Order Nonlinear Optical Processes Research Articles

Self‐Referenced Subcycle Metrology of Quantum Fields

AbstractA new time‐domain method for subcycle metrology of quantum electric fields using a combination of a third order nonlinear optical process and homodyne detection with a local oscillator (LO) field is proposed and analyzed. The new method enables isolation of intrinsically weak quantum noise contribution by subtraction of the shot noise of the LO on a pulse‐by‐pulse basis. Together with the centro‐symmetric character of the nonlinearity, this method unlocks novel opportunities toward terahertz and mid‐infrared quantum field metrologies.

First Order Hyper polarizability and Intramolecular Charge Transfer of N-Ethyl-N-(2-Hydroxyethyl)-4-(4-Nitrophenylazo) Aniline for Photonic Applications

We report a computational methodology for estimating the first order hyperpolarizability ((3) of N-ethyl-N-(2-hydroxyethyl)-4-(4-nitrophenylazo) aniline, a nonlinear optical (NLO) chromophore being used as anazobenzene dye. The planar and non-planar structures of N-ethyl-N-(2-hydroxyethyl)-4-(4-nitrophenylazo) aniline were optimized by B3LYP/6-311++G (D,P) basis set using GAUSSIAN’09W program package. The dipole moment, static polarizability, first order hyperpolarizability were studied using HF/6-31G (D) basis set. The (3 value of the planar and non-planar structure of N-ethyl-N-(2-hydroxyethyl)-4-(4-nitrophenylazo) aniline is 196 and 124 times higher than that of urea standard, respectively, which qualify both of the novel molecular systems as highly efficient for second order NLO applications and adds evidence to the importance of derealization of ^-electrons in a system for effective second order NLO processes. Experiments were also performed using an Nd-YAG laser of pulses in the range of 5-10 nanoseconds with a tunable peak power of 4.7 W.

Spatially co-registered wide-field nonlinear optical imaging of living and complex biosystems in a total internal reflection geometry.

Nonlinear optical microscopy that leverages an objective based total internal reflection (TIR) excitation scheme is an attractive means for rapid, wide-field imaging with enhanced surface sensitivity. Through select combinations of distinct modalities, one can, in principle, access complementary chemical and structural information for various chemical species near interfaces. Here, we report a successful implementation of such a wide-field nonlinear optical microscope system, which combines coherent anti-Stokes Raman scattering (CARS), two-photon fluorescence (TPF), second harmonic generation (SHG), and sum frequency generation (SFG) modalities on the same platform. The intense optical fields needed to drive these high order nonlinear optical processes are achieved through the use of femtosecond pulsed light in combination with the intrinsic field confinement induced by TIR over a large field of view. The performance of our multimodal microscope was first assessed through the experimental determination of its chemical fidelity, intensity and polarization dependences, and spatial resolution using a set of well-defined model systems. Subsequently, its unique capabilities were validated through imaging complex biological systems, including Hydrangea quercifolia pollen grains and Pantoea sp. YR343 bacterial cells. Specifically, the spatial distribution of different molecular groups in the former was visualized via vibrational contrast mechanisms of CARS, whereas co-registered TPF imaging allowed the identification of spatially localized intrinsic fluorophores. We further demonstrate the feasibility of our microscope for wide-field CARS imaging on live cells through independent characterization of cell viability using spatially co-registered TPF imaging. This approach to TIR enabled wide-field imaging is expected to provide new insights into bacterial strains and their interactions with other species in the rhizosphere in a time-resolved and chemically selective manner.

Enhanced Four-Wave Mixing in Doubly Resonant Si Nanoresonators

Frequency conversion is one of the main applications of nonlinear optical processes in which a signal is produced at a different wavelength from the excitation wavelength. In particular, four-wave mixing (FWM) is a third order nonlinear optical process that allows, for instance, the generation of visible frequencies by tuning near-infrared laser pumps. Here, in order to augment the very weak FWM conversion efficiency, we design silicon Mie resonators that exhibit two resonances of the internal electric field intensity around the frequency range of the laser pumps. The linear extinction spectrum of the individual Si resonator is first measured by bright field spectroscopy and compared with numerical simulations to confirm the existence of the two resonances corresponding to electric and magnetic dipole excitations. The FWM signal is then measured for a single Si nanoresonator when the first pump is set to the electric resonance while tuning the frequency of the second pump across the magnetic dipolar resonance. We show that the FWM signal generated in the visible spectrum is maximum when the frequency of the tunable pump corresponds to the maximum of the internal electric field intensity. At this position, the FWM signal is enhanced by more than 2 orders of magnitude compared with the FWM signal generated by the unpatterned silicon film.

(Invited) Inhomogeneous Strain in Silicon Photonics

The lack of a dipolar second order susceptibility (χ(2)) in silicon due to its centrosymmetric diamond lattice usually inhibits efficient second order nonlinear optical processes in the silicon bulk. Depositing stressed silicon nitride layers or growing a thermal oxide layer introduces an inhomogeneous strain into the silicon lattice and breaks the centrosymmetry of its crystal structure thereby creating a χ(2). This causes enhanced second harmonic generation and was observed in reflection and transmission measurements for wavelengths in the infrared. However strain is not the only means to break the structures symmetry. Fixed charges at the silicon nitride/silicon interface cause a high electric field close to the silicon interface which causes electric-field-induced-second-harmonic (EFISH) contributions too. The combination of both effects leads to χ(2) values which are estimated to be of the order as classic χ(2) materials like KDP or LiNiO3. This paves the way for the exploitation of other second order nonlinear processes in the area of silicon photonics and is an example how fundamental optical properties of materials can be formed by strain.

Second-Order Nonlinearity in Triangular Lattice Perforated Gold Film due to Surface Plasmas Resonance

We have studied the excitation second-order nonlinearity through a triangular lattice perforated gold film instead of square lattice in many papers. Under the excitation of surface plasmas resonance effect, the second order nonlinearity exists in the noncentrosymmetric split-ring resonators arrays. Reflection of fundamental frequency wave through a triangular lattice perforated gold film is obtained. We also described the second harmonic conversion efficiencies in the second order nonlinear optical process with the spectra. Moreover, the electric field distributions of fundamental frequency above the gold film region are calculated. The light propagation through the holes results in the enhancement of the second order nonlinearity including second harmonic generation as well as the sum (difference) frequency generation.

Polarization-Resolved SHG towards Collagen Imaging

Collagen is a triple-helix protein that self-assembles into supramolecular fibrils, essential for the biomechanical integrity and physical properties of biological tissues and organs. Second Harmonic Generation(SHG) microscopy exploits a second order nonlinear coherent optical process to image macromolecules with non-centrosymmetric structure, as collagen fibers(1). Such a label-free approach provides three-dimensional(3D) imaging of the structural organization of the collagen fibers in tissues at a sub-cellular resolution with intrinsic optical sectioning, high deep penetration and reduction of out-of-focus photobleaching and phototoxicity(2). Here, we collected the endogenous SHG signal of the collagen to evaluate the hierarchical structure, organization and orientation of collagen fibers in different types of specimen, from ex-vivo biological tissues to bioengineered samples(3). To conduct this study, we coupled a femtosecond Ti:Sapphire Chameleon Ultra II laser(Coherent, Santa Clara, CA, USA) with a Leica TCS STED-CW confocal microscope(Leica-Microsystems, Mannheim, Germany). This allowed collecting the forward, the backward SHG signal and the TPE autofluorescence of the samples(2). Moreover, we also focused our attention on the SHG signal as function of polarization states of the incoming light to distinguish among different collagen fiber types and orientations(4). Analysis of the polarization of the outcoming light and the ratio FSHG/BSHG was carried out due to its potential in providing more detailed information about the sample, for instance a relationship with the diameter and the functional and structural organization of the collagen fibers variability in various tissues. For example, this allows realizing a set of features useful to evaluate the assembly of artificial tissues depending on the scaffold role in the collagen fibers assembly when mimicking a target tissue.1. Chen X. et al. Nat Protoc. 7(4),654(2012).2. Bianchini P. et al., J. Biophotonics, 1,6(2008).3. Scaglione S. et al. Nature Sci. Rep. 2,(274): 1-6(2012).4. Odin C. et al, Opt.Express, 16,20(2008).

Investigation of ultra-broadband terahertz time-domain spectroscopy with terahertz wave gas photonics

Recently, air plasma, produced by focusing an intense laser beam to ionize atoms or molecules, has been demonstrated to be a promising source of broadband terahertz waves. However, simultaneous broadband and coherent detection of such broadband terahertz waves is still challenging. Electro-optical sampling and photoconductive antennas are the typical approaches for terahertz wave detection. The bandwidth of these detection methods is limited by the phonon resonance or carrier’s lifetime. Unlike solid-state detectors, gaseous sensors have several unique features, such as no phonon resonance, less dispersion, no Fabry-Perot effect, and a continuous renewable nature. The aim of this article is to review the development of a broadband terahertz time-domain spectrometer, which has both a gaseous emitter and sensor mainly based on author’s recent investigation. This spectrometer features high efficiency, perceptive sensitivity, broad bandwidth, adequate signal-to-noise ratio, sufficient dynamic range, and controllable polarization. The detection of terahertz waves with ambient air has been realized through a third order nonlinear optical process: detecting the second harmonic photon that is produced by mixing one terahertz photon with two fundamental photons. In this review, a systematic investigation of the mechanism of broadband terahertz wave detection was presented first. The dependence of the detection efficiency on probe pulse energy, bias field strength, gas pressure and third order nonlinear susceptibility of gases were experimentally demonstrated with selected gases. Detailed discussions of phase matching and Gouy phase shift were presented by considering the focused condition of Gaussian beams. Furthermore, the bandwidth dependence on probe pulse duration was also demonstrated. Over 240 times enhancement of dynamic range had been accomplished with n-hexane vapor compared to conventional air sensor. Moreover, with sub-20 fs laser pulses delivered from a hollow fiber pulse compressor, an ultra-broad spectrum covering from 0.3 to 70 THz was also showed. In addition, a balanced detection scheme using a polarization dependent geometry was developed by author to improve signal-to-noise ratio and dynamic range of conventional terahertz air-biased-coherent-detection (ABCD) systems. Utilizing the tensor property of third order nonlinear susceptibility, second harmonic pulses with two orthogonal polarizations was detected by two separated photomultiplier tubes (PMTs). The differential signal from these two PMTs offers a realistic method to reduce correlated laser fluctuation, which circumvents signal-to-noise ratio and dynamic range of conventional terahertz ABCD systems. A factor of two improvement of signal-to-noise ratio was experimentally demonstrated. This paper also introduces a unique approach to directly produce a broadband elliptically polarized terahertz wave from laser-induced plasma with a pair of double helix electrodes. The theoretical and experimental results demonstrated that velocity mismatch between excitation laser pulses and generated terahertz waves plays a key role in the properties of the elliptically polarized terahertz waves and confirmed that the far-field terahertz emission pattern is associated with a coherent process. The results give insight into the important influence of propagation effects on terahertz wave polarization control and complete the mechanism of terahertz wave generation from laserinduced plasma. This review provides a critical understanding of broadband terahertz time-domain spectroscopy (THz-TDS) and introduces further guidance for scientific applications of terahertz wave gas photonics.

Plasmonic enhancement of the third order nonlinear optical phenomena: Figures of merit

Recent years have seen increased interest in the plasmonic enhancement of nonlinear optical effects, yet there remains an uncertainty as to the limits of this enhancement. We present a simple and physically transparent theory for the plasmonic enhancement of third order nonlinear optical processes and show that while a huge enhancement of the effective nonlinear index can be attained, the most relevant figure of merit, the phase shift per one absorption length, remains very low. This suggests that while nonlinear plasmonic materials are not suitable for applications requiring high efficiency, for example in all-optical switching and wavelength conversion, they can be very useful for applications where overall high efficiency is not critical, such as in sensing.

Selective observation of local carrier dynamics at step bunches on vicinal TiO2(110) by time-resolved pump-probe second harmonic generation method

We report on a step-selective time-resolved second harmonic generation (SHG) method using vicinal TiO${}_{2}$ (110) with regularly aligned step bunches. The step selectivity was realized by taking advantage of the symmetry-selective properties of second order nonlinear optical processes. In the time-resolved pump-probe SHG measurement, the step bunches displayed a unique temporal response or a sharp spike decaying within \ensuremath{\sim}100 ps, while no decay kinetics was observed for the (110) terraces within a nanosecond. The observed unique local dynamics at the step bunches was attributed to a transient change in their local carrier density. This carrier density change at the step bunches was discussed from the aspect of their local density of states (LDOS) by using step-selective second harmonic and sum frequency generation (SHG/SFG) spectroscopy and density functional theory (DFT) calculation.

Effect of nonlinear absorption in estimation of order of nonlinear optical process by fluorescence intensity

We report the effect of nonlinear absorption on the fluorescence signal. Attenuation of the incident beam intensity ( I) in the medium due to nonlinear absorption reduces the fluorescence signal. We show that fluorescence signal proportional to I 2 is not always indicative of two-photon absorption process but such a dependence can be obtained for three or four-photon absorption process due to attenuation of the pump beam by nonlinear absorption. This reduction in the fluorescence signal due to nonlinear absorption is found to be more sensitive in the higher order nonlinear optical processes.

Skeletal muscle sarcomeric SHG patterns photo-conversion by femtosecond infrared laser

Femtosecond laser at 780 nm excitation wavelength was used to photo-convert the physiological sarcomeric single band (SB) second harmonic generation (SHG) pattern into double band (DB) in Xenopus laevis premetamorphic tail muscles. This photo-conversion was found to be a third order non-linear optical process and was drastically reduced at 940 nm excitation wavelength. This effect was no longer observed in paraformaldehyde fixed muscles and was enhanced by hydrogen peroxide. The action of hydrogen peroxide suggests that reactive oxygen species (ROS) could contribute to this photo-conversion. These results demonstrate that sarcomeric DB SHG pattern is a marker of sarcomere photodamage in xenopus tadpole muscles and highlight the need of being very careful at using two-photon excitation while observing living tissues. Moreover they open new avenues for in situ intravital investigation of oxidative stress effects in muscle dysfunctions and diseases.

Mechanism of effective three-photon induced lasing

The experimental and theoretical results in this letter reveal that three-photon absorption effect can help light wave to form solitonlike filament; and a stable solitonlike filament is observed in solution with high quintic nonlinearity. This stable solitonlike filament makes pumping infrared laser be localized within the filament and reach high pumping density for a long distance. This high density pumping laser in the filament generates high efficiency lasing induced by three-photon absorption. This work is an approach to make practical application of high order nonlinear optical processes possible.

Temporal and Spatial Interference between Four-Wave Mixing and Six-Wave Mixing Channels

Using phase control between four-wave mixing (FWM) and six-wave mixing (SWM) channels in a four-level atomic system, we demonstrate temporal and spatial interferences between these two nonlinear optical processes. Efficient and coexisting FWM and SWM signals are produced in the same electromagnetically induced transparency window via atomic coherence. The temporal interference has a femtosecond time scale corresponding to the optical transition frequency. Such studies of intermixing between different order nonlinear optical processes with a controllable phase delay can have important applications in high-precision measurements, coherence quantum control, and quantum information processing.

Time-Resolved Spectroscopy of Laser-Induced Light Emission from an Evaporated Au Film in the Kretschmann Geometry

We have investigated laser-induced light emission from Au film evaporated on the bottom of a hemispherical glass prism in the Kretschmann geometry. Picosecond laser pulses tuned at a photon energy of 1.35 eV were focused onto the Au film from the vacuum side of the prism, and the time- and photon-energy-resolved spectra of light emitted through the prism were measured in a photon energy range from 1.5 to 2.5 eV for a time span of 2 ns by a streak camera operated in synchronization with the laser pulses. The total intensity of emission was proportional to the square of incident laser power, suggesting that the emission is excited via a second order nonlinear optical process. The time-integrated spectrum of the emission was successfully reproduced by the dielectric theory of light emission that treats radiation by surface plasmon polaritons (SPP) confined in this sample structure. Hence we see that the emission is radiated by SPP being excited via the nonlinear optical process. This feature is not consistent with the temporal behavior of emission, i.e., the lifetime of the emission was as long as 240 ps.

Investigation of Interfacial Structure of Electrode/Electrolyte Interfaces by Nonlinear Spectroscopic Techniques

Information on the structure and surface reaction dynamics of an electrode/electrolyte interface is essential to reveal the reaction mechanisms and to control electrochemical reactions. Since the second order nonlinear optical processes such as second harmonic generation (SHG) and sum-frequency generation (SFG) are forbidden in the media of centro-symmetry, these techniques provide interface specific information and can be used to probe buried interfaces as far as they are accessible by light. We applied SHG and SFG to obtain information on electronic and molecular structure at the electrochemical interfaces and two examples are presented here. First, the electrochemical reaction HCHO at Pt surface was investigated by SHG spectroscopy. Next, the structure of interfacial water was characterized under potential control by SFG spectroscopy.

Self-Consistent Approach for Simplifying the Molecular Interpretation of Nonlinear Optical and Multiphoton Phenomena

A method is developed for simplifying molecular interpretations of nonlinear optical phenomena. General sum-over-states expressions derived from perturbation theory can be written identically and self-consistently as simple products of lower-order effects. Electric dipole-allowed expressions for the nonlinear polarizability reduce to straightforward formulas directly connected to intuitive molecular properties without sacrificing mathematical rigor. This approach is sufficiently general to allow its application in treating electronic, vibrational, and vibronic interactions for both parametric (passive) processes (e.g., wave-mixing spectroscopies, sum- and difference-frequency generation, harmonic generation, etc.) and nonparametric (active) processes (e.g., hyper-Raman spectroscopy, multiphoton absorption, etc.). Explicit examples for sum-frequency generation and for four-wave mixing provide a convenient context for interpreting higher order nonlinear optical processes.

Effect of higher order nonlinear optical processes on optical absorption in the photorefractive BSO and BGO crystals

The processes of nonlinear refraction and nonlinear absorption are studied in the photorefractive Bi12SiO20 (BSO) and Bi12GeO20 (BGO) crystals at a wavelength of a picosecond Nd:YAG laser of 1064 nm. The nonlinear refraction in the crystals is shown to be related to the Kerr effect, and the nonlinear absorption at this wavelength, to three-photon absorption. The three-photon absorption coefficients of the BSO and BGO crystals are equal, respectively, to (2.5±0.8) ×10−20 and (4.4±1.3) ×10−20 cm3W−2.

Stationary state and dynamics of birefringence and nonlinear optical properties induced by electric field poling in polymeric films

AbstractWe present a theoretical study concerning the effect of the electric field poling process on the molecular angular distribution of polar nonlinear‐optical molecules in a polymeric environment. This is required for investigating the contribution of the molecular order to the anisotropy and nonlinear‐optical processes (second‐harmonic generation (SHG), electro‐optic Pockels (EOPE) and Kerr (EOKE) effects). We demonstrate mathematically that the order parameters at thermodynamical equilibrium are defined exactly by the spherical modified Bessel functions (An(μE/kT) = in(μE/kT)/io(μE/kT)). They can be related to Langevin functions but with complicated relations for high orders of n. Their evolution with μE/kT confirms that the second order nonlinear‐optical processes (SHG and EOPE) are more sensitive to the strength of the poling field than are the linear (birefringence) and third‐order nonlinear‐optical effects (EOKE). We show that it is possible to measure the molecular anisotropy of nonlinear‐optical molecules by quadratic electro‐optic experiments. The transients of the poling are studied with the rotational diffusion equation, characterized by a rotational diffusion constant D. This is solved using important recurrence relations of Legendre polynomials. An almost exact analytical solution is found for the physical and practical case where μE/kT is close to 1, and the nonvanishing order parameters are almost equal to the rigourous expressions given by the spherical modified Bessel functions. It is shown that the onset of birefringence and nonlinear‐optical processes (SHG, EOPE and EOKE) involves two time constants τ1,2 = [2D(2 ± √1–(μE/kT)2/5)]−1 which depend on D and μE/kT. After the removal of the poling field, the relaxation of the linear and nonlinear‐optical properties is also discussed.

Symmetry Properties of Second Order Hyperpolarizabilities

Abstract Time-reversal symmetry property of a second order nonlinear optical hyperpolarizability is examined in terms of the Manley-Rowe power relation to find relationship to the overall permutation symmetry. An extended symmetry relation is discovered reducing the independent number of the hyperpolarizability tensor components describing the second order nonlinear optical processes. Experimental implications are discussed.