Third-harmonic Signal Research Articles

Third-harmonic signal generation and enhancement in nonlinear photonic crystals with an efficient continuation finite-element method

A computational study of the third-harmonic (TH) generation (THG) and enhancement through an χ(3) process in one-dimensional nonlinear photonic crystals is presented in this paper. We have introduced a canonical variational problem with a small increment factor to solve the THG problem. The problem with a large input pump intensity or strong nonlinear susceptibilities can be handled by a versatile and accurate method, which combines finite-element methods and a continuation fixed-point iteration algorithm. The TH signal generation and enhancement through the direct χ(3) process are displayed by two periodic structures. Numerical experiments show that the TH signal is significantly enhanced when the frequencies of the fundamental wave and the TH wave are turned to the corresponding photonic band edges to meet the phase-matching condition. Results of numerical experiments also indicate that our proposed method is computationally efficient and precise to handle strong nonlinearities, i.e., large values of input pump power.

Highly Sensitive Third-Harmonic Detection Method of Magnetic Nanoparticles Using an AC Susceptibility Measurement System for Liquid-Phase Assay

Magnetic sensing techniques have been recently developed to detect biomarkers using magnetic nanoparticles (MNPs) in liquid-phase assays. In the case of alternating current (ac) magnetic susceptibility when detecting a low number of MNPs, the diamagnetic signal of water becomes a major problem at a low signal-to-noise ratio. Therefore, we developed a high-temperature superconducting-quantum-interference-device-based ac susceptibility measurement system that can detect third-harmonic signals from MNPs. On the basis of the nonlinear characteristic of MNPs with large ac magnetic excitation (1.06 kHz), the third-harmonic signal detection (3.18 kHz) of MNPs leads to the elimination of the diamagnetic signal of water. The system consists of excitation and gradiometer pickup coils and a multifunctional circuit device. To improve the signal-to-noise ratio of the third-harmonic measurement, the system has two cancelation functions regarding the fundamental magnetic field. The MNPs are magnetized by using the fundamental magnetic field using the excitation coil. Third-harmonic signals from the MNPs were then detected during the up-and-down movement of the MNPs. We evaluated the detection sensitivity of our system using MNPs. We confirmed that the limit of detection consistency of MNPs was 10 ng by using the third-harmonic measurement method.

<italic>In Vitro</italic> Viscosity Measurement on Superparamagnetic Nanoparticle Suspensions

In this paper, we propose and demonstrate a Brownian relaxation-based mixing-frequency method to test sample viscosities. This method uses excitatory and detection coils and Brownian relaxation-dominated superparamagnetic nanoparticles, which are sensitive to the characteristics of the liquid environment such as viscosity. Oscillating magnetic fields can induce harmonics through the nonlinear magnetization curve of superparamagnetic nanoparticles. Phase lag of the third-harmonic signal and the induced voltage ratio of the fifth over the third harmonic signals are collected. We build up standard graphs by plotting collected data from eight magnetic nanoparticle (MNP) mixtures with different viscosities. For any unknown liquids mixed with MNPs, we can collect phase lag and voltage ratio information and insert these data into the aforementioned standard graphs. This in vitro viscosity test can be done in 1 min. Our experimental result showed a 0.3% error rate for the liquid viscosity test.

Ultrafast Optical Modulation of Second- and Third-Harmonic Generation from Cut-Disk-Based Metasurfaces

We design and fabricate a metasurface composed of gold cut-disk resonators that exhibits a strong coherent nonlinear response. We experimentally demonstrate all-optical modulation of both second- and third-harmonic signals on a subpicosecond time scale. Pump–probe experiments and numerical models show that the observed effects are due to the ultrafast response of the electronic excitations in the metal under external illumination. These effects pave the way for the development of novel active nonlinear metasurfaces with controllable and switchable coherent nonlinear response.

Gap Plasmon Enhanced Metasurface Third-Harmonic Generation in Transmission Geometry

The influence of gap plasmons in the third-harmonic generation of annular and H-shaped aperture arrays has been investigated. Surprisingly, the maximum third harmonic in the annular ring structures is not from the smallest gap, but rather appears for a gap of 14 nm. We interpret this result in terms of resonant plasmonic antenna design to match scattering and absorption cross sections. Unlike the annular aperture, continuous gold apertures, like the H-structure, achieve 0.45% conversion efficiency for 2 mW/μm2 CW pump power of a 100 fs pulse, which is 9 times larger than rectangular apertures we have reported in the past. Nonlinear scattering theory has been used to estimate the transmitted third-harmonic signal and is in generally good agreement with the experimental results.

Comparison of Signal Detection of GaAsP and GaAs PMTs for Multiphoton Microscopy at the 1700-nm window

Multiphoton microscopy (MPM) enables noninvasive optical imaging into the deep tissue in animal models in vivo . Recently, 1700 nm has been demonstrated as a promising excitation window for deeper penetration. Signal depletion is currently the limiting factor for imaging depth at the 1700-nm window in MPM. As a result, efficient signal detection is an effective means to further boost imaging depth. GaAsP and GaAs photomultiplier tubes (PMTs) are commonly used for signal detection in MPM. Here, we demonstrate a comparison investigation of signal detection of a GaAsP and a GaAs PMT for several modalities of MPM at 1700 nm. The two PMTs are identical in structure, connected to the same electronics, and mounted at exactly the same place in the microscope, facilitating a fair comparison. Our results show that with a 1667-nm excitation, GaAsP PMT is more efficient for signal detection of a 3-photon fluorescence of quantum dot Qtracker 655, third-harmonic generation signal, and a 4-photon fluorescence of fluorescein, whereas GaAs PMT is far superior in detecting a second-harmonic generation signal. The measured results are in good agreement with theoretical calculations based on wavelength-dependent cathode radiant sensitivities. We expect that our results will offer guidelines for PMT selection for MPM at the 1700-nm window.

Nonlinear optics of complex plasmonic structures: linear and third-order optical response of orthogonally coupled metallic nanoantennas

We investigate the polarization-resolved linear and third-order optical response of plasmonic nanostructure arrays that consist of orthogonally coupled gold nanoantennas. By rotating the incident light polarization direction, either one of the two eigenmodes of the coupled system or a superposition of the eigenmodes can be excited. We find that when an eigenmode is driven by the external light field, the generated third-harmonic signals exhibit the same polarization direction as the fundamental field. In contrast, when a superposition of the two eigenmodes is excited, third-harmonic can efficiently be radiated at the perpendicular polarization direction. Furthermore, the interference of the coherent third-harmonic signals radiated from both nanorods proves that the phase between the two plasmonic oscillators changes in the third-harmonic signal over $$3\pi$$ when the laser is spectrally tuned over the resonance, rather than over $$\pi$$ as in the case of the fundamental field. Finally, almost all details of the linear and the nonlinear spectra can be described by an anharmonic coupled oscillator model, which we discuss in detail and which provides deep insight into the linear and the nonlinear optical response of coupled plasmonic nanoantennas.

Enhanced photon lifetime in silicon nanowire arrays and increased efficiency of optical processes in them

Silicon nanowire (SiNW) arrays formed by metal-assisted chemical etching of boron low-doped crystalline silicon (c-Si) substrates were studied regarding enhanced efficiency of optical interactions in them. Along with high diffuse reflection of the structures under study, Raman and third-harmonic signals exhibited an order of magnitude growth compared to c-Si response in the near-infrared spectral region. Changes in the orientation dependencies of the third-harmonic intensity with SiNW length increase promoted the explanation of the optical peculiarities of SiNW arrays. Cross-correlation of the scattered radiation function evidenced that the effects could be explained by enhanced photon lifetime inside mesoscopic structure of SiNW arrays due to multiple scattering. Hence a correlation between the photon lifetime and the Raman and third-harmonic efficiency in SiNWs was revealed.

Photon lifetime correlated increase of Raman scattering and third-harmonic generation in silicon nanowire arrays

Light propagation in silicon nanowire layers is studied via Raman scattering, third-harmonic generation and cross-correlation function measurements. The studied silicon nanowire arrays are characterized by a wire diameter of 50–100 nm and a layer thickness ranging from 0.2–16 μm. These structures are mesoscopic for light in the visible and near infrared ranges. The Raman signal increases monotonically with layer thickness increases at a 1.064 μm pump wavelength. The Stokes component for silicon nanowire arrays with a thickness larger than 2 μm exceeds that for crystalline silicon by more than an order. At the mentioned thicknesses, an increase is also registered for the third-harmonic signal, one that is up to fourfold greater than that for crystalline silicon for a 1.25 μm pump wavelength. Measurements of cross-correlation functions for the scattered photons evidence the significant photon lifetime increase in the silicon nanowire layers at their thickness increase. This fact can be connected with multiple scattering inside the studied mesoscopic structures and the increase of the interaction length for the Raman and third-harmonic generation processes.

Controlling the effective second-order susceptibility in random quadratic media.

We study systematically the effect of spatial disorder of ferroelectric domains in nonlinear media on the polarization properties of optical frequency conversion. Experimentally, different statistics of domain sizes are created using electric field poling at room temperature. We analyze the evolution of polarization properties of the second- and third-harmonic signals for each created statistic by determining the corresponding relative strength of non-zero components of the second-order susceptibility tensor, d24, d32 and d33. The relative strengths are labeled by means of the control parameter E on the characteristic P-E loop of the studied ferroelectric medium.

Narrowband Magnetic Particle Imaging Utilizing Electric Scanning of Field Free Point

We developed a narrowband magnetic particle imaging (MPI) system that uses third-harmonic signal detection and electrical scanning of the field free point (FFP). Comparing with mechanical scanning, we can decrease the measurement time significantly and increase the signal-to-noise ratio as well. For electrical scanning, we designed and constructed gradient and shift coils. The gradient coil consisting of four pieces of planar coils generated the gradient field with a field gradient of 0.4 T/m at a height of 25 mm from the coil surface. The FFP can be moved ±8 mm by supplying a current of ±6.6 A to the shift coil. Using the developed system, we detected two magnetic nanoparticle (MNP) samples located at a depth of 35 mm below the pickup coil with a spacing of 10 mm. By applying an excitation field of 1 mT at 22.75 kHz, we measured the third-harmonic signal from the MNP samples and obtained a contour map of the signal field in an area of 16 × 16 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Then, we converted the field map into an MNP distribution using singular value decomposition method. It was shown that the spatial resolution of the reconstructed MNP distribution was improved compared with that of the measured contour map of the signal field. The spatial resolution for MNP detection in MNP distribution was 5 mm and two MNP samples were distinguished clearly. This result indicated that MPI using electrical scanning of the FFP was successfully performed.

Third-harmonic generation in the presence of classical nonlocal effects in gap-plasmon nanostructures

Classical nonlocality in conducting nanostructures has been shown to dramatically alter the linear optical response by placing a fundamental limit on the maximum field enhancement that can be achieved. This limit directly extends to all nonlinear processes, which depend on field amplitudes. A numerical study of third-harmonic generation in metal film-coupled nanowires reveals that for subnanometer vacuum gaps, the nonlocality may boost the effective nonlinearity by 5 orders of magnitude as the field penetrates deeper inside the metal than that predicted assuming a purely local electronic response. We also study the impact of a nonlinear dielectric placed in the gap region. In this case the effect of nonlocality could be masked by the third-harmonic signal generated by the spacer. By etching the dielectric underneath the nanowire, however, it is possible to muffle such contributions. Calculations are performed for both silver and gold nanowire.

Widely tunable third-harmonic generation in a tellurite microstructured optical fiber.

We designed and fabricated a tellurite (76.5TeO(2)-6Bi(2)O(3)-11.5Li(2)O-6ZnO, mol. %) microstructured optical fiber (TMOF) with four air holes for widely tunable third-harmonic generation (THG). The loss of the TMOF is ~0.2 dB/m at 1550 nm. Widely tunable THG from ~567 to 902 nm is obtained when the TMOF is pumped by an optical parametric oscillator with the pump wavelength changing from ~1700 to 2700 nm. The mechanism of THG in this work is further investigated through the third-harmonic signal pattern, which is due to the high nonlinearity of the TMOF and the high pump power, not from the phase-matching process between the fundamental mode and the high-order TH mode.

Usefulness of Magnetic Particle Imaging for Predicting the Therapeutic Effect of Magnetic Hyperthermia

Purpose: To investigate the usefulness of magnetic particle imaging (MPI) for predicting the therapeutic effect of magnetic hyperthermia (MH). Materials and Methods: First, we performed phantom experiments to investigate the relationship between the MPI value and the temperature rise of magnetic nanoparticles (MNPs) under an alternating magnetic field (AMF). The MPI value was defined as the pixel value of the transverse image reconstructed from the third-harmonic signals. Samples filled with various iron concentrations of MNPs (Resovist®) were prepared and were imaged using our MPI scanner. These samples were also heated using the AMF, and the specific loss power (SLP) and volume-specific loss power (vSLP) were calculated from the initial slope of the time-dependent temperature rise. Second, we performed animal experiments using tumor-bearing mice, which were divided into untreated (n = 10) and treated groups (n = 20). The tumors in the treated group were injected with Resovist® at an iron concentration of 250 mM (n = 10) or 500 mM (n = 10), and received MH for 20 min, during which the temperatures in the tumor and rectum were measured. The relative tumor volume growth (RTVG) was calculated from (V15 - V0)/V0, where V0 and V15 represented the tumor volume on day 0 and day 15 after MH, respectively. Results: In phantom experiments, the MPI value had significant correlations with the iron concentration of MNPs (r = 0.997), temperature rise (r = 0.981), and vSLP (r = 0.961). In animal experiments, the MPI value had significant correlations with the temperature rise in the tumor (r = 0.731) and RTVG (r = ﹣0.687). Conclusion: Our preliminary results suggest that MPI is useful for predicting the therapeutic effect of MH.

Application of Magnetic Particle Imaging to Pulmonary Imaging Using Nebulized Magnetic Nanoparticles

Purpose: To investigate the feasibility of applying magnetic particle imaging (MPI) to pulmonary imaging using nebulized magnetic nanoparticles (MNPs) and to quantify the mucociliary clearance in the lung, using small animal experiments. Materials and Methods: Intrapulmonary administration of MNPs was performed in seven-week-old male ICR (Institute of Cancer Research) mice (n = 8) using a nebulized microsprayer connected to a high-pressure syringe containing 50 μL of MNPs (500 mM Resovist®). We imaged the lungs using our MPI scanner 2.5 hours, 1 day, 3 days, and 7 days after the intrapulmonary administration of MNPs. The average MPI value was calculated by drawing a region of interest (ROI) on the lungs by taking the threshold value for extracting the contour as 20% of the maximum MPI value within the ROI. The MPI value was defined as the pixel value of the transverse image reconstructed from the third-harmonic signals. Mice were sacrificed immediately after the last MPI and X-ray CT studies on day 7, and 5 lobes of the lung in each mouse were extracted to confirm the accumulation of iron using Berlin blue staining. Results: We could visualize the distribution of MNPs in the lungs as positive contrast using MPI with use of nebulized MNPs. The presence of iron in the lung was confirmed by Berlin blue staining. The average MPI value decreased with time and tended to saturate. The clearance rate was calculated to be 0.505 day−1 from the time course of the average MPI value in the lungs. Conclusion: Our preliminary results suggest that MPI can be applied to pulmonary imaging by nebulizing MNPs and can be useful for quantifying the mucociliary clearance in the lung.

Magnetic Particle Imaging Utilizing Orthogonal Gradient Field and Third-Harmonic Signal Detection

We have developed a 2-D magnetic nanoparticle (MNP) imaging system using an orthogonal gradient held and third-harmonic signal detection. An ac excitation held was applied to generate third-harmonic signals from MNP on the basis of their nonlinear magnetization curves, and a dc gradient held was applied perpendicular to the excitation held. The dependence of the third-harmonic signal on the dc held was very different from that in the conventional parallel case. We obtained a contour map of the signal held from the MNP located at z = 35 mm below the pickup coil using an excitation held of 1 mT and gradient held of 0.4 T/m. We could obtain spatial resolution of 10 mm even in this small gradient held. Then, we analyzed the contour map using singular value decomposition (SVD) to improve the spatial resolution of the position estimation of MNP. Using SVD, we converted the held map to the MNP distribution. The spatial resolution was improved from 10 to 6.7 mm. We could clearly distinguish three MNP samples separated with 10 mm spacing located at z = 35 mm.

Third-harmonic generation with a more than 500 nm tunable spectral range in a step-index tellurite fiber

We demonstrate third-harmonic generation (THG) with a tunable spectral range of more than 500 nm in a step-index tellurite fiber. Third-harmonic (TH) signals with a peak wavelength from 524 to 1043 nm are obtained in a 3 cm-long fiber when the fundamental wavelength shifts from 1560 to 3100 nm. To our knowledge, the tunable spectral range covering almost one octave is the widest tunable range of THG in fibers so far. The far-field patterns of the TH signals by 1560 nm to 2100 nm pumping are recorded by a charge coupled device camera, which are close to the fundamental mode profile. The THG in such a wide tunable range is attributable to the high nonlinearity of the tellurite fiber and the high pump peak power of the pump pulse.

Magnetic particle imaging of blood coagulation

We investigated the feasibility of visualizing blood coagulation using a system for magnetic particle imaging (MPI). A magnetic field-free line is generated using two opposing neodymium magnets and transverse images are reconstructed from the third-harmonic signals received by a gradiometer coil, using the maximum likelihood-expectation maximization algorithm. Our MPI system was used to image the blood coagulation induced by adding CaCl2 to whole sheep blood mixed with magnetic nanoparticles (MNPs). The “MPI value” was defined as the pixel value of the transverse image reconstructed from the third-harmonic signals. MPI values were significantly smaller for coagulated blood samples than those without coagulation. We confirmed the rationale of these results by calculating the third-harmonic signals for the measured viscosities of samples, with an assumption that the magnetization and particle size distribution of MNPs obey the Langevin equation and log-normal distribution, respectively. We concluded that MPI can be useful for visualizing blood coagulation.

Noncollinear third-harmonic Maker fringes for the determination of third-order nonlinear optical susceptibilities

We describe noncollinear third-harmonic Maker fringes for the determination of third-order optical nonlinearities. This method builds on the same principles as conventional Maker fringes experiments, but thanks to the limited interaction length of two intersecting beams, it allows to eliminate the requirement of taking into account the contribution of air to the third-harmonic signal. Thus, third-order susceptibilities can be accurately determined without the need for a vacuum chamber. We review the theoretical underpinnings of the method, and discuss the dependence of the coherence length for harmonic generation on the intersection angle between the beams and the sample orientation, and the effect this has on the Maker fringes pattern.

Atomic wave-packet dynamics and third-harmonic generation in sodium

In femtosecond degenerate four-wave mixing experiments in sodium vapor, quantum beats are observed at the wavelength of the third harmonic when the fundamental beams are three-photon resonant. The period of beating, which corresponds to fine structure energy-level splitting, does not change with the atomic number density, buffer gas pressure, or laser intensity. Surprisingly, the third-harmonic signal is observed only at negative time delays for the transient grating pulse sequence. We relate this to the well-known interference effect between excitation pathways involving the fundamental and the third-harmonic fields, which leaves atoms virtually unexcited and prevents formation of population grating.