A sensitive single-beam technique for measuring both the nonlinear refractive index and nonlinear absorption coefficient for a wide variety of materials is reported. The authors describe the experimental details and present a comprehensive theoretical analysis including cases where nonlinear refraction is accompanied by nonlinear absorption. In these experiments, 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 nonlinear refraction are easily deduced from such a transmittance curve (Z-scan). Employing this technique, a sensitivity of better than lambda /300 wavefront distortion is achieved in n/sub 2/ measurements of BaF/sub 2/ using picosecond frequency-doubled Nd:YAG laser pulses. >

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Sensitive measurement of optical nonlinearities using a single beam

The rise time of intense radiation determines the maximum field strength atoms can be exposed to before their polarizability dramatically drops due to the detachment of an outer electron. Recent progress in ultrafast optics has allowed the generation of ultraintense light pulses comprising merely a few field oscillation cycles. The arising intensity gradient allows electrons to survive in their bound atomic state up to external field strengths many times higher than the binding Coulomb field and gives rise to ionization rates comparable to the light frequency, resulting in a significant extension of the frontiers of nonlinear optics and (nonrelativistic) high-field physics. Implications include the generation of coherent harmonic radiation up to kiloelectronvolt photon energies and control of the atomic dipole moment on a subfemtosecond $(1{\mathrm{f}\mathrm{s}=10}^{\mathrm{\ensuremath{-}}15}\mathrm{}\mathrm{s})$ time scale. This review presents the landmarks of the 30-odd-year evolution of ultrashort-pulse laser physics and technology culminating in the generation of intense few-cycle light pulses and discusses the impact of these pulses on high-field physics. Particular emphasis is placed on high-order harmonic emission and single subfemtosecond extreme ultraviolet/x-ray pulse generation. These as well as other strong-field processes are governed directly by the electric-field evolution, and hence their full control requires access to the (absolute) phase of the light carrier. We shall discuss routes to its determination and control, which will, for the first time, allow access to the electromagnetic fields in light waves and control of high-field interactions with never-before-achieved precision.

Intense few-cycle laser fields: Frontiers of nonlinear optics

We demonstrate microfabrication of ultra-high-Q microcavities on a chip, exhibiting a novel toroid-shaped geometry. The cavities possess Q-factors in excess of 100 million which constitutes an improvement close to 4 orders-of-magnitude in Q compared to previous work [B. Gayral, et al., 1999].

Ultra-high-Q toroid microcavities on a chip

Measurements of two-photon fluorescence excitation (TPE) spectra are presented for 11 common molecular fluorophores in the excitation wavelength range 690 nm < λ < 1050 nm. Results of excitation by ∼100-fs pulses of a mode-locked Ti:sapphire laser are corroborated by single-mode cw Ti:sapphire excitation data in the range 710 nm < λ < 840 nm. Absolute values of the TPE cross section for Rhodamine B and Fluorescein are obtained by comparison with one-photon-excited fluorescence, assuming equal emission quantum efficiencies. TPE action cross sections for the other nine fluorophores are also determined. No differences between one-photon- and two-photon-excited fluorescence emission spectra are found. TPE emission spectra are independent of excitation wavelength. With both pulsed and cw excitation the fluorescence emission intensities are strictly proportional to the square of the excitation intensity to within ±4% for excitation intensities sufficiently below excited-state saturation.

Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm

Physical Review B

We present a simple yet highly sensitive single-beam experimental technique for the determination of both the sign and magnitude of n2. 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 n2 is easily calculated. A transmittance change of 1% corresponds to a phase distortion of ≃ λ/250. We demonstrate this method on several materials using both CO2 and Nd:YAG laser pulses.

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

A two-hand model is used to calculate the scaling and spectrum of the nondegenerate nonlinear absorption. From this, the bound electronic nonlinear refractive index n/sub 2/ is obtained using a Kramers-Kronig transformation. The authors include the effects of two-photon and Raman transitions and the AC Stark shift (virtual band blocking). The theoretical calculation for n/sub 2/ shows excellent agreement with measured values for a five-order-of-magnitude variation in the modulus of n/sub 2/ in semiconductors and wide-gap optical solids. Beam distortion methods were used to measure n/sub 2/ in semiconductors. The observations result in a comprehensive theory that allows a prediction of n/sub 2/ at wavelengths beneath the band edge, given only the bandgap energy and the linear index of refraction. Some consequences for all-optical switching are discussed, and a wavelength criterion for the observation of switching is derived. >

Dispersion of bound electron nonlinear refraction in solids

We monitor the induced phase change produced by a cascaded χ(2):χ(2) process in KTP near the phase-matching angle on a picosecond 1.06-μm-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 n2eff≅±2×10−14 cm2/W (±1 × 10−11 esu) for an angle detuning of ±5° from phase match for this 1-mm-thick crystal with a measured deff of 3.1 pm/V For a fixed phase mismatch, this n2eff scales linearly with length and as deff2; however, for the maximum n2eff the nonlinear phase distortion becomes sublinear with irradiance for phase shifts near π/4.

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

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.

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Mansoor Sheik-Bahae

Papers

Sensitive measurement of optical nonlinearities using a single beam

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

Dispersion of bound electron nonlinear refraction in solids

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

Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe