Multiphoton Absorption Rate Research Articles

Dynamics and stability of cw and pulse lasers in Kerr optical media with K-photon absorption

The laser dynamics in inscription processes involving transparent media is carried out, by considering an optical field propagating in a transparent medium with Kerr nonlinearity. The study takes into account multi-photon absorption phenomena, as well as a possible modification of the material structure resulting in the generation of a plasma of nearly free electrons. The model is described by a complex Ginzburg–Landau equation governing the laser dynamics, in which an extra Kth-order nonlinear term is induced by K-photon absorption processes. The model also takes into consideration the electron plasma generation via a linear term in the optical field. A global stability analysis of the system dynamics reveals a rich variety of fixed points consisting of no, one or two singular points in the amplitude-frequency plane. The modulational instability of plane waves gives rise to period-halving bifurcations in the continuous-wave amplitude growth rate, reminiscent of dominant multi-pulse structures in the nonlinear regime at large multi-photon absorption rate K. Pulses and multi-pulses are observed in numerical simulations of the nonlinear equations for the full system dynamics, the first structures are clearly associated with the case K = 2 whereas multi-pulse structures of increasing amplitudes and shorter perioids are dominant at larger values of K.

Modelling of the ultrafast dynamics and surface plasmon properties of silicon upon irradiation with mid-IR femtosecond laser pulses

We present a theoretical investigation of the yet unexplored ultrafast processes and dynamics of the produced excited carriers upon irradiation of Silicon with femtosecond pulsed lasers in the mid-infrared (mid-IR) spectral region. The evolution of the carrier density and thermal response of the electron-hole and lattice subsystems are analysed for various wavelengths {\lambda}L in the range between 2.2 {\mu}m and 3.3 {\mu}m where the influence of two and three-photon absorption mechanisms is explored. The role of induced Kerr effect is highlighted and it manifests a more pronounced influence at smaller wavelengths in the mid-IR range. Elaboration on the conditions that leads to surface plasmon (SP) excitation indicate the formation of weakly bound SP waves on the material surface. The lifetime of the excited SP is shown to rise upon increasing wavelength yielding a larger than the one predicted for higher laser frequencies. Calculation of damage thresholds for various pulse durations {\tau}p show that they rise according to a power law (~\tau_p^{\zeta(\lambda_L) ) where the increasing rate is determined by the exponent \zeta(\lambda_L). Investigation of the multi-photon absorption rates and impact ionization contribution at different {\tau}p manifests a lower damage for {\lambda}L=2.5 {\mu}m compared to that for {\lambda}L=2.2 {\mu}m for long {\tau}p.

Saturation of the all-optical Kerr effect in solids

We discuss the influence of the higher-order Kerr effect (HOKE) in wide bandgap solids at extreme intensities below the onset of optically induced damage. Using different theoretical models, we employ multiphoton absorption rates to compute the nonlinear refractive index by a Kramers-Kronig transform. Within this theoretical framework we provide an estimate for the appearance of significant deviations from the standard optical Kerr effect predicting a linear index change with intensity. We discuss the role of the observed saturation behavior in practically relevant situations, including Kerr lens mode-locking and supercontinuum generation in photonic crystal fibers. Furthermore, we present experimental data from a multiwave mixing experiment in BaF2, which can be explained by the appearance of the HOKE.

Kramers-Kronig relations and high-order nonlinear susceptibilities

As previous theoretical results recently revealed, a Kramers-Kronig transform of multiphoton absorption rates allows for a precise prediction on the dispersion of the nonlinear refractive index ${n}_{2}$ in the near infrared. It was shown that this method allows reproduction of recent experimental results on the importance of the higher-order Kerr effect. Extending these results, the current manuscript provides the dispersion of ${n}_{2}$ for all noble gases in excellent agreement with reference data. It is furthermore established that the saturation and inversion of the nonlinear refractive index is highly dispersive with wavelength, which indicates the existence of different filamentation regimes. While shorter laser wavelengths favor the well-established plasma clamping regime, the influence of the higher-order Kerr effect (HOKE) dominates in the long-wavelength regime.

Multiphoton absorption in germanium using pulsed infrared free-electron laser radiation

We report wavelength- and intensity-dependent transmission measurements of intense mid-infrared radiation from the Vanderbilt free-electron laser in single-crystal Ge(100) in the wavelength range of 2.8--5.2 \ensuremath{\mu}m. This range accesses both the direct and indirect energy gaps in Ge, requiring in each case either two or three photons (2PA or 3PA) for absorption. Large changes in the multiphoton absorption rate are seen at the direct-to-indirect and 2PA-to-3PA transitions. Photon interactions are dominated by free-carrier absorption (FCA), primarily due to holes. The entire absorption process is modeled with the two- and three-photon absorption coefficients ($\ensuremath{\beta}$ and $\ensuremath{\gamma}$) as fitting parameters. Using newly measured values of the low-intensity FCA cross sections, we find a best fit to the data at 2.8 \ensuremath{\mu}m that is in agreement with theory and previous measurements. We report a ratio of 175 for $\ensuremath{\beta}$ across the direct-to-indirect transition, and a ratio of 5 across the same transition for $\ensuremath{\gamma}$. These ratios are independent of systematic variations in free-carrier cross sections and beam diameter.

An optical parametric oscillator as a high-flux source of two-mode light for quantum lithography

We investigate the use of an optical parametric oscillator (OPO), which can generate relatively high-flux light with strong non-classical features, as a source for quantum lithography. This builds on the proposal of Boto et al (2000 Phys. Rev. Lett. 85 2733), for etching simple patterns on multi-photon absorbing materials with sub-Rayleigh resolution, using two-mode entangled states of light. We consider an OPO with two down-converted modes that share the same frequency but differ in field polarization or direction of propagation, and derive analytical expressions for the multi-photon absorption rates when the OPO is operated below, near and above its threshold. Because of strong non-classical correlations between the two modes of the OPO, the interference patterns resulting from the superposition of the two modes are characterized by an effective wavelength that is half of their actual wavelength. The interference patterns resulting when the two modes of the OPO are used for etching are also characterized by an effective wavelength half that for the illuminating modes. We compare our results with those for the case of a high-gain optical amplifier source and discuss the relative merit of the OPO.

Fundamental Quantum Limit to the Multiphoton Absorption Rate for Monochromatic Light

The local multiphoton absorption rate for an arbitrary quantum state of monochromatic light, taking into account the photon number, momentum, and polarization degrees of freedom, is shown to have an upper bound that can be reached by coherent fields. This surprising result rules out any quantum enhancement of the multiphoton absorption rate by momentum entanglement.

Relationship between resolution enhancement and multiphoton absorption rate in quantum lithography

The proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733 (2000)] is studied via a rigorous formalism. It is shown that, contrary to Boto et al.'s heuristic claim, the multiphoton absorption rate of a (|N,0>+|0,N>) quantum state is actually lower than that of a classical state with otherwise identical parameters. The proof-of-concept experiment of quantum lithography [D'Angelo et al., Phys. Rev. Lett. 87, 013602 (2001)] is also analyzed in terms of the proposed formalism, and the experiment is shown to have a reduced multiphoton absorption rate in order to emulate quantum lithography accurately. Finally, quantum lithography by the use of a jointly Gaussian quantum state of light is investigated to illustrate the trade-off between resolution enhancement and multiphoton absorption rate.

Linear and nonlinear optical properties of borate crystals as calculated from the first principles

With the development of the state-of-the-art band calculation scheme and massively parallel processing in the high performance computing, we are now able to calculate all important physical properties, including (i) the nonlinear susceptibility; (ii) the multiphoton absorption rate; (iii) the birefringence; and (iv) the energy gap, from the first principles for complex practical nonlinear optical crystals, such as the borate crystal series, with an accuracy acceptable for materials development/design, and answer the questions often raised by the material scientists.

Molecular photodissociation with diverging couplings: An application to H2+ in intense cw laser fields. II. The multiphoton problem.

A nonperturbative time-independent method of calculating accurately partial widths of resonances formed in fragmentation processes is presented. It is based on a complex-energy probability-flux analysis performed in the adiabatic representation and turns out to be applicable whatever the strength or the spatial dependence of the interchannel couplings is. The method is applied to the photodissociation resonances of ${\mathrm{H}}_{2}^{+}$ exposed to an intense continuous-wave (cw) laser field. The photon channel pathways followed during the fragmentation are determined in terms of partial fluxes. Multiphoton absorption rates and branching ratios are extracted and compared with other recent studies. In the limit of weak laser intensities the formulas for the partial widths reduce to those resulting from the standard Siegert form for the open-channel components of the resonance wave functions.

Second Harmonic Generation in Optical Fibres: Multiphoton Absorption and Translation-inversion Symmetry

Abstract Multiphoton absorption provides a route to x (2) grating formation in optical fibres. It explains the efficacy of ‘seeding’ the fibre with green light to induce fibre second harmonic generation. The process depends on absorption sites with spatially inverted configurations having different multiphoton absorption rates.

Absorption of Circularly Polarized Light by Solids

AbstractThe multiphoton absorption rate of circularly polarized light, by direct‐gap crystals, is investigated following a non‐perturbative scheme proposed by Jones and Reiss. It is possible to derive closed analytical solutions, for the N‐photon transition rate, valid for all field strengths of practical interest. The accuracy of the approximations introduced in deriving these results is determined comparing the numerical computations of the multiphoton transition rate (“exact”) with the analytical solutions. Specific calculations are done for ZnS and GaAs in the presence of a Nd laser. It is shown that this formalism leads to a total transition rate which has not the tunneling behavior previously discussed by several authors within similar contexts.

Quantum correlation functions for radiation fields with stationary independent modes

The quantum field correlation functions arising in the calculations of multiphoton absorption rate are considered in detail. General expressions of functions, evaluated at two space-time points, are derived forM-mode fields having aP-representation. The normalized correlation functions, taken at one point in the space and time g 1...M (n) (x,t), are investigated in the case of radiation with stationary independent modes. Comparisons between typical fields, thermal, ideal laser, signal plus noise and second harmonic generated by chaotic field, are presented. The influence of the number of modesM on g 1...M (n) (x, t) is numerically discussed. In particular, the limiting values which are reached whenM becomes increasingly large, are examined. A condition is derived, which is sufficient in order that g 1...M () be n! in the limit of an infinite number of independent modes.