Harmonic Conversion Efficiency Research Articles

Twin echo-enabled harmonic generation for enhanced coherent bunching at short wavelengths

Harmonic up-conversion schemes represent the most successful approach in externally seeded free-electron lasers (FELs) for obtaining radiation with laserlike properties at short wavelengths. They are, however, limited in the shortest achievable wavelengths, as the harmonic conversion efficiency decreases with increasing harmonic number, even for echo-enabled harmonic generation (EEHG). In the following, we introduce a novel externally seeded cascaded FEL scheme based on two EEHG stages, capable of obtaining unprecedented bunching fraction that is independent on the final FEL wavelength. The second stage can be operated both in conventional harmonic up-conversion but also in down-conversion, i.e., going toward (slightly) longer wavelengths. Higher bunching enables emission of laserlike radiation in the soft x-rays with large output power in a compact scheme. Its performance at 4 nm and shorter is investigated, demonstrating the ability to achieve multi-GW level, fully coherent pulses with laserlike properties and paving the way for externally seeded radiation at 1 nm and beyond. Published by the American Physical Society 2024

Second harmonic generation and third harmonic enhancement in silicon by a composite metasurface and intense terahertz.

The compression and integration of nonlinear optical processes to the nanoscale are expected to have significant implications for quantum optics, biology, and medicine. In this work, a composite metasurface consisting of a hollow-bow-tie-shaped metal metasurface and a patterned amorphous silicon metasurface is proposed. An external terahertz (THz) electric field enhanced by the hollow-bow-tie structure is employed to break the centrosymmetry, which allows the generation of optical second harmonic. Meanwhile, the amorphous silicon nanocolumns inside the hollow-bow-tie-shaped structure enhance the optical laser field and improve the conversion efficiency of second and third harmonics. The numerical results indicate that at an incident optical laser intensity of 1.20 GW/cm2 and a y-component of the incident THz electric field of 10 kV/cm, the powers of the generated second and third harmonics are 3.96 × 10-6 W and 7.42 × 10-6 W, respectively, with conversion efficiencies of 3.93 × 10-7 and 7.18 × 10-7. The conversion efficiency of the third harmonic is increased by a factor of 700 compared to that of unpatterned silicon. The configuration proposed in this paper offers a solution for applications that need to take into account both high nonlinear efficiency and ultra-fast tunability.

Enhancing second harmonic generation in lithium niobate metasurfaces through symmetric protection bound states in the continuum

In order to address the issue of high loss and low field effect in the generation process of traditional second harmonic, we employ lithium niobate (LN), a highly efficient nonlinear material. Our designed structure exhibits a symmetry-protected bound state in a continuum medium (BIC) when subjected to a y-polarized incident wave, resulting in an impressive second-harmonic conversion efficiency of 5.5 % at a pump strength of 0.4MW/cm2. Moreover, it also shows accidental BIC when subjected to an x-polarized incident wave, exhibiting a second harmonic conversion efficiency of 1.83 %. We conducted a Cartesian multipole analysis to investigate the underlying cause of BIC formation, and the results are in excellent agreement with the electromagnetic field map. Subsequently, we explored the correlation between asymmetry degree, Q value, and second harmonic conversion efficiency. Our study presents novel approaches for enhancing symmetry-protected BICs in second harmonic waves while providing simplified indicators for evaluating second harmonic transformation efficiency.

Bloch-Wave Phase Matching of High Harmonic Generation in Solids.

There has been a longstanding doubt that the conversion efficiency of high harmonics in solids is much lower than expected at such a high level of electron density. To address this issue, we revisit the dynamical process of high harmonic generation (HHG) in solids in terms of wavelet interference. We find that the constructive interference among the wavelets has intrinsic consistency with the phase matching of coupled waves in nonlinear optics, which we call Bloch-wave phase matching. Our analysis indicates that most of the wavelets are out of phase and coherently canceled out during the solid HHG process, leading to only a small fraction of excited electrons effectively contributing to HHG. Consequently, the conversion from the excited electron to HHG is fairly low. Moreover, a Bloch-wave phase-matching scheme is proposed and a nearly 3 orders of magnitude enhancement of solid HHG can be achieved by engineering the crystal structures. Our Letter addresses a longstanding doubt and provides a novel idea and theoretical guidance for realizing efficient all-solid-state tabletop ultraviolet light sources.

Harmonic Generation in Molecular Ag2S Plasma.

The molecular laser-induced plasma (LIP) produced during the ablation of silver sulfide (Ag2S) was used as a medium for high-order harmonic generation in the extreme ultraviolet range. The role of LIP formation, the plasma components, and the geometry of plasma in the harmonic conversion efficiency was analyzed. We also analyzed the influence of the driving pulses (chirp, single-color pump, two-color pump, and delay between heating and converting pulses) on the harmonic yield in Ag2S LIP. The application of molecular plasma was compared with the application of atomic plasma, which comprised similar metallic elements (Ag) as well as other metal LIPs. The harmonics from the Ag2S LIP were 4 to 10 times stronger than those from the Ag LIP. The harmonics up to the 59th order were achieved under the optimal conditions for the molecular plasma.

Time-varying coding digital double-layered Huygens' metasurface for high-efficiency harmonic frequency conversion

Time-varying metasurfaces offer an efficient means of controlling nonlinear harmonics by manipulating component geometries and modulating signals. This ability renders them valuable across various fields, such as wireless communication, radar sensing, and biological monitoring. However, most of the energy in time-varying metasurfaces is concentrated in the fundamental wave, as well as scattered at various harmonic orders, which reduces the energy efficiency at the desired harmonic. Existing approaches have employed time-varying coding digital metasurfaces to achieve efficient harmonic conversion but are primarily designed for reflection. Reflection-based designs require a feed source to excite the metasurface, which can cause certain shielding effects and limit their application in specific scenarios. Thus, designing transmissive time-varying coding digital metasurfaces for efficient harmonic conversion is currently an urgent problem that needs to be addressed. To solve this problem, this paper develops a time-varying coding digital double-layered Huygens' metasurface, which achieves efficient conversion of the desired transmitted harmonics. The unit structure of the metasurface consists of a pair of reverse-symmetric split rings located on the upper and lower sides of a dielectric substrate, enabling nearly non-reflective Huygens' resonance. Based on a continuous periodic phase modulation strategy, we achieved efficient conversion of transmitted harmonics by loading a time-varying voltage (phase) modulation signal with a 5-bit resolution bit width onto the designed double-layered Huygens' metasurface. This study presents a solution for designing a transmissive time-varying coding digital metasurface to achieve efficient conversion of harmonics, thereby enhancing the application capabilities of time-varying coding digital metasurfaces.

Enhanced terahertz third-harmonic generation based on the graphene-assisted meta-grating structure

The nonlinear response of optical materials provides a valuable approach for optical switching and nonlinear frequency conversion. However, the nonlinear responses of bulk crystals are often very weak, requiring higher pump energy for pumping. In this work, we investigate the significant enhancement of third harmonic generation (THG) at terahertz frequencies using an ultra-thin nonlinear meta-grating metasurface assisted by graphene strips. In this structure, the incident pump light experiences strong confinement and enhancement along the graphene surface caused by the generation of strongly localized surface plasmon resonances. Utilizing the significant third-order nonlinear conductivity of graphene, it becomes possible to achieve high THG conversion efficiency even at low pump intensities. The research results indicate that, at low incident intensity of 10 kW/cm2, the third harmonic wave conversion efficiency can reach approximately 2.8 %. We also thoroughly investigate the impact of meta-grating structural parameters, graphene Fermi level, incident angle, and pump light intensity on THG operation characteristics. Our study findings provide an effective approach for greatly boosting the THG conversion efficiency in the terahertz frequency bands, opening new avenues in the development of novel compact frequency converters and modulators that are emerging in terahertz chip integration and nonlinear devices.

A novel scheme based on angular dispersion-induced microbunching mechanism for harmonic generation in storage ring

Angular dispersion-induced microbunching (ADM) scheme was proposed to generate high harmonic coherent radiation in the storage ring with weak energy modulation amplitude. However, it is still difficult to convert the external UV seed laser into the sub-nanometer wavelength. In this paper, we proposed a novel scheme based on ADM mechanism. By properly choosing the parameters, theory and one order simulation demonstrate that it is possible to produce ultrahigh harmonic coherent radiation in the storage ring. The high harmonic conversion efficiency of the proposed scheme may open up a new opportunity to produce sub-nanometer X-ray coherent radiation in the storage ring.

Survey of second harmonic generation in commercial germanium-doped fibers

Seeded optical poling is a promising and simple method to write an effective quadratic coefficient in silica optical fibers doped with germanium. We considered commercial solid core fibers since these fibers could allow for a wide adoption of optical poling. For each fiber, we optimized the poling process and analyzed the second harmonic conversion efficiencies in relation with the fiber chemical composition as obtained resorting to energy-dispersive X-ray spectroscopy. Our comprehensive investigation shows that segments of fibers spanning 20 cm, featuring a germanium content of around 6%, can effectively convert 30 mW of 1064 nm light with efficiencies hovering around 1%.

Mid-infrared second harmonic generation in p-type Ge/SiGe quantum wells: Toward waveguide integration

In this work we investigate a structure based on p-doped Ge/SiGe asymmetric-coupled quantum wells (ACQW) that enables the second harmonic generation in SiGe waveguide by double-resonant intersubband transitions (ISBTs). These transitions lead to χ(2) coefficients in the range 104-105 pm/V, significantly higher compared to the one of conventional nonlinear materials. We developed a model for the integration of Quantum Wells (QWs) into the active region of the waveguide through an adiabatic taper. Furthermore, we modelled the second harmonic (SH) conversion efficiency as a function of the propagation length, under both non-phase matching and phase-matching conditions. Our work demonstrates that the SiGe ACQWs can be used in spectral ranges not covered by the majority of conventional non-linear crystals, while allowing for the ready-integration with the CMOS technologies.

Second harmonic enhancement effect in double U split-ring resonators

Frequency multiplication plays an important role in spectrum research; therefore, in order to achieve enhancement of the second harmonic, the internal structure of nonlinear plasma metamaterial cells becomes more and more complex. The original harmonic oscillator model only regards the cell as a single harmonic oscillator, and a complete understanding of the physical processes involved in harmonic generation experiments in plasmonics is still lacking. In the case in which the plasma structure in a single cell becomes more and more complex, it is not reasonable to regard the entire cell as a single nonlinear oscillator. So expanding the harmonic oscillator model becomes more significant. In this paper, the internal structure of the proposed double U split-ring resonators (DU-SRRs) is regarded as two harmonic oscillators with different resonant frequencies, and the generation process of the enhanced second harmonic is explained by the resonance theorem. The second and third order nonlinear coefficients of the metamaterial are calculated, and the theoretical second harmonic conversion efficiency is obtained by using the second order nonlinear coefficients. Compared with the simulation results of the DU-SRR based on the split-ring resonator, we validate this classical theory as well as the associated numerical algorithm. The ability of the DU-SRR to enhance the second harmonic is proved, and the physical changes inside the cell and the reasons for the enhancement are explained in detail. This method can be used to analyze the nonlinear phenomena in metamaterials with complex cell structures.

Effect of magnesium and zinc doping of lithium niobate crystals on nonlinear optical characteristics

The theoretical and experimental values of nonlinear optical susceptibilities for lithium niobate crystals double doped with cations (Zn2+:Mg2+) with similar concentrations obtained using the method of direct and homogeneous impurity introduction were analyzed. The length of Li-O bonds in double-doped crystals (LiNbO3:Zn2+:Mg2+) determined the value of the nonlinear optical second harmonic generation (SHG) coefficients. It was found that impurity and intrinsic defects make a positive contribution to the tensor coefficients of the second-order nonlinear optical susceptibility (dij). The results indicated that the LiNbO3:Zn2+:Mg2+ (3.83:0.97 mol%) crystal is the most suitable medium for SHG application among the crystals studied in the paper, as it showed the maximum calculated value of the nonlinear optical coefficient d33 which was equal to −55.26(2) × 10−9 cm/statV. The measured second harmonic conversion efficiency for this crystal was η = 36%.

Extreme nonlinear optics in a long pulse regime: High harmonic generation of picosecond mid-IR pulses in polycrystalline zinc selenide.

High harmonic generation (HHG) in semiconductors has been extensively studied recently in the high-intensity limit using middle infrared (mid-IR) femtosecond laser pulses resulting in emission spectra of self-phase modulated harmonics resting on top of a broadband continuum. In this report, a different approach to HHG in polycrystalline zinc selenide (poly-ZnSe) was explored utilizing a relatively low power regime (1-40 GW/cm2) and much longer (30 ps) mid-IR laser pulses. Through a combination of low power, picosecond excitation, and narrowband (<10 nm full width at half maximum) mid-IR excitation, the nonlinear optical effects in poly-ZnSe could be isolated and studied independently. From the clearly distinguishable HHG peaks, harmonic conversion efficiencies of 10-4-10-12 for second to ninth harmonic in poly-ZnSe were measured, and the relationship between the Nth harmonic intensity and excitation intensity (I0) was found to follow a power law, I0x with x ≤ N/2, as a result of the random quasi-phase matching process.

Comparison of high average-power femtosecond green and ultraviolet laser emissions generated by K3B6O10Br and K3B6O10Cl nonlinear crystals

We investigate the second harmonic generation (SHG) and third harmonic generation (THG) processes of femtosecond (fs) laser that occurred in type Ⅰ phase-matched K3B6O10X (X = Cl, Br; KBOC and KBOB) crystals. The high average power of 515 nm green and 343 nm ultraviolet (UV) fs lasers output were efficiently generated from these two crystals with an incident fundamental 773 fs 1030-nm laser source. Experimental results show that the highly effective nonlinear coefficient of the KBOC crystal causes higher harmonic conversion efficiency than that of KBOB crystal in the same fundamental laser parameters. The average power of 10.4 W 515 nm green and 4.6 W 343 nm UV lasers output were obtained from two pieces of 4.5 mm KBOC crystals, corresponding to 42.3 % and 19.7 % high optical conversion efficiency respectively, without temporal pulse walk-off time compensation between 1030 nm and 515 nm laser pulses. Our research will stimulate in-depth research on nonlinear frequency conversion in nonlinear optical systems and have potential applications in future applications.

Three orders of magnitude enhancement of second and third harmonic generation in the visible and ultraviolet ranges from plasmonic gold nanogratings

We report experimental observations and numerical simulations of second and third harmonic generation from a gold nanograting, which exhibits a plasmonic resonance in the near infrared. The resonance is tunable, with a spectral position that depends on the angle of incidence. All things being equal, the enhancement of nonlinear optical processes produced by the field localization in the nanograting when compared with a flat gold mirror manifests itself dramatically from the ultraviolet to the visible range: second harmonic generation conversion efficiencies increase by more than three orders of magnitude, while we report a third harmonic generation conversion efficiency enhancement factor of 3200, both in excellent agreement with our theoretical predictions. The clear inferences one may draw from our results are that our model describes the dynamics with unprecedented accuracy and that much remains to be revealed in the development of nonlinear optics of metals at the nanoscale.

General solution of phase mismatched second harmonic conversion efficiency in periodically poled nonlinear medium

In this work we provide for the first time a novel and more accurate second harmonic generation (SHG) conversion efficiency equation for periodically poled nonlinear medium. We believe the equation derived in this work is more useful than equations reported in previous works which are limited because it is considering the case of either nondepleted pump regime or perfect phase matching. The equation derived in this work tackles the general case: depleted pump regime and phase mismatching which makes it important for theoretical – experimental study. We used MgO:PPLN crystal as an example to illustrate SHG conversion efficiency as function of crystal length, laser power density, crystal temperature and beam divergence. We included fundamental and second harmonic waves reflection at entrance and exit surfaces respectively and performed numerical solution using fifth-order Runge-Kutta method. The numerical results show excellent match with analytical results obtained from the derived formula. We compared our theoretical results with experimental results reported in the literature and the comparison shows a good match. Finally, we performed a comparison between depleted and nondepleted pump regime. The results show a difference of 20% between two efficiencies making nondepleted efficiency equation, which used in many theoretical – experimental comparisons, not accurate at high power densities.

Dead-Time Impact on the Harmonic Distortion and Conversion Efficiency in a Three-Phase Five-Level Cascaded H-Bridge Inverter: Mathematical Formulation and Experimental Analysis

To avoid leg short-circuit in inverters, dead time must be introduced on leg gate signals. Dead time affects the inverter output voltage fundamental harmonic amplitude, voltage harmonic distortion and inverter efficiency by introducing additional voltage drops. In this regard, dead time effects have been widely investigated for traditional two-level three-phase voltage source inverters in the literature but not extensively for multilevel topology structures. This paper provides a detailed analysis of dead time impact on the harmonic distortion and efficiency of Cascaded H-Bridges Multilevel Inverters (CHBMIs). For this purpose, a general mathematical formulation to determine voltage drop due to dead time effects, also taking into account the adopted Multicarrier PWM strategy, has been provided and experimentally validated for a five-level three-phase CHBMI structure. As a comparison tool between expected and ideal inverter output voltage, the percentage voltage error <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> % is introduced. In most of the cases, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> % is lower than 5%, and it starts increasing for very low amplitude modulation index or for specific working points where nonlinearities occur. Furthermore, several experimental investigations have been carried out to evaluate the CHBMI performance in terms of harmonic distortion and efficiency by changing, the values of dead time, modulation index and switching frequency for ten different multi-carried PWM strategies. Experimental results confirm the strong dependency between the dead time impact on the converter performance and the adopted Multi Carrier-PWM (MC-PWM) strategy: as a way of example, converter efficiency can be reduced from 80% to 60% when dead time is increased from 0.5 μs to 1.5 μs and Phase Shifted-PWM (PS-PWM) is adopted.

Milliwatt terahertz harmonic generation from topological insulator metamaterials

Achieving efficient, high-power harmonic generation in the terahertz spectral domain has technological applications, for example, in sixth generation (6G) communication networks. Massless Dirac fermions possess extremely large terahertz nonlinear susceptibilities and harmonic conversion efficiencies. However, the observed maximum generated harmonic power is limited, because of saturation effects at increasing incident powers, as shown recently for graphene. Here, we demonstrate room-temperature terahertz harmonic generation in a Bi2Se3 topological insulator and topological-insulator-grating metamaterial structures with surface-selective terahertz field enhancement. We obtain a third-harmonic power approaching the milliwatt range for an incident power of 75 mW—an improvement by two orders of magnitude compared to a benchmarked graphene sample. We establish a framework in which this exceptional performance is the result of thermodynamic harmonic generation by the massless topological surface states, benefiting from ultrafast dissipation of electronic heat via surface-bulk Coulomb interactions. These results are an important step towards on-chip terahertz (opto)electronic applications.

Influence of self-focused high power Cosh-Gaussian beam on second harmonic generation in cold quantum plasma

The objective of present work is to investigate influence of self-focused high power Cosh-Gaussian (ChG) beam on second harmonic generation (SHG) in cold quantum plasma (CQP). WKB and Paraxial approximations are utilized for acquiring 2nd order differential equation representing propagation characteristics of ChG beam with normalized propagation distance. The modification in dielectric function of plasma is observed on account of relativistic nonlinearity causing self-focusing of ChG beam. The density gradients are produced in transverse direction. These density gradients cause electron plasma wave (EPW) excitation at main wave frequency. Further, the nonlinear interaction between pump wave and excited EPW produces 2nd harmonics in plasma. We have performed numerical simulations for exploring impact of various laser & plasma parameters on beam waist of ChG beam and conversion efficiency of 2nd harmonics. We have also made the comparison of given work with classical relativistic plasma (CRP) regime.

Efficient second harmonic generation of a Yb fiber-based amplified stimulated emission source

Efficient second harmonic generation (SHG) of ytterbium (Yb)-doped fiber-based amplified spontaneous emission (ASE) light with temporally low coherence is reported. A Yb-fiber ASE light with a tunable bandwidth was amplified in two power amplifier stages and was frequency-converted by a periodically-poled lithium tantalite waveguide. The second harmonic conversion efficiency of the ASE light achieved in the experiment was inversely proportional to the bandwidth, which was in very good agreement with theoretically calculated value using the self-convolution relationship of the power spectral density for nonlinear frequency conversion of low coherent light. The prospects for further improvement in nonlinear frequency conversion of the fiber ASE source will be discussed.