Third Harmonic Generation Measurements Research Articles

Dynamical interplay between superconductivity and pseudogap in cuprates as revealed by terahertz third-harmonic generation spectroscopy

We report on nonlinear terahertz third-harmonic generation (THG) measurements on YBa 2 Cu 3 O 6+ x thin films. Different from conventional superconductors, the THG signal starts to appear in the normal state, which is consistent with the crossover temperature T * of pseudogap over broad doping levels. Upon lowering the temperature, the THG signal shows an anomaly just below T c in the optimally doped sample. Notably, we observe a beat pattern directly in the measured real-time waveform of the THG signal. We elaborate that the Higgs mode, which develops below T c , couples to the mode already developed below T * , resulting in an energy level splitting. However, this coupling effect is not evident in underdoped samples. We explore different potential explanations for the observed phenomena. Our research offers valuable insight into the interplay between superconductivity and pseudogap.

Extreme Polarization Anisotropy in Resonant Third-Harmonic Generation from Aligned Carbon Nanotube Films.

Carbon nanotubes (CNTs) possess extremely anisotropic electronic, thermal, and optical properties owing to their 1D character. While their linear optical properties have been extensively studied, nonlinear optical processes, such as harmonic generation for frequency conversion, remain largely unexplored in CNTs, particularly in macroscopic CNT assemblies. In this work, macroscopic films of aligned and type-separated (semiconducting and metallic) CNTs are synthesized and polarization-dependent third-harmonic generation (THG) from the films with fundamental wavelengths ranging from 1.5 to 2.5µm is studied. Both films exhibited strongly wavelength-dependent, intense THG signals, enhanced through exciton resonances, and third-order nonlinear optical susceptibilities of 2.50×10-19 m2 V-2 (semiconducting CNTs) and 1.23×10-19 m2 V-2 (metallic CNTs), respectively are found, for 1.8µm excitation. Further, through systematic polarization-dependent THG measurements, the values of all elements of the susceptibility tensor are determined, verifying the macroscopically 1D nature of the films. Finally, polarized THG imaging is performed to demonstrate the nonlinear anisotropy in the large-size CNT film with good alignment. These findings promise applications of aligned CNT films in mid-infrared frequency conversion, nonlinear optical switching, polarized pulsed lasers, polarized long-wave detection, and high-performance anisotropic nonlinear photonic devices.

Highly Sensitive Detection of Microstructure Variation Using a Thickness Resonant Transducer and Pulse-Echo Third Harmonic Generation.

In nonlinear ultrasound testing, the relative nonlinear parameter is conveniently measured as a sensitive means of detecting and imaging overall variation of microstructures and damages. Compared to the quadratic nonlinear parameter (β'), the cubic nonlinear parameter (γ'), calculated as the third harmonic amplitude divided by the cube of the fundamental amplitude, has generally a higher value, providing better sensitivity in nonlinear parameter mapping. Since the third harmonic amplitude is about two orders of magnitude lower than the fundamental amplitude, efficient excitation and highly sensitive reception of third harmonic is very important. In this paper, we explore an odd harmonic thickness resonant transducer that meets the requirements for pulse-echo third harmonic generation (THG) measurements. We also address the problem of source nonlinearity that may be present in the measured amplitude of the third harmonic and propose a method to properly correct it. First, we measure γ' for a series of aluminum specimens using the through-transmission method to observe the behavior of γ' as a function of specimen thickness and input voltage, and examine the effects of various corrections such as attenuation, diffraction and source nonlinearity. Next, we apply the odd harmonic resonant transducer to pulse-echo THG measurements of precipitation heat-treated specimens. It is shown that such transducer is very effective in generation and detection of fundamental and third harmonics under finite amplitude toneburst excitation. The highly sensitive detectability of γ' are presented as a function of aging time, and the sensitivity of γ' is compared with that of β' and β'2.

Third-Order Optical Nonlinearities of 2D Materials at Telecommunications Wavelengths

All-optical signal processing based on nonlinear optical devices is promising for ultrafast information processing in optical communication systems. Recent advances in two-dimensional (2D) layered materials with unique structures and distinctive properties have opened up new avenues for nonlinear optics and the fabrication of related devices with high performance. This paper reviews the recent advances in research on third-order optical nonlinearities of 2D materials, focusing on all-optical processing applications in the optical telecommunications band near 1550 nm. First, we provide an overview of the material properties of different 2D materials. Next, we review different methods for characterizing the third-order optical nonlinearities of 2D materials, including the Z-scan technique, third-harmonic generation (THG) measurement, and hybrid device characterization, together with a summary of the measured n2 values in the telecommunications band. Finally, the current challenges and future perspectives are discussed.

Demonstrating quantum properties of triple photons generated by chi ^3 processes

Triple-photon generation (TPG) is based on a third-order nonlinear optical interaction, which is the most direct way to produce pure quantum three-photon states. These states can exhibit three-body quantum correlations, and their statistics cannot be reproduced by any Gaussian statistics of coherent sources or optical parametric twin-photon generator, making them potentially useful for quantum information processing tasks such as quantum state distillation, quantum error-correction and universal quantum computing. Furthermore, the generation of entangled photon pairs heralded by the detection of a third photon can be used in advanced quantum communication protocols. We made the first experimental demonstration of TPG in 2004 using a bi-stimulation scheme in a bulk KTP crystal, followed by the quantum theory. The new challenges are now to achieve a spontaneous TPG and the corresponding quantum experiments and protocols using oriented ridge KTP waveguides, which ensures both birefringence phase-matching and light confinement. The waveguides are cut by a precision dicing saw. We recently performed their characterization using third-harmonic generation measurements, which showed their good quality. A rate of about 5 triplets per second is expected when pumping a 5-cm-long waveguide with a 5-W 532 nm beam in the CW regime. Such a spontaneous TPG exhibits low rate of triple photons, which makes the certification of quantum features hard. In this article, we review our theoretical and experimental work on TPG and the associated quantum modeling. We also develop theoretical tools for the certification of quantum features of spontaneous triple-photon states.Graphic abstract

Third-harmonic generation in excitonic insulators

We study third-harmonic generation (THG) in an excitonic insulator (EI) described in a two-band correlated electron model. Employing the perturbative expansion with respect to the external electric field, we derive the THG susceptibility taking into account the collective dynamics of the excitonic order parameter. In the inversion-symmetric EI, the collective order parameter motion is activated at second order of the external field and its effects arise in THG. We find three peaks in the THG susceptibility at energies $\hbar \Omega = \Delta_g/3$, $\Delta_g/2$, and $\Delta_g$, where $\Delta_g$ is the band gap. While the THG response at $\Delta_g/3$ is caused by bare three-photon excitation of the independent particle across the band gap, the latter two peaks involve the motion of the order parameter activated at second order. The resulting resonant peaks are prominent in particular in the BCS regime but they become less significant in the BEC regime. We demonstrate that the resonant peak originated by the collective excitation is observable in the temperature profile of the THG intensity. Our study suggests that the THG measurement should be promising for detecting the excitonic collective nature of materials.

Layered and Cubic Semiconductors AGaM'Q4 (A+ = K+, Rb+, Cs+, Tl+; M'4+ = Ge4+, Sn4+; Q2- = S2-, Se2-) and High Third-Harmonic Generation.

Eighteen new quaternary chalcogenides AGaM'Q4 (A+ = K+, Rb+, Cs+, Tl+; M'4+ = Ge4+, Sn4+; Q2- = S2-, Se2-) have been prepared by solid-state syntheses and structurally characterized using single-crystal X-ray diffraction techniques. These new phases crystallize in a variety of layered structure types. The tin analogues also adopt an extended three-dimensional network structure as polymorphs. The polymorphism and phase-stability in these cases were studied by thermal analysis and high-temperature in situ X-ray powder diffraction. All compounds are semiconductors with the colored selenides absorbing light in the infrared-green region (1.8 eV < Eg < 2.3 eV) and the mostly white sulfides absorbing light in the blue-ultraviolet range (2.5 eV < Eg < 3.6 eV). Based on third-harmonic generation (THG) measurements, the third-order nonlinear optical (NLO) susceptibilities χ(3) of the new and previously reported AGaM'Q4 compounds were determined. These measurements revealed an apparent correlation between the THG response of the sample and its band gap, rather than the crystal structure type. While low-gap materials possess higher nonlinearity in general, we found that layered orthorhombic RbGaGeS4 exhibits an impressive χ(3) value (about four times larger than that of AgGaS2) even with a large band gap and shows stability under ambient conditions with no significant irradiation damage.

Synthesis, structure, and third-harmonic generation measurements of a mixed alkali metal iodate, KLi2(IO3)3

Pure polycrystalline samples and single crystals of a mixed alkali metal iodate, KLi2(IO3)3 were synthesized through standard solid state and hydrothermal reactions, respectively, by using Li2CO3, K2CO3, and I2O5 as reagents. Single-crystal X-ray diffraction analysis suggests that KLi2(IO3)3 exhibits a corrugated layered structure consisting of IO3 distorted trigonal pyramids, LiO4 tetrahedra, and K+ cations. Within the layer, both five-membered rings (5-MRs) and six-membered rings (6-MRs) exist. UV–vis diffuse reflectance spectral data suggest that KLi2(IO3)3 has a wide optical band gap of ca. 4.25 ​eV. Infrared spectrum of the title compound clearly confirms the existence of IO3 groups in the backbone. The framework of the iodate is thermally stable to ca. 450 ​°C. Third-harmonic generation measurements using 1500 ​nm radiation indicate that the third-order nonlinear optical susceptibility of KLi2(IO3)3 is ca. 3 times that of α-SiO2. The laser-induced damage threshold of KLi2(IO3)3 is comparable to that of α-SiO2. Calculated local dipole moment values of IO3 polyhedra are also reported to better understand the asymmetric coordination environment.

Degenerate Four-Wave Mixing in a Multiresonant Germanium Nanodisk

Dielectric nanoantennas excited at Mie resonances are becoming suitable candidates for nonlinear optical effects due to their large intrinsic nonlinearity and capability to highly confine electromagnetic fields within subwavelength volumes. In this work, we show that a single Ge nanodisk, recently demonstrated as an efficient source of third-harmonic generation (THG), can also be exploited for four-wave mixing (FWM) phenomena. The high field enhancement inside the disk yields effective third-order susceptibilities as high as 2 × 10–8 esu (2.8 × 10–16 m2/V2), which were determined by single pump wavelength THG measurements tuned to high-order Mie modes. A similar nonlinear optical response is observed in the case of degenerate FWM where two different pump wavelengths are coupled to a single high-order resonant mode. However, when the two pump wavelengths are coupled to different high-order modes, the FWM process is partially suppressed due to a diminished near-field spatial overlap of the mixed wavelengths...

Strong and anisotropic third-harmonic generation in monolayer and multilayer ReS2

We report observation of strong and anisotropic third harmonic generation (THG) in monolayer and multilayer ReS$_2$. The third-order nonlinear optical susceptibility of monolayer ReS$_2$, $\left| \chi^{(3)} \right|$ is on the order of $10^{-18} $ m$^2$/V$^2$, which is about one order of magnitude higher than reported results for hexagonal-lattice transition metal dichalcogenides such as MoS$_2$. A similar magnitude for the third-order nonlinear optical susceptibility was also obtained for a multilayer sample. The intensity of the THG field was found to be dependent on the direction of the incident light polarization for both monolayer and multilayer samples. A point group symmetry analysis shows that such anisotropy is not expected from a perfect $1T$ lattice, and must arise from the distortions in the ReS$_2$ lattice. Our results show that THG measurements can be used to characterize lattice distortions of two-dimensional materials, and that lattice distortions are important for the nonlinear optical properties of such materials.

Large optical third-order nonlinearities in a switchable Prussian blue analogue

We report on the observation of an efficient coherent up-conversion via third harmonic generation (THG) in Rb0.94Mn[Fe(CN)6]0.98.0.3H2O material. Our THG measurements at fundamental wavelengths ranging from 1200 to 2400 nm show that, in this spectral range, the THG signal overcomes the signal generated by frequency doubling. This demonstrates that this material possesses significant third-order nonlinear optical (NLO) responses. Its effective χ(3) value is at least two orders of magnitude greater than α-Quartz. We also demonstrate that this material exhibits a broad thermal hysteresis loop around room temperature, which makes it possible to simultaneously photo-commute its linear and third-order nonlinear optical properties.

Efficient Third Harmonic Generation in a Metal–Organic Framework

As a recently emerged class of inorganic–organic hybrid crystals, metal–organic frameworks (MOFs) have been investigated for their capabilities for doubling light frequency. We report, for the first time, our observation of an efficient coherent up-conversion via third harmonic generation (THG) in a MOF. It is achieved by utilizing a MOF with a constituent ligand that possesses significant third-order nonlinear optical (NLO) responses. Our THG measurements at fundamental wavelengths ranging from 1200 to 1600 nm show that the MOF constructed with the An2Py ligand exhibits an effective χ(3) value that is 3 orders of magnitude greater than α-quartz. Our findings demonstrate a new avenue to realize efficient third-order NLO responses by utilizing MOFs consisting of strong third-order NLO ligands.

On the generation of polarization-dependent supercontinuum and third harmonic in air

Filamentation and supercontinuum (SC) generation occur in transparent media during the propagation of intense femtosecond laser pulses. We report experimental results of polarization-dependent SC generation and third harmonic generation (THG) in air using intense 40 fs, 800 nm pulses under varying focusing conditions. We observe that tight focusing enhances the extent of the SC compared to when there is weak external focusing. Moreover, we observe that when the incident beam is linearly polarized the SC yield is more than that obtained using circularly polarized light of the same energy, but this difference reduces as focusing becomes tighter and depolarization begins to take effect. We have also carried out measurement for THG in air under the same conditions as for SC generation. A THG efficiency of 0.5% is measured for linearly polarized light in air. Although conservation of spin angular momentum precludes THG with circularly polarized light, we do observe THG with circularly polarized light in our experiments because of depolarization effects. We show that THG measurements allow in situ measurements of the extent to which incident light is depolarized.

An Azo-Bridged Ferroelectric Liquid Crystal with Highly Enhanced Second and Third Harmonic Generation

A laterally azo-bridged trimer ferroelectric liquid crystal (FLC) incorporating a strong chromophore along its polar axis was synthesized and characterized by polarized-light optical microscopy, differential scanning calorimetry, two-dimensional X-ray diffraction analysis, electro-optical measurements, and nonlinear optical (NLO) investigations. This mesogen exhibits a thermodynamically stable enantiotropic SmC* phase and a bistable ferroelectric switching in a surface stabilized cell with bookshelf geometry. It gives the resonance-enhanced d(22) coefficient of 28 pm V(-1) (λ = 1.369 μm) for second harmonic generation (SHG), the largest NLO susceptibility reported to date for all FLCs. At the same wavelength, a new type of helicoidal phase matching assisted by the helical SmC* structure was identified. When the second harmonic wavelength of 780 nm is far away from the resonance wavelength (λ(max) = 572 nm), the d(22) coefficient is reduced to 6.8 pm V(-1) (λ = 1.56 μm). In addition to a strong SHG activity, the trimer also shows a strong third harmonic generation (THG) with an estimated third-order nonlinear susceptibility of χ((3)) = ~3 × 10(-11) esu (λ = 1.56 μm), among the largest χ((3)) value reported from THG measurements for liquid crystals. This work enables viable applications of FLCs in nonlinear optics and offers an innovative approach to develop new FLCs with larger NLO strength.

Third-harmonic generation measurement of nonlinear optical susceptibility χ^(3) of Ge-Ga-Sb-S chalcogenide glasses proposed for highly nonlinear photonic fibers

We measured the nonlinear optical susceptibility &#x3C7;(3) of some Ge-Ga-Sb-S chalcogenide glasses feasible for the fabrication of highly nonlinear photonic crystal fibers. The &#x3C7;(3) values of Ge17Ga4Sb10S69, Ge20Ga5Sb10S65, and Ge20Ga5Sb6S69 glasses were found to be 3.5, 2.6, and 1.8&#xD7;10&#x2212;19m2/V2 (6.3, 4.6, and 3.2&#xD7;10&#x2212;12esu, where &#x201C;esu&#x201D; stands for electrostatic unit) at the fundamental wavelength &#x3BB;=1.9&#x3BC;m, i.e., 227, 167, and 117 times higher than that of standard silica [1.55&#xD7;10&#x2212;21m2/V2 (2.79&#xD7;10&#x2212;14esu)]. Their nonlinear refractive indices n2 were then obtained as 1.8, 1.3, and 1&#xD7;10&#x2212;17m2/W (5.1, 3.7, and 2.7&#xD7;10&#x2212;11esu). They are &#x223C;78, 56, and 43% of n2=2.3&#xD7;10&#x2212;17m2/W (7&#xD7;10&#x2212;11esu) of the As2S3 glass used as the chalcogenide glass reference.

ChemInform Abstract: Nonlinear Optical Processes in Short Polyenes: Configuration Interaction Description of Two-Photon Absorption and Third-Harmonic Generation.

We use a multireference determinant single–double configuration interaction approach within a Pariser–Parr–Pople Hamiltonian (based on long‐range hopping integrals and the use of the Ohno formula) to investigate linear polyenes containing from four to sixteen carbons. We calculate the low‐lying excited states, the two‐photon absorption spectrum, and the third‐harmonic generation (THG) response. The mAg state, essential to the cubic nonlinear optical response, is found to saturate as the 6Ag state when chain length increases; for the longer polyenes, another high‐lying Ag state also becomes important. We analyze the length dependence of the static third‐order susceptibility χ(3); indication of the beginning of saturation behavior is found. Focusing our attention to the two‐photon resonance peak present in the free‐electron laser THG measurements on polyacetylene, we conclude that the experimental data can be explained within the strongly correlated electron one‐dimensional model used in this work, in addit...

Correlation between structural studies and third order NLO properties of selected new quinolinium semi-organic compounds

New quinolinium semi-organic compounds of formula ( C 9 H 8 N ) 2 + · SO 4 2 - , H 2 O ( I) (bis-quinolinium sulphate monohydrate) and ( C 9 H 8 N ) + · NO 3 - ( II) (quinolinium nitrate) have been synthesized and characterized by UV–Vis absorption spectroscopy, nonlinear optical (NLO) measurements and by single crystal X-ray diffraction. The third order nonlinear optical properties of ( I) and ( II) were investigated using two methods: the degenerate four wave mixing technique (DFWM) performed in solution at λ = 532 nm and the third-harmonic generation (THG) measurements carried out on thin films at λ = 1064 nm. The NLO measurements showed that compound ( I) presents better nonlinear optical properties compared to compound ( II). To understand further the optical behaviour of ( I) and ( II), the crystal structures of both compounds were determined from accurate single crystal X-ray diffraction measurements performed at 100 K. The crystallographic studies revealed the key role of the intermolecular interactions and the molecular arrangements in the enhancement of the NLO properties.

Comparison of Z-scan and THG derived nonlinear index of refraction in selected organic solvents

Nonlinear index of refraction of a series of organic solvents, measured by the nonlinear imaging (z-scan) technique, is compared with the same values derived from optical third-harmonic generation (THG). The systematic differences in the values obtained from the z-scan measurements and from THG are attributed to three factors: the value of the standard used in THG measurements, important rotational contribution in z-scan measurements, and the difference in dispersion for n2 derived from Kerr susceptibility and those derived from THG measurements. Using the recently proposed standard silica susceptibility value, one obtains a very good agreement for silica and significant differences for the solvents, particularly for CS2 and chlorobenzene. A correction based on a three-level model for centrosymmetric media is applied for dispersion.

In vivo imaging of cellular structures in Caenorhabditis elegans by combined TPEF, SHG and THG microscopy

In this study, we use combined two-photon excitation fluorescence (TPEF), second-harmonic generation (SHG) and third-harmonic generation (THG) measurements to image cellular structures of the nematode Caenorhabditis elegans, in vivo. To our knowledge, this is the first time that a THG modality is employed to image live C. elegans specimens. Femtosecond laser pulses (1028 nm) were utilized for excitation. Detailed and specific structural and anatomical features can be visualized, by recording THG signals. Thus, the combination of three image-contrast modes (TPEF-SHG-THG) in a single instrument has the potential to provide unique and complementary information about the structure and function of tissues and individual cells of live biological specimens.

Raman characteristics and nonlinear optical properties of tellurite and phosphotellurite glasses containing heavy metal oxides with ultrabroad Raman bands

A family of glasses suitable for ultrabroadband Raman amplifications was designed and fabricated. In addition to the bandwidth the gain characteristics of these glasses are expected to be much higher than those of the silica based materials. The thermal stabilities of these glasses in view of fiber fabrication were discussed. The various structural units which contribute to the overall Raman band were unraveled. Accordingly the various bands were tailored in such a way to get a wide continuous Raman band. The nonlinear optical properties which are vital for optical switching and other nonlinear processes were studied via third-harmonic generation measurements.