one half the corresponding values for ZnSe. Previously, with ZnSe, the large two-photon absorption (2PA) and negative bound-electronic nonlinear refraction were combined with defocusing from 2PA-generated free carriers to provide effective optical limiting for visible picosecond input pulses. For nanosecond pulses thermal refraction is a problem because it leads to self focusing, and thus damage in ZnSe and most other semiconductors studied. However, the thermal refraction in CuCl is reported to be self-defocusing. Thus one might expect the self-protection properties of CuCl to be better than those of ZnSe for optical-limiting applications for nanosecond input pulses.

An investigation of cascaded second-order optical effects resulting in effective third-order interactions, temporal and spatial self-action, are presented for N-(4-nitrophenyl)-l-prolinol (NPP) a molecular single crystal with one of the largest phase-matchable second-order nonlinear coefficients known in the visible and near-infrared portions of the spectrum. We emphasize the effects of temporal and spatial walk-off in the nonlinear-optical propagation in NPP and discuss their consequences for cascaded second-order nonlinear applications. Walk-off effects play a detrimental role in cascaded all-optical switching. Whereas in standard second-harmonic generation walk-off reduces the efficiency but does not prevent the generation, in the case of cascading backconversation is required and more-deleterious effects occur: a portion of the field is lost in that the overlap between fundamental and second-harmonic wavelengths is reduced.

The authors describe how the phase-sensitivity problem of optical transistors based on second order nonlinearities may be avoided using two type-II SHG crystals. The first crystal couples the mutually incoherent signal and pump, and the second crystal amplifies this signal. All inputs and outputs may be at the same wavelength.

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.

We introduce a temporal delay in one beam of the two-color Z-scan apparatus, which measures nondegenerate nonlinear absorption and nondegenerate nonlinear refraction. This technique allows us to time resolve separately the sign and the magnitude of the nonlinear absorption and refraction at frequency ωp that are due to the presence of a strong excitation at frequency ωe. For example, in semiconductors we specifically measure the bound electronic, nondegenerate nonlinear refraction and nondegenerate two-photon absorption, as well as the two-photon-generated free-carrier refraction and absorption as functions of time. We demonstrate this technique on ZnSe, ZnS, and CS2, using picosecond pulses at 1.06 and 0.532 μm.

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.

We introduce a method for measuring the anisotropy of nonlinear absorption and nonlinear refraction in crystals by incorporating a wave plate into the Z-scan apparatus. We demonstrate this method by measuring the polarization dependence of the nonlinear refractive index or two-photon absorption coefficient in BaF2, KTP, and GaAs at wavelengths of 532 and 1064 nm.

We extend the application of the Z-scan experimental technique to determine free-carrier nonlinearities in the presence of bound electronic refraction and two-photon absorption. We employ this method, using picosecond pulses in CdTe, GaAs, and ZnTe at 1.06 μm and in ZnSe at 1.06 and 0.53 μm, to measure the refractive-index change induced by two-photon-excited free carriers (coefficient σr,), the two-photon absorption coefficient β, and the bound electronic nonlinear refractive index n2. The real and imaginary parts of the third-order susceptibility (i.e., n2 and β, respectively) are determined by Z scans with low inputs, and the refraction from carriers generated by two-photon absorption (an effecitve fifth-order nonlinearity) is determined from Z scans with higher input energies. We compare our experimental results with theoretical models and deduce that the three measured parameters are well predicted by simple two-band models. n2 changes from positive to negative as the photon energy approaches the band edge, in accordance with a recent theory of the dispersion of n2 in solids based on Kramers–Kronig transformations [ Phys. Rev. Lett.65, 96 ( 1990); IEEE J. Quantum Electron.27, 1296 ( 1991)]. We find that the values of σr are in agreement with simple band-filling models.

A simple dual-wavelength (two-color) Z-scan geometry is demonstrated for measuring nonlinearities at frequency omega(p) owing to the presence of light at omega(e). This technique gives the nondegenerate two-photon absorption (2PA) coefficient beta(omega(p); omega(e)) and the nondegenerate nonlinear refractive index n(2)(omega(p); omega(e)), i.e., cross-phase modulation. We demonstrate this technique on CS(2) for n(2) and on ZnSe where 2PA and n(2) are present simultaneously.

We have performed experiments to characterize permanent laser-induced darkening in CdSxSe1−x semiconductor-doped glasses with picosecond pulses as a function of fluence, repetition rate, and pulse width. We find that the darkening occurs by means of a nonlinear process that exhibits an anomalous dependence on pulse width. Transmission spectra show that the induced darkening is uniform over the spectral range from the absorption edge out to 820 μm. Darkening in a number of different glasses is compared. On the basis of our results we propose a mechanism that involves photoassisted trapping of electrons from the semiconductor microcrystallites into states within the glass host material.

We experimentally and theoretically investigate optical beam propagation in nonlinear refractive materials having a thickness greater than the depth of focus of the input beam (i.e., internal self-action). A simple model based on the "constant shape approximation" is adequate for analyzing the propagation of laser beams within such media under most conditions. In a tight focus geometry, we find that the position of the sample with respect to the focal plane, z, is an important parameter in the fluence limiting characteristics of the output. The behavior with z allows us to perform a "thick sample Z-scan" from which we can determine the sign and magnitude of the nonlinear refraction index. In CS2, we have used this method to independently measure the negative thermally induced index change and the positive Kerr nonlinearity with nanosecond and picosecond CO2 laser pulses, respectively. We have experimentally examined the limiting characteristics of thick CS2 samples that qualitatively agree with our analysis for both positive and negative nonlinear refraction. This analysis is useful in optimizing the limiting behavior of devices based on self-action.

Degenerate four wave mixing (DFWM) in indium antimonide has been observed at 80 K with a low power c.w. CO laser. Phase conjugate reflectivities of up to 20% have been observed without saturation effects. In addition, a cross-modulation component has been identified which co-exists with the DFWM signal. From the experimental results a third order nonlinear susceptibility x (3) = 1.1 ± 0.3 esu has been established.

We report a range of experiments in both the degenerate and nondegenerate regimes of four-wave mixing in indium antimonide using CW CO laser sources. For the degenerate case, we specify all the polarization source terms and the signals which they radiate. We identify the dominant term for the phase-conjugate signal experimentally, and confirm that this involves a large-period grating formed by the forward pump and probe. The third-order susceptibility was measured as X^{(3)} \sim 1.1 esu. This was shown to be highly resonant with the InSb bandgap. By varying the pump-probe input angle, the period of the grating was changed, and thus a carrier diffusion length of l_{D} = 60 \mu m was determined. By probing the grating with a second laser, the dispersion of the grating was measured over a wide range of frequencies, and was found to be much less resonant with the band edge than X^{(3)} . Saturation of X^{(3)} was observed and possible sources are identified and discussed. The results of near-resonant nondegenerate mixing experiments are presented and the measured value of X^{(3)} = 5 \times 10^{-7} esu under these conditions is discussed in relation to the much larger degenerate, resonant X^{(3)} .

The dependence of switching power upon input beam spot radius for an optically bistable InSb etalon has been measured. The results show that the irradiance required for switching increases as the spot radius is reduced. There is no evidence of any lower limit to the switching power, even for spot radii much less than the ambipolar diffusion length. Studies of the transmitted beam intensity profile in the near‐field demonstrate the role of diffusion in our observations. The implications of our results for digital optical processing are briefly discussed.

We report on measurements of the effects of transverse diffusive coupling both on single bistable elements, and on multi-element parallel transphasor and bistable switch arrays in Indium Antimonide.