Second-harmonic Conversion Research Articles

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.

The role of doping technology in the formation of nonlinear optical properties of LiNbO3:Mg:B crystals

Nonlinear optical coefficients dij were calculated quantitatively for two series of LiNbO3 crystals double-doped with Mg and nonmetallic B obtained by the methods of the solid-phase (SP) synthesis and homogeneous introduction (HG) of impurities. The addition of boron and the presence of MgLi extrinsic defects increased the efficiency of second-harmonic conversion. Homogeneously doped crystals have been found to be the most suitable medium for second-harmonic generation (SHG). The high value of the total nonlinear optical coefficient d33 (−70.742(5) × 10−9 cm/statV) and the extremely low photorefractive response make the LiNbO3:Mg:B crystal (4.2 mol%) obtained by the HG method promising for use in nonlinear optics.

Second harmonic of higher-order Poincaré sphere beam with two orthogonal 5%MgO:PPLN crystals

In this work, the second harmonic (SH) of higher-order Poincaré sphere (HOPS) beam was introduced and demonstrated with two orthogonal 5%MgO:PPLN crystals. Based on the quasi-phase-matching technique, the vectorial coupled wave equations were derived to simulate the SH of HOPS beams through the two crystals, including the cylindrical vector beams (CVBs), elliptically polarized CVBs (EPCVBs), and circularly polarized vortex beams. Then, the experimental setup was established to reveal that the SH of CVBs and EPCVBs present the four-lobed structure and still exhibit vector characteristics. Meanwhile, the circularly polarized vortex beams become the linearly polarized vortex beams with double phase topology, confirming the conservation of orbital angular momentum. Moreover, the maximum SH conversion efficiency of CVBs, EPCVBs, and circularly polarized vortex beams can reach 25.3%, 23.4%, and 29.4%, respectively, which may be instructive for promoting the SH generation of vector vortex beams with high efficiency.

Efficient second-harmonic generation of quasi-bound states in the continuum in lithium niobate thin film enhanced by Bloch surface waves.

Nonlinear optics has generated a wide range of applications in the fields of optical communications, biomedicine, and materials science, with nonlinear conversion efficiency serving as a vital metric for its progress. However, the weak nonlinear response of materials, high optical loss, and inhomogeneous distribution of the light field hamper the improvement of the conversion efficiency. We present a composite grating waveguide structure integrated into a Bragg reflector platform. This design achieves high Q in the spectral range by exploiting the unique properties exhibited by the bound states in the Bloch surface wave-enhanced continuum, and efficient second-harmonic generation by close-field amplification with the optical field tightly localized in a nonlinear material. By manipulating the symmetry of the grating, a precise tune over the near field within a designated wavelength range can be achieved. Specifically, we select a photonic crystal configuration supporting surface waves, employing TE polarization conditions and an asymmetry factor of -0.1 between the composite gratings. This configuration resonates at a fundamental wavelength of 783.5 nm, exhibiting an impressive Q-factor of 106. Notably, at an incident light intensity of 1.33 GW/cm2, we achieve a normalized electric field strength of up to 940 at the fundamental frequency and a second-harmonic conversion efficiency of up to 6×10-3, significantly amplifying the second-harmonic response. The proposed configuration in this investigation has the potential to be integrated into the field of nonlinear optics for sensing frequency conversion applications.

A kinetic theory approach to second harmonic generation by high power laser in magnetized plasma with nonextensive distribution

The present study presents a kinetic theory approach to second-harmonic generation (SHG) through high-power laser in collisionless plasma with nonextensively-distributed electrons. The study applied a relativistic Vlasov equation to obtain nonlinear current density and second-harmonic (SH) conversion efficiency. It was observed that the power conversion efficiency (PCE) of second-harmonic generation depends on plasma and laser parameters such as dimensionless cyclotron frequency, plasma density, normalized thermal velocity, the nonextensive q-parameter, and laser intensity. Moreover, cyclotron frequency associated with plasma electrons has been found to play an important role in increasing the power conversion efficiency of SH generation.

High-Efficiency Second-Harmonic Generation Using Quasi-Bound State in LiNbO3 Metasurface

We numerically demonstrated a high-efficiency second-harmonic generation (SHG) using quasi-bound state in the continuum (quasi–BIC) in thin film LiNbO3 (TFLN) metasurface. The TFLN possessed exceptionally high second-order nonlinear coefficients, contributing to the enhanced SHG performance. An eccentric cylinder unit cell was presented to achieve high Q–factor resonances associated with the asymmetric parameter introduced. Simulations showed that the high efficiency of the second-harmonic conversion was obtained by using the high Q–factor of the asymmetric dielectric cylinder metasurface, and it achieved a high SHG efficiency of 6.5% at pump intensities as low as 1 MW/cm2 at a normal incident. Furthermore, the simulation results indicated that breaking the symmetry through oblique incidence was more effective in achieving a higher Q–factor compared to altering the structural parameters. Specifically, under 1° oblique incidences, the conversion efficiency could reach 1.2% at an incident power of 1 kW/cm². We have proposed a method to achieve a high conversion efficiency of second-harmonic generation in low-refractive-index materials. Our work not only offers theoretical support but also provides valuable insights for the advancement of efficient nonlinear frequency doubling technology, optical communication, and sensing applications.

Integrated Pockels laser

The development of integrated semiconductor lasers has miniaturized traditional bulky laser systems, enabling a wide range of photonic applications. A progression from pure III-V based lasers to III-V/external cavity structures has harnessed low-loss waveguides in different material systems, leading to significant improvements in laser coherence and stability. Despite these successes, however, key functions remain absent. In this work, we address a critical missing function by integrating the Pockels effect into a semiconductor laser. Using a hybrid integrated III-V/Lithium Niobate structure, we demonstrate several essential capabilities that have not existed in previous integrated lasers. These include a record-high frequency modulation speed of 2 exahertz/s (2.0 × 1018 Hz/s) and fast switching at 50 MHz, both of which are made possible by integration of the electro-optic effect. Moreover, the device co-lases at infrared and visible frequencies via the second-harmonic frequency conversion process, the first such integrated multi-color laser. Combined with its narrow linewidth and wide tunability, this new type of integrated laser holds promise for many applications including LiDAR, microwave photonics, atomic physics, and AR/VR.

Control of second-harmonic generation in all-dielectric intersubband metasurfaces by controlling the polarity of χ(2).

All-dielectric metasurfaces have recently led to a paradigm shift in nonlinear optics as they allow for circumventing the phase matching constraints of bulk crystals and offer high nonlinear conversion efficiencies when normalized by the light-matter interaction volume. Unlike bulk crystals, in all-dielectric metasurfaces nonlinear conversion efficiencies primarily rely on the material nonlinearity, field enhancements, and the modal overlaps, therefore most efforts to date have only focused on utilizing these degrees of freedom. In this work, we demonstrate that for second-harmonic generation in all-dielectric metasurfaces, an additional degree of freedom is the control of the polarity of the nonlinear susceptibility. We demonstrate that semiconductor heterostructures that support resonant nonlinearities based on quantum-engineered intersubband transitions provide this new degree of freedom. We can flip and control the polarity of the nonlinear susceptibility of the dielectric medium along the growth direction and couple it to the Mie-type photonic modes. Here we demonstrate that engineering the χ(2) polarity in the meta-atom enables the control of the second-harmonic radiation pattern and conversion efficiency. Our results therefore open a new direction for engineering and optimizing second-harmonic generation using all-dielectric intersubband nonlinear metasurfaces.

In-fibre second-harmonic generation with embedded two-dimensional materials

Silica-based optical fibres are a workhorse of nonlinear optics, providing ready access to a range of nonlinear phenomena including solitons and self-phase modulation. However, they have one fundamental limitation: due to the amorphous nature of silica, they do not exhibit second-order nonlinearity, except for negligible contributions from surfaces. Here we demonstrate second-harmonic generation in functionalized optical fibres by using a monolayer of highly nonlinear MoS2 directly grown on the fibre’s core. The MoS2-functionalized fibre exhibits a second-order susceptibility (χ(2)) value of 44 pm V–1 and a second-harmonic generation conversion efficiency of 0.2 × 10–3 m−2 W−1. This approach is scalable and can be generalized to other transition metal dichalcogenides and a wide range of waveguide systems. Our results demonstrate a new approach towards efficient in-fibre second-harmonic generation sources and may establish a platform for χ(2)-based nonlinear fibre optics, optoelectronics, photonics platforms, integrated optical architectures and active fibre networks.

Nonlinear optical properties of lithium niobate crystals doped with alkaline earth and rare earth elements

Nonlinear optical properties of lithium niobate crystals doped with alkaline-earth (Zn2+) and rare-earth (Er3+) elements were quantitatively studied from the chemical bond viewpoint of crystal. The different influences of Zn and Er dopants on the dielectric response of LiNbO3 were compared. The value of nonlinear optical second-harmonic generation coefficients was determined mainly by the Li–O bonds both in LiNbO3:Zn and LiNbO3:Er crystals. We observed sharp changes in the second order nonlinear optical response of Zn-doped LiNbO3 single crystals at 1064 nm with increasing Zn concentration in the crystal. The calculated values of the nonlinear optical coefficients for the LiNbO3:Zn crystals exceed those for the LiNbO3:Er crystals. The LiNbO3:Zn crystal with dopant concentration 5.48 mol.% is the most suitable crystal for the second-harmonic conversion.

Broadband second-harmonic generation in step-chirped periodically poled lithium niobate waveguides.

Periodically poled lithium niobate (PPLN) structures on a chip enable efficient second-order nonlinear optical effects, benefiting from the tight light confinement and the utilization of d33. Here, we report a broadband second-harmonic (SH) generation in a step-chirped PPLN waveguide on X-cut lithium niobate on insulator (LNOI). The high fidelity of the poling period is demonstrated over the whole length of 7 mm using a non-destructive technique of piezoresponse force microscopy. The SH signal was continuously observed in the step-chirped PPLN waveguides while scanning the wavelength of the pump laser from 1550 nm to 1660 nm. The SH conversion efficiency was measured to be 9.6 % W-1 cm-2 at 1642 nm. This work will benefit wavelength conversions of light sources with wideband spectra.

An All-Dielectric Polaritonic Metasurface with a Giant Nonlinear Optical Response.

Enhancing the efficiency of second-harmonic generation using all-dielectric metasurfaces to date has mostly focused on electromagnetic engineering of optical modes in the meta-atom. Further advances in nonlinear conversion efficiencies can be gained by engineering the material nonlinearities at the nanoscale, however this cannot be achieved using conventional materials. Semiconductor heterostructures that support resonant nonlinearities using quantum engineered intersubband transitions can provide this new degree of freedom. By simultaneously optimizing the heterostructures and meta-atoms, we experimentally realize an all-dielectric polaritonic metasurface with a maximum second-harmonic generation power conversion factor of 0.5 mW/W2 and power conversion efficiencies of 0.015% at nominal pump intensities of 11 kW/cm2. These conversion efficiencies are higher than the record values reported to date in all-dielectric nonlinear metasurfaces but with 3 orders of magnitude lower pump power. Our results therefore open a new direction for designing efficient nonlinear all-dielectric metasurfaces for new classical and quantum light sources.

Voltage-Tunable Thin Film Graphene-Diode-Based Microwave Harmonic Generator

This work presents the design, implementation, and characterization of the first thin-film integrated tunable microwave harmonic generator. The design is realized by exploiting the nonlinearity of four chemical vapor deposition (CVD) graphene-based diodes arranged in a nonlinear transmission-line (NLTL) approach. The used thin-film monolithic microwave integrated circuit (MMIC) technology is substrate independent. The fabricated prototype is realized on a 500- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> transparent quartz substrate and occupies less than 1.2 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of chip area including pads. Measurement results show a wide input frequency range from 0 to 2.8 GHz with measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{11}$ </tex-math></inline-formula> better than −10 dB. The measured second-harmonic conversion gain (CG) for an output frequency of 3.4 GHz is −21.6 dB. The measured third-harmonic CG for an output frequency of 3.15 GHz is −31 dB. To the best knowledge of the authors, the proposed circuit is the first tunable microwave harmonic generator combining graphene diodes in a NLTL topology on thin-film technology.

Highly efficient second harmonic generation of thin film lithium niobate nanograting near bound states in the continuum

Bound states in the continuum (BICs) are ubiquitous physical phenomena where such states occur due to strong coupling between leaky modes in side lossy systems. BICs in meta-optics and nanophotonics enable optical mode confinement to strengthen local field enhancement in nonlinear optics. In this study, we numerically investigate second-harmonic generation (SHG) in the vicinity of BICs with a photonic structure comprising one-dimensional nanogratings and a slab waveguide made of lithium niobate (LiNbO3, LN). By breaking the symmetry of LN nanogratings, BICs transition to quasi-BICs, which enable strong local field confinement inside LN slab waveguide to be supported, thereby resulting in improving SHG conversion with lower pump power of fundamental frequency (FW). With a peak intensity of 1.33 GW cm−2 at the FW, our structure features a second-harmonic conversion efficiency up to 8.13 × 10−5 at quasi-BICs. We believe that our results will facilitate the application of LN in integrated nonlinear nanophotonic.

High-power, low-coherence laser driver facility.

We report the first (to the best of our knowledge) high-power, low-coherence Nd:glass laser delivering kilojoule pulses with a coherent time of 249 fs and a bandwidth of 13 nm, achieving the 63%-efficiency second-harmonic conversion of the large-aperture low-coherence pulse and good beam smoothing effect. It provides a new type of laser driver for laser plasma interaction and high energy density physics research.

Toward 1% single-photon anharmonicity with periodically poled lithium niobate microring resonators

The absence of the single-photon nonlinearity has been a major roadblock in developing quantum photonic circuits at optical frequencies. In this paper, we demonstrate a periodically poled thin film lithium niobate microring resonator (PPLNMR) that reaches 5,000,000%/W second-harmonic conversion efficiency—almost 20-fold enhancement over the state-of-the-art—by accessing its largest χ ( 2 ) tensor component d 33 via quasi-phase matching. The corresponding single-photon coupling rate g / 2 π is estimated to be 1.2 MHz, which is an important milestone as it approaches the dissipation rate κ / 2 π of best-available lithium niobate microresonators developed in the community. Using a figure of merit defined as g / κ , our device reaches a single-photon nonlinear anharmonicity approaching 1%. We show that, by further scaling of the device, it is possible to improve the single-photon anharmonicity to a regime where photon blockade effect can be manifested.

Analytical approximation of the second-harmonic conversion efficiency.

The second-harmonic generation process of a focused laser beam inside a nonlinear crystal is described by the Boyd-Kleinman theory. Calculating the actual conversion efficiency and upconverted power requires the solution to a double integral that is analytically intractable. We provide an expression that predicts the exact gain coefficient within an error margin of less than 2% over several orders of magnitude of the confocal parameter and as a function of the walk-off parameter. Our result allows for readily tuning the beam parameters to optimize the performance of the upconversion process and improve optical system designs.

Second-harmonic generation of temporally low-coherence light

In this Letter, we study the second-harmonic (SH) generation of temporally low-coherence light using the statistical optics method. By introducing the statistical characteristics of low-coherence light into the nonlinear coupled wave equation, we predict the self-convolution relationship between the power spectral density of the second-harmonic and that of the fundamental wave and demonstrate it in experiments. The effects of phase matching and group velocity matching on the second-harmonic bandwidth and conversion efficiency are analyzed, which is beneficial to improve the efficiency of low-coherent SH light. Combining the statistics optics and nonlinear optics, our research provides a suitable mathematical model for the study of nonlinear frequency conversion processes of temporally low-coherence light. Due to its statistical characteristics and temporal incoherence, low-coherence SH light would have further applications in uniform illumination, quantum optics, metrology, and so on.

Shallow-etched thin-film lithium niobate waveguides for highly-efficient second-harmonic generation.

High-fidelity periodic poling over long lengths is required for robust, quasi-phase-matched second-harmonic generation using the fundamental, quasi-TE polarized waveguide modes in a thin-film lithium niobate (TFLN) waveguide. Here, a shallow-etched ridge waveguide is fabricated in x-cut magnesium oxide doped TFLN and is poled accurately over 5 mm. The high fidelity of the poling is demonstrated over long lengths using a non-destructive technique of confocal scanning second-harmonic microscopy. We report a second-harmonic conversion efficiency of up to 939 %.W-1 (length-normalized conversion efficiency 3757 %.W-1.cm-2), measured at telecommunications wavelengths. The device demonstrates a narrow spectral linewidth (1 nm) and can be tuned precisely with a tuning characteristic of 0.1 nm/°C, over at least 40 °C without measurable loss of efficiency.

Second-harmonic generation from 2D photonic crystal waveguide with simultaneous near-flat dispersions at fundamental frequency and second harmonic

Photonic crystal waveguides (PCW) have shown great potential to generate second harmonic (SH), but the available schemes with cavity or defect suffer from a lack of multiple wavelengths operation and excessive phase-matching requirement. Here we propose a 2D PCW structure comprised of a modulated single line defect, which is capable of independently controlling the fundamental frequency (FF) and SH modes. Therefore, two near-flat group velocity dispersions can be achieved for these modes, and they simultaneously satisfy phase matching conditions. Based on multiply scattering method, we theoretically demonstrate that the SH resonant modes originated from the nonradiative near-flat dispersion have high quality factors (nearly 6.5×104 for the maximum value). And the maximum SH conversion efficiency for these resonant modes are 2 orders of magnitude higher than that of off-resonant modes. In addition, benefitting from the matching of the group velocities of the second harmonic and the fundamental, the central wavelength of SH can be modulated within wavelength range ∼3nm. These results can provide potential applications in on-chip integration of photonics and quantum optics.