Study on contribution of the asymmetric stress to the birefringence induced by an ultrashort single laser pulse inside fused silica glass

Abstract: The nonlinear optical response of a material is conventionally assumed to be very much smaller than its linear response. Here we report that the nonlinear contribution to the refractive index of a sample of indium-tin oxide can be much larger than the linear contribution when the optical wavelength is close to the material’s bulk plasma wavelength, where the material exhibits epsilon-near-zero behavior. In particular, we demonstrate that a change in refractive index as large as 0.7 can be obtained in an ultra-thin indium-tin oxide film using an optical intensity of 140 GW/cm2. Nonlinear optical phenomena result from the light-induced modification of the optical properties of a material lead to a broad range of applications, including microscopy, all-optical data processing, and quantum information. However, nonlinear (NL) effects are typically extremely weak. The size of nonlinear effects is typically limited by the largest intensity that can be used without permanently damaging of the material. Consequently, the resulting change in refractive index is typically of the order of 0.001 or smaller. A long-standing goal of nonlinear optics (NLO) has been the development of materials that can display a light-induced change in the refractive index of the order of unity. Such materials would lead to exciting new applications of NLO. Indeed, much effort in the fields of plasmonics and metamaterials is devoted to the development of such materials. Furthermore, it has been suggested that materials with vanishing permittivity, commonly known as epsilon-nearzero (ENZ) materials, can be used to induce highly nonlinear phenomena and unusual phase-matching behavior. In this work, we describe our studies of indium-tin oxide (ITO) at its ENZ wavelength, and we demonstrate a refractive index change of 0.7. Materials possessing free charges, such as metals and doped semiconductors, exhibit a vanishing permittivity at the bulk plasmon wavelength. The zero-permittivity wavelength in doped semiconductors typically lies at infrared wavelengths and can be fine tuned by controlling the level of doping. Here we study the case of an ultra-thin layer of ITO exhibiting ENZ behavior at wavelengths around 1.24 µm. We show that in this spectral region the nonlinear response (intensity-dependent change in refractive index, Δn) is enhanced approximately 2000-fold with respect to that observed at shorter wavelengths and that a Δn of the order of unity can be observed.

Heat equations can estimate the thermal distribution and phase transformation in real-time based on the operating conditions and material properties. Such wonderful features have enabled heat equations in various fields, including laser and electron beam processing. The integral transform technique (ITT) is a powerful general-purpose semi-analytical/numerical method that transforms partial differential equations into a coupled system of ordinary differential equations. Under this category, Fourier and non-Fourier heat equations can be implemented on both equilibrium and non-equilibrium thermo-dynamical processes, including a wide range of processes such as the Two-Temperature Model, ultra-fast laser irradiation, and biological processes. This review article focuses on heat equation models, including Fourier and non-Fourier heat equations. A comparison between Fourier and non-Fourier heat equations and their generalized solutions have been discussed. Various components of heat equations and their implementation in multiple processes have been illustrated. Besides, literature has been collected based on ITT implementation in various materials. Furthermore, a future outlook has been provided for Fourier and non-Fourier heat equations. It was found that the Fourier heat equation is simple to use but involves infinite speed heat propagation in comparison to the non-Fourier heat equation and can be linked with the Two-Temperature Model in a natural way. On the other hand, the non-Fourier heat equation is complex and involves various unknowns compared to the Fourier heat equation. Fourier and Non-Fourier heat equations have proved their reliability in the case of laser–metallic materials, electron beam–biological and –inorganic materials, laser–semiconducting materials, and laser–graphene material interactions. It has been identified that the material properties, electron–phonon relaxation time, and Eigen Values play an essential role in defining the precise results of Fourier and non-Fourier heat equations. In the case of laser–graphene interaction, a restriction has been identified from ITT. When computations are carried out for attosecond pulse durations, the laser wavelength approaches the nucleus-first electron separation distance, resulting in meaningless results.

We discuss the interaction of ultrashort near-infrared laser pulses with sharp metal tips at moderate nominal intensities (I0 ∼ 1011 W cm−2). As external electric fields are strongly enhanced at such tips (enhancement factor ∼10) our system turns out to be an ideal miniature laboratory to investigate strong-field effects at solid surfaces. We analyse the electron-energy spectra as a function of the strength of the laser field and the static extraction field and present an intuitive model for their interpretation. The size of the effective field acting on the metal electrons can be determined from the electron spectra. The latter are also reproduced by time-dependent density functional theory (TDDFT) simulations.

We consider the generation of IR radiation during the interaction of a high-power ultrashort laser pulse with a gas jet using numerical simulation by the particle-in-cell method. The laser pulse parameters correspond to the capabilities of the PEARL sub-petawatt laser facility in Nizhny Novgorod (Russia) when using the compression after compressor approach (CafCA). It is demonstrated that about 1 % of the energy can be converted into radiation in the wavelength range of 5 – 10 μm.

Recent experimental and theoretical investigations are reviewed concerning the generation of fast charged particles and superstrong magnetic fields in the interaction of ultrashort laser pulses with solid targets. The mechanisms of generating fast charged particles in superstrong light fields of laser radiation with intensities ranging from 1017 to 1021 W cm–2 are considered. Electron acceleration due to vacuum heating, the ponderomotive potential, resonance absorption, the laser-driven wake field in the underdense part of plasma, cyclotron mechanism and some other mechanisms are thoroughly analyzed. Experimental data on the acceleration of protons and atomic ions by spatial charge fields on thin and thick solid targets are presented and theoretically interpreted. Particular attention is paid to the generation of superstrong quasistatic magnetic fields in laser plasmas and methods for measuring them under the action of various laser pulses of both femto- and picosecond durations. The possible formation of magnetic plasma configurations and magnetic plasma confinement are discussed.

An experiment investigating the production of relativistic electrons from the interaction of ultrashort multi-terawatt laser pulses with an underdense plasma is presented. Electrons were accelerated to tens of MeV and the maximum electron energy increased as the plasma density decreased. Simulations have been performed in order to model the experiment. They show a good agreement with the trends observed in the experiment and the spectra of accelerated electrons could be reproduced successfully. The simulations have been used to study the relative contribution of the different acceleration mechanisms: plasma wave acceleration, direct laser acceleration and stochastic heating. The results show that in low density case (1 percent of the critical density) acceleration by laser is dominant mechanism. The simulations at high density also suggest that direct laser acceleration is more efficient that stochastic heating.

Laser Microbeam-induced Spatiotemporal Change in Refractive Index of Chromosomes in Living PTK2 Cells

Wave theory and geometrical optics are used to investigate the effect of small changes in size and index of refraction on the resonance wavelength of spherical microresonators. It is shown that changes in the index of refraction have two effects: These changes affect the phase jump on the surface and the optical path length in the resonator. Under certain conditions the effect of the external or internal index of refraction becomes negligible. The influence of the order number of the resonance modes is investigated. Finally, the results of the theoretical analyses are applied to calculate the effect of temperature on the resonance wavelength.

GeO<SUB>2</SUB>-B<SUB>2</SUB>-O<SUB>3</SUB>-SiO<SUB>2</SUB> thin films were fabricated by plasma enhanced chemical vapor deposition method. Boron codoping into a GeO<SUB>2</SUB>-SiO<SUB>2</SUB> thin film induced large absorption in the vicinity of 240nm, and OH absorption decreased compared to GeO<SUB>2</SUB>-SiO<SUB>2</SUB> films. These films of 5 micrometers in thickness exhibited large positive refractive index change without hydrogen loading by irradiation with ArF (193nm) excimer laser pulses. Induced refractive index change was approximately 0.002 which was measured by the prism coupling method. A waveguide was written in this high photosensitive glass film by UV irradiation. The guided mode of the waveguide seems to be single and estimated refractive index change was approximately from 0.003 to 0.004. Three unique phenomena were found in 0.2micrometers thick films on Si substrate. First, these films exhibited large negative refractive index and positive thickness changes by irradiation with ArF laser pulses. Induced negative index change was larger than 0.02 and thickness change was more than 1%. Silica films doped only boron or germanium didn't exhibit such negative index changes. Second, the annealing before laser irradiation decreased the photosensitivity of these films remarkably. Third, these induce refractive index and thickness changes were decreased with time rapidly. These mechanisms were under investigation.

In our previous work, a highly sensitive waveguide Bragg grating (WBG) sensor for measuring small changes in the refractive index of a surrounding liquid was developed (1). We proposed a technique for creating a temperature insensitive refractometer that utilizes core and cladding modes in an open-top ridge waveguide architecture in order to discriminate between Bragg wavelength changes in temperature and refractive index (2). In this work, a technique for creating a temperature insensitive refractometer that utilizes TE and TM modes in an open-top ridge waveguide design is presented. By using the TE mode resonance as a temperature reference, the relative shift of the TM mode can be monitored in order to measure the refractive index of liquids under test. Specifically, the device fabricated here produces a relative resonance shift of 1 pm for every 1×10 -4 of measured index change, with a temperature sensitivity For temperature insensitive sensors based on fiber Bragg gratings, several techniques have been proposed to discriminate between Bragg resonance spectral shifts associated with refractive index measurements and those induced by fluctuations in temperature. These techniques are implemented by using: a second Bragg grating in a side-polished fiber Bragg grating refractometer (3-4), higher order modes in an etched-core of a fiber Bragg grating sensor (5-6), and higher order modes in a tilted fiber Bragg grating sensor (7-12). We proposed a technique for creating a temperature insensitive refractometer that utilizes core and cladding modes in an open-top ridge waveguide architecture in order to discriminate between Bragg wavelength changes in temperature and refractive index. The relative shift of the core mode resonance to cladding mode resonance is used to measure the refractive index of substances under test. The device fabricated produced a relative resonance shift of 1 pm for every 5×10 -4 of measured index change, with a temperature sensitivity ~ 0.5 pm/°C (2). Taking a similar approach, here, we reported another technique for creating a temperature insensitive refractometer that utilizes TE and TM modes in an open-top ridge waveguide architecture in order to discriminate between changes in temperature and refractive index. In our previous work (1), a highly sensitive waveguide Bragg grating (WBG) sensor for measuring small changes in the refractive index of a surrounding liquid was developed. The structure of the open-top ridge waveguide is as shown in Fig.1. The center ridge waveguide with the Bragg grating is tested as a refractometer by coupling the light source into the end of the waveguide. The function of the two adjacent waveguides is to act as a barrier and to partially prevent the liquid from flowing away from the waveguide containing the grating. The guided light of the center waveguide couples evanescently into the surrounding liquid through the top and sides of the waveguide. When a Bragg grating is induced in the core of an open-top ridge waveguide with a larger birefringence, TE and TM resonances are observed when the light guided by the core is phase matched by the grating structure. Both TE and TM resonances are sensitive to the liquid refractive index on the top layer of the open-top ridge waveguide. The TE and TM sensitivities to temperature fluctuations however, are more closely matched. These characteristics can be used to decouple fluctuations of the Bragg resonance of the core mode due to temperature from those changes that are due to variation in the refractive index of the analyte liquid. In the experiments presented here, the variation of TE and TM resonances are investigated as a function of temperature and the external refractive index nt. A theoretical model is developed to investigate the performance of some potential waveguide structures. Relationships between the waveguide core size, refractive index distribution, as

: The optical distortion in neodynium doped glass which is induced by pump radiation is discribed. Optical distortion was observed at 6328A and the optical path length was found to be dependent on four primary effects: (1) change in physical length; (2) Change in refractive index due to temperature rise; (3) Change in index resulting from stress; (4) Change in index associated with an excited state population of neodymium ions. The experimental techniques used and the results obtained are presented. Included are measurements of optical path length variations, pump-induced birefringence, change in physical length, change in refractive index, bulk temperature rise, and the deflection of a light beam. The theory of thermal optic distortion was developed for the first time to include Fermat's principle. This approach leads to equations defining both the slope and trajectory of rays through the material. The resulting equations are employed to predict ray refraction, beam divergence, and the optical path length through the material as a function of radius, time, and polarization. Good agreement between theory and experiment is achieved provided a new term is added to the expression for the change in refractive index. This term arises from the fact that the polarizability of the neodymium ion in its excited 4F(3/2) level is different from its value in the 4I(9/2) ground level. The inclusion of this new term in the expression for the change in refractive index implies that large optical distortions can exist in 'athermalized' glass.

Interaction of ultrashort laser pulses with transparent materials is a powerful technique of modification of material properties for various technological applications. The physics behind laser-induced modification phenomenon is rich and still far from complete understanding. We present an overview of our models developed to describe processes induced by ultrashort laser pulses inside and on the surface of bulk glass. The most sophisticated model consists of two parts. The first part solves Maxwell’s equations supplemented by the rate and hydrodynamics equations for free electrons. The model resolves spatiotemporal dynamics of free-electron population and yields the absorbed energy map. The latter serves as an initial condition for thermoelastoplastic simulations of material redistribution. The simulations performed for a wide range of irradiation conditions have allowed to clarify timescales at which modification occurs after single laser pulses. Simulations of spectrum of laser light scattered by laser-generated plasma revealed considerable blueshifting which increases with pulse energy. To gain insight into temperature evolution of a glass material under the surface irradiation conditions, we employ a model based on the rate equation describing free electron generation coupled with the energy equations for electrons and lattice. Swift heating of electron and lattice subsystems to extremely high temperatures at fs timescale has been found at laser fluences exceeding the threshold fluence by 2-3 times that can result in efficient bremsstrahlung emission from the irradiation spot. The mechanisms of glass ablation with ultrashort laser pulses are discussed by comparing with the experimental data. Finally, a model is outlined, developed for multi-pulse irradiation regimes, which enables gaining insight into the roles of defects and heat accumulation.

Ultrashort laser pulses recently found extensive application in micro- and nanostructuring, in refractive surgery of the eye, and in biophotonics. Due to the high laser intensity required to induce optical breakdown, nonlinear plasma formation is generally accompanied by a number of undesired nonlinear side-effects such as self-focusing, filamentation and plasma-defocusing, seriously limiting achievable precision and reproducibility. To reduce pulse energy, enhance precision, and limit nonlinear side effects, applications of ultrashort pulses have recently evolved towards tight focusing using high numerical aperture microscope objectives. However, from the theoretical and numerical point of view generation of optical breakdown at high numerical aperture focusing was barely studied. To simulate the interaction of ultrashort laser pulses with transparent materials, a comprehensive numerical model taking into account nonlinear propagation, plasma generation as well as the pulse's interaction with the generated plasma is introduced. By omitting the widely used scalar and paraxial approximations a novel nonlinear propagation equation is derived, especially suited to meet the conditions of high numerical aperture focusing. The multiple rate equation (MRE) model is used to simultaneously calculate the generation of free electrons. Nonparaxial and vectorial diffraction theory provides initial conditions. The theoretical model derived is applied to numerically study the generation of optical breakdown plasmas, concentrating on parameters usually found in experimental applications of cell surgery. Water is used as a model substance for biological soft tissue and cellular constituents. For focusing conditions of numerical aperture NA < 0.9 generation of optical breakdown is shown to be strongly influenced by plasma defocusing, resulting in spatially distorted breakdown plasmas of expanded size. For focusing conditions of numerical aperture NA &ge; 0.9 on the other hand generation of optical breakdown is found to be almost unaffected by distortive side-effects, perfectly suited for material manipulation of highest precision.

We report stress-induced channel waveguides formed in epitaxial BaTiO 3 films. BaTiO 3 epitaxial films (doped with and without erbium) were grown on MgO (001) single- crystal substrates using rf magnetron sputtering. In the channel waveguides developed, the lateral confinement of light is achieved via the photoelastic effect in BaTiO 3 induced by thin-film stress. As a stress-inducing film, a 0.5- micrometer-thick SiO 2 film was sputter-deposited on top of a 3.0-micrometer-thick BaTiO 3 film with a 7 to 10- micrometer-wide window opening. The fabricated structures were characterized in terms of their guided mode profiles at 1.3 and 1.55 micrometer wavelength. The measurement result clearly shows both the lateral and vertical confinement of light in the channel region. The stress distribution in the channel structure was calculated by solving the coupled equations that describe the elastomechanical and piezoelectric effects in the ferroelectric material. The refractive index changes were than calculated taking into account both the photoelastic and electro-optic effects of BaTiO 3 . The simulation results show a good agreement with the measurement results. The waveguide structure developed in this work does not require etching of BaTiO 3 , and is expected to be useful as a simple and economical method for forming channel waveguides with other ferroelectric films as well.

Ultrashort laser pulses recently found extensive application in micro-and nanostructuring, in refractive surgery of the eye, and in biophotonics.Due to the high laser intensity required to induce optical breakdown, nonlinear plasma formation is generally accompanied by a number of undesired nonlinear side-effects such as self-focusing, filamentation and plasma-defocusing, seriously limiting achievable precision and reproducibility.To reduce pulse energy, enhance precision, and limit nonlinear side effects, applications of ultrashort pulses have recently evolved towards tight focusing using high numerical aperture microscope objectives.However, from the theoretical and numerical point of view, generation of optical breakdown at high numerical aperture focusing was barely studied.To simulate the interaction of ultrashort laser pulses with transparent materials at high NA focusing, a comprehensive numerical model was introduced by the authors in [1], taking into account nonlinear propagation, plasma generation as well as the pulse's interaction with the generated plasma.The multiple rate equation (MRE) model [2] is used to simultaneously calculate the generation of free electrons.Nonparaxial and vectorial diffraction theory provides initial conditions.The theoretical model derived in [1] is applied to numerically study the generation of optical breakdown plasmas, concentrating on parameters usually found in experimental applications of cell surgery.Water is used as a model substance for biological soft tissue and cellular constituents.For focusing conditions of low to moderate numerical aperture (NA < 0.9) generation of optical breakdown is shown to be strongly influenced by plasma defocusing, resulting in spatially distorted breakdown plasmas of expanded size.For focusing conditions of high numerical aperture (NA ≥ 0.9) on the other hand generation of optical breakdown is found to be almost unaffected by distortive side-effects, perfectly suited for material manipulation of highest precision.