Intensity-dependent Refractive Index Research Articles

New ducting model for analyzing the Gaussian beam propagation in nonlinear Kerr media and its application to spatial self-phase modulations

Knowing the Gaussian beam parameters, such as its radius of curvature and spot size during propagation in nonlinear Kerr media, is of paramount importance in describing the observable far-field diffraction ring patterns as well as in design and stability analysis of Kerr-lens mode-locked resonators. Specifically, the sign of the beam radius of curvature after exiting these media has been proposed to be of assistance in recognizing their optical nonlinearity sign through determining the type of diffraction ring pattern in the far field. In order to be able to trace the evolution of the beam parameters in the Gaussian beam formalism, we have used the common aberration-free theory. We have shown that the nonlinear propagation problem of a fundamental Gaussian beam in a Kerr medium with an intensity-dependent index of refraction can be handled by assuming a ducting index profile along the propagation direction. Knowing the familiar ABCD matrix of a duct, the evolution of the mentioned beam parameters can be traced during propagation using the ABCD law in Gaussian beam theory. We have validated our ducting model by comparing its results with the outcomes of one widely used and accepted model which has been known to yield consistent results when electronic optical nonlinearity prevails. We have shown that when thermal optical nonlinearity is dominant, as in diffraction ring observation experiments, our ducting model yields sensible results and should be used. Our model predicts that when the sign of the thermal nonlinearity and the beam radius of curvature on the entrance plane of the medium are positive, the sign of the beam radius of curvature on the exit plane may have either sign, depending on the medium thickness used in the experiment. Hence, two types of diffraction ring pattern may be obtained using the same medium with two different thicknesses and this may cast doubt on the validity of the methods proposing the detection of the optical nonlinearity signs by observing these patterns. We have proposed a simple procedure for experimentally obtaining the two different types of diffraction pattern from the same medium.

Nonlinear studies of malachite green polymer

Solid-state dye-doped polymer is an attractive alternative to the conventional liquid dye solution. In this paper the spectral characteristics and the nonlinear optical properties of the dye malachite green in polymethylmethacrylate is studied. The spectral characteristics are studied by recording steady state absorption and fluorescence spectra. Thermally induced nonlinearity of malachite green dye in n-butyl Acetate is studied using cw He–Ne laser at 632.8nm as source of excitation, both in solution and solid film. The property of dye in solid matrix is compared with that in liquid medium. The optical response is characterized by measuring the intensity dependent refractive index (n2) of the medium, using z-scan technique. The origin of optical nonlinearity in this dye may be attributed due to laser-heating induced nonlinear effect. The dye exhibited negative (defocusing) nonlinearity and it can be a promising material for optical limiting applications.

Competition between electronic Kerr and free-carrier effects in an ultimate-fast optically switched semiconductor microcavity

We have performed ultrafast pump-probe experiments on a GaAs-AlAs microcavity with a resonance near 1300 nm in the "original" telecom band. We concentrate on ultimate-fast optical switching of the cavity resonance that is measured as a function of pump-pulse energy. We observe that at low pump-pulse energies the switching of the cavity resonance is governed by the instantaneous electronic Kerr effect and is achieved within 300 fs. At high pump-pulse energies the index change induced by free carriers generated in the GaAs start to compete with the electronic Kerr effect and reduce the resonance frequency shift. We have developed an analytic model which predicts this competition in agreement with the experimental data. Our model includes a new term in the intensity-dependent refractive index that considers the effect of the probe pulse intensity, which is resonantly enhanced by the cavity. We calculate the effect of the resonantly enhanced probe light on the refractive index change induced by the electronic Kerr effect for cavities with different quality factors. By exploiting the linear regime where only the electronic Kerr effect is observed, we manage to retrieve the nondegenerate third order nonlinear susceptibility for GaAs from the cavity resonance shift as a function of pump-pulse energy.

Electronic and Vibrational Nonlinear Optical Properties of Five Representative Electrides.

The electrides have a very special electronic structure with diffuse excess electrons not localized on any specific atom. Such systems are known to have huge electronic nonlinear optical (NLO) properties. Here, we determine and analyze the vibrational, as compared to the electronic, NLO properties for a representative set of electrides: Li@Calix, Na@Calix, Li@B10H14, Li2(•+)TCNQ(•-), and Na2(•+)TCNQ(•-). The static and dynamic vibrational (hyper)polarizabilities are computed by the nuclear relaxation method (with field-induced coordinates and the infinite optical frequency approximation) at the UB3LYP level using a hybrid Pople basis set. In general, the static vibrational βvec and γ∥ exceed the corresponding static electronic property values by up to an order of magnitude. The same comparison for dynamic vibrational hyperpolarizabilities shows a smaller ratio. For the intensity-dependent refractive index (IDRI) and dc-Kerr processes, the ratio is on the order of unity or somewhat larger; it is less for the dc-Pockels and the electric field induced second harmonic (EFISH) effects (as well as the static α̅) but still important. The role of anharmonicity, motion of the alkali atoms, and substitution of Na for Li is discussed along with specific aspects of the charge distribution associated with the excess electron.

Dynamic (hyper)polarizabilities of the sulphur dioxide molecule: Coupled cluster calculations including vibrational corrections

In this work we report results for dynamical (hyper)polarizabilities of the sulphur dioxide molecule with inclusion of vibrational corrections. The electronic contributions were computed analytically at the single and double coupled cluster level through response theories for the frequencies 0, 0.0239, 0.0428, 0.0656, 0.0720, and 0.0886 hartree. Contributions of the connected triple excitations to the dynamic electronic properties were also estimated through the multiplicative correction scheme. Vibrational corrections were calculated by means of the perturbation theoretical method. The results obtained show that the zero point vibrational correction is very small for all properties studied while the pure vibrational correction is relevant for the dc-Pockels effect, intensity dependent refractive index, and dc-Kerr effect. For these nonlinear optical processes, the pure vibrational corrections represent approximately 75%, 13%, and 6% of the corresponding electronic contributions for the higher frequencies quoted. The results presented for the polarizability are in good agreement with experimental values available in the literature. For the hyperpolarizabilities we have not obtained experimental results with precision sufficient for comparison.

Off-resonance and non-resonant dispersion of Kerr nonlinearity for symmetric molecules [Invited

The exact formula is derived from the "sum over states" (SOS) quantum mechanical model for the frequency dispersion of the nonlinear refractive index coefficient n₂ for centrosymmetric molecules in the off-resonance and non-resonant regimes. This expression is characterized by interference between terms from two-photon transitions from the ground state to the even-symmetry excited states and one-photon transitions between the ground state and odd-symmetry excited states. When contributions from the two-photon terms exceed those from the one-photon terms, the non-resonant intensity-dependent refractive index n₂>0, and vice versa. Examples of the frequency dispersion for the three-level SOS model are given. Comparison is made with other existing theories.

Measurement of nonlinear refractive index of Ag and Au nano-particles using moiré technique

In this paper we have measured second order nonlinear refractive index of Ag and Au nano-particles using the moiré deflectometry with a CW He–Ne laser at wavelength of 632.8 nm. The main advantages of this technique are its extreme experimental simplicity and low sensitivity to external distribution in comparison with other interfrometric methods that need very stable experimental set-up. Because of self-focusing (or self-defocusing) that is due to intensity dependent refractive index, presence of sample in the moiré deflectometry set-up lead to rotation of moiré fringes. By moving the sample in set-up we have measured these rotation angles in different displacements from focus point of lens used in this set-up and then we have calculated the nonlinear refractive index of Ag and Au nano-particles using their values. Also we have obtained the sign of n 2 regard to the direction of rotations. Consequently by using the Mathematica software we have exhibited the suitable fitness of theoretical curve with experimental results.

Dynamic (hyper)polarizabilities of the ozone molecule: Coupled cluster calculations including vibrational corrections

In this work, we present results for dynamical (hyper)polarizabilities of the ozone molecule with inclusion of vibrational corrections. Electronic contributions for dynamic properties were computed analytically at the single and double coupled cluster level through response theories for the frequencies 0, 0.0239, 0.0428, and 0.0656 hartree. In the static limit, the electronic contributions were also computed at the single and double coupled cluster with perturbative correction of connected triple excitations level by means of the finite-field method. It was found that the inclusion of connected triple excitations is important, especially for a reliable description of the hyperpolarizabilities. Vibrational corrections were calculated by means of the perturbation theoretical method. The zero-point vibrational average correction was found to be relevant only for the linear polarizability, representing approximately 8% of the corresponding electronic contribution. Results also showed that the pure vibrational correction is relevant for the dc-Pockels effect, dc-second harmonic generation, intensity dependent refractive index, and dc-Kerr effect nonlinear optical processes. The double-harmonic approximation is in general suitable to compute this correction, the anharmonicity being small for the dc-Kerr effect and negligible for the other processes.

Lossy double negative guiding layer optical sensors

AbstractWe proposed a three-layer waveguide as an optical sensor for homogeneous sensing applications. A guiding layer of the proposed structure is considered as lossy left-handed material (LHM) with simultaneously the complex negative electric permittivity ɛ and the complex negative magnetic permeability µ. We also assume a cladding layer to have an intensity-dependent refractive index. Sensitivity of the proposed optical waveguide sensor is derived and its dependence on different parameters of a waveguide is studied.

Optical and dielectric properties of nitrophenolate based nonlinear optical crystal

A semi-organic nonlinear optical (NLO) material, lithium-p-nitrophenolate trihydrate (LPNP) was synthesized. Single crystals of dimensions 20 × 7 × 3 mm3 were harvested following the solvent evaporation technique. The functional groups present in the compound were identified from FT-IR and FT-Raman spectral analyses, and its molecular structure was confirmed. Identification of the compound was accomplished by X-ray diffraction technique (powder and single crystal XRD). The unit-cell dimensions and the morphology of the grown crystals were identified from single crystal XRD measurements. The thermal transport properties, thermal effusivity (e), thermal diffusivity (α), thermal conductivity (k) and heat capacity (C p) were measured by the photopyroelectric technique at room temperature. Dielectric constant and dielectric loss were also measured as a function of frequency between 42 Hz and 5 MHz, and temperature between 32 and 100 °C. From optical transmittance measurements, the direct optical band gap of the LPNP crystal was estimated to be 2.47 eV. Laser damage threshold is 60.91 GW cm−2. Powder second harmonic generation (SHG) measurement was carried out using a modified Kurtz–Perry technique. Third order nonlinear response was studied using Z-scan technique with a He–Ne laser (632.8 nm, 35 mW). The magnitude and the sign of the nonlinear absorption and nonlinear refraction are derived from a transmittance curve. The NLO parameters Intensity dependent refractive index n 2, nonlinear absorption coefficient β and third order susceptibility χ(3) were estimated.

Irreducible spherical representation of some fourth-rank tensors

A process of decomposition of fourth-rank tensors into parts irreducible with reference to the continuous group of rotation is presented. The transformation matrices between the Cartesian and spherical reducible and irreducible fourth-rank tensors are given and discussed. We have focused our attention to the purely dipolar fourth-rank tensor $C_{i;jkl}$ symmetric to its last three indices and the dipole-octopole fourth-rank multipolar polarizability tensor E$^{(1,3)}$. The fourth-rank tensors intervene in a number of very important nonlinear optics processes like Kerr effect, intensity-dependent refractive index phenomena, four wave mixing, third harmonic generation and several other effects. Tensors of this kind are also very important in piezo-electric phenomena and in elasticity studies. Cartesian tensor index permutation is discussed as well as its influence on the tensor irreducible spectrum is studied. Several examples concerning fourth-rank tensors are given.

Propagation of low-intensity Gaussian fields in photorefractive media with real and imaginary intensity-dependent refractive index components

A theoretical analysis of a low power Gaussian field propagating in unbiased self-defocussing photorefractive media that includes both real and imaginary components of the intensity-dependent refractive index is presented. The analysis, which is in excellent agreement with experimental observations, shows that the imaginary component of the intensity-dependent refractive index can have a focussing effect independent of the focussing or defocussing effect of the real component of the intensity-dependent refractive index. These findings suggest that the imaginary component of the intensity-dependent refractive index is the cause of the previously observed apparent self-focussing in unbiased self-defocussing photorefractive media.

A spacetime cloak, or a history editor

We introduce a new type of electromagnetic cloak, the spacetime cloak (STC), whichconceals events rather than objects. Non-emitting events occurring during a restrictedperiod are never suspected by a distant observer. The cloak works by locally manipulatingthe speed of light of an initially uniform light distribution, whilst the light rays themselvesalways follow straight paths. Any ‘perfect’ spacetime cloak would necessarilyrely upon the technology of electromagnetic metamaterials, which has alreadybeen shown to be capable of deforming light in ways hitherto unforeseen—toproduce, for example, an electromagnetic object cloak. Nevertheless, we showhow it is possible to use intensity-dependent refractive indices to construct anapproximate STC, an implementation that would enable the distinct signatureof successful event cloaking to be observed. Potential demonstrations includesystems that apparently violate quantum statistics, ‘interrupt-without-interrupt’computation on convergent data channels and the illusion of a Star Trek transporter.

ChemInform Abstract: Synthesis, Vapor Growth, Polymerization, and Characterization of Thin Films of Novel Diacetylene Derivatives of Pyrrole. The Use of Computer Modeling to Predict Chemical and Optical Properties of These Diacetylenes and Poly(diacetylen

In the present work two diacetylene derivatives of pyrrole which are predicted by semiempirical AM1 calculations to have very different properties, are synthesized; the polymerizability of these diacetylenes in the solid state is determined, and the results are compared to the computer predictions. Diacetylene 1 is novel in that the monomer is a liquid at room temperature; this may allow for the possibility of polymerization in the liquid state as well as the solid state. Thin poly(diacetylene) films are obtained from compound 1 by growing films of the monomer using vapor deposition and polymerizing with UV light; these films are then characterized. Interestingly, while the poly(diacetylene) from 1 does not possess good nonlinear optical properties, the monomer exhibits very good third-order effects (phase conjugation) in solution. Dilute acetone solutions of the monomer 1 give intensity-dependent refractive indices on the order of 10 exp -6 esu; these are 10 exp 6 times better than for CS2.

Self-phase modulation at visible wavelengths in nonlinear ZnO channel waveguides

We report the observation of nonlinear optical effects in the visible spectrum using ZnO channel waveguides. We demonstrate sixfold spectral broadening and a 2π phase shift due to self-phase modulation in ZnO channel waveguides using femtosecond optical pulses with a center wavelength of 840 nm. We measured a value for the nonlinear parameter γ of 13.9±3.0 W−1 m−1, which is more than 1300 times that of a highly nonlinear fiber. The calculated intensity-dependent refractive index is found to be consistent with previously reported values of bulk single-crystal ZnO.

Investigation of third-order nonlinear optical properties of conjugated benzodioxal derivatives

An investigation of third-order nonlinear optical characterization of newly synthesized conjugated benzodioxal derivatives has been done by using nanosecond Z-scan technique at 532 nm. The molecules demonstrate self-defocusing effect with intensity dependent refractive index ( n 2) of the order of 10 −14 cm 2/W. The measured molecular TPA cross-section is ranging from 2.47 ×10 −47 cm 4 s/photon to 6.00 cm 4 s/photon. Their input-output curves indicate that there is a clear optical power limiting behavior with the limiting threshold in the range 125–181 μJ. The main factor to exhibit the observed nonlinearity in these molecules is the presence of charge donor and acceptor groups. The increased conjugation length increases the nonlinear refraction and increased electron density enhances the nonlinear absorption. The molecules exhibit good nonlinear optical properties, comparable to those of regular azoaromatic compounds. Therefore, the molecules investigated here are promising candidates for optical power limiting devices.

Thermo-optic properties and nonlinear responses of copper nanoparticles in polysiloxaneoil

Thermo-optic properties and thermal nonlinear effects of copper nanoparticles (CuNPs) inpolysiloxane oil are investigated under irradiation with a continuous wave low power laser at532 nm. The CuNPs are synthesized by nanosecond pulsed laser ablation of a copper plate inthe polysiloxane oil. Far field diffraction ring patterns are observed, arising from thermallyinduced self-phase modulation in the laser beam as it traverses the CuNP colloids. Lowpower optical limiting with low limiting thresholds is obtained in the sample on the basis ofthermal defocusing and self-diffraction. The nonlinear optical response is characterizedby measuring the intensity dependent refractive index of the medium using theZ-scan technique.The closed Z-scan measurements of the colloidal CuNPs exhibit an asymmetric behavior at differentapplied laser power levels of 5–20 mW. A theoretical analysis is presented for the observednonlinear behavior on the basis of nonlocal thermo-optic processes, without using thephotothermal thin lens approximation. Excellent agreements are found for the closedZ-scan measurements of the colloidal CuNPs with the analysis presented. Thevalues of nonlinear refractive index and thermo-optic coefficients are found to be − 1.52 × 10 − 7 cm2 W − 1 and − 1.0 × 10 − 4 K − 1, respectively.

Spatial phase filtering based on the intensity-dependent refractive index of PbS nanocomposite film

We demonstrate the use of stable films containing PbS nanocrystals as media for self-adaptive phase filtering in phase contrast imaging of transparent objects by a cost-effective exploitation of nonlinear optical refraction in a simple, all-optical, and self-adjusting 4f imaging system. The optical nonlinearity is characterized by z-scan technique using a continuous wave He-Ne laser as the excitation source. The mechanism of nonlinearity in this case is mainly due to the nonlocal thermo-optical interaction between the laser beam and the sample. The value of nonlinear refractive index coefficient is found to be -3.5x10(-7) cm(2)/W. The nanocomposite material shows a thermal lens effect and is a potential candidate for phase contrast imaging.

Nonlinear optical properties of conducting polyaniline and polyaniline–Ag composite thin films

The intensity dependent refractive indices of polyaniline and polyaniline–silver nanocomposites are measured. While the material are not good candidates for all-optical switching, they do exhibit reversible processes of saturable and reverse saturable absorption at the same wavelength, a trait that makes them suitable materials for optical pulse compression and limiting.

Enhanced nonlinear optical responses in metal–glass nanocomposites

The “engineered” nonlinear nanocomposite materials with extremely large values of optical Kerr susceptibility and fast temporal responses that can be precisely tuned to satisfy the requirements of switching applications is of current interest in photonics. Metal quantum-dot composite glasses can exhibit enhanced optical susceptibility, χ (3), whose real and imaginary parts are related to the intensity-dependent refractive index and two-photon absorption coefficient, respectively. Classical (dielectric) and quantum confinement effects come into play in the nonlinear optical responses of these nanocomposites. Metal nanocluster–glass composites have been synthesized by 200 keV Cu + and 1.5 MeV Au + ion implantations in fused silica glasses at a dose of 3 × 10 16 ions/cm 2, followed by thermal annealing in reducing atmosphere to promote cluster growth. UV–Visible spectroscopy has revealed prominent linear absorption bands at characteristic surface plasmon resonance (SPR) frequencies signifying appreciable formation of copper and gold colloids in glass matrices. Third-order optical properties of the composite materials have been studied by Z-Scan and Anti-Resonant Interferometric Nonlinear Spectroscopy (ARINS) measurements. The sign of nonlinear refraction is readily obtained from the Z-Scan signatures. The ARINS technique utilizes the dressing of two unequal-intensity counter-propagating pulsed light beams with differential nonlinear phases, which occur upon traversing the sample if it exhibits nonlinear optical response. This difference in phase manifests itself in the intensity-dependent transmission. The nonlinear refractive index, nonlinear absorption coefficient, the real and imaginary parts of the third-order optical susceptibility have been extracted.