Phase-matched Third-harmonic Generation Research Articles

Phase-matched third-harmonic generation in silicon nitride waveguides.

Third-harmonic generation (THG) in silicon nitride waveguides is an ideal source of coherent visible light, suited for ultrafast pulse characterization, telecom signal monitoring and self-referenced comb generation due to its relatively large nonlinear susceptibility and CMOS compatibility. We demonstrate third-harmonic generation in silicon nitride waveguides where a fundamental transverse mode at 1,596 nm is phase-matched to a TM02 mode at 532 nm, confirmed by the far-field image. We experimentally measure the waveguide width-dependent phase-matched wavelength with a peak-power-normalized conversion efficiency of 5.78 × 10-7 %/W2 over a 660-μm-long interaction length.

Birefringence phase-matched direct third-harmonic generation in a ridge optical waveguide based on a KTiOPO4 single crystal

Birefringence phase-matched third-harmonic generation at 1594 nm is performed for the first time in a KTiOPO4 single crystal micrometric ridge waveguide. The energy conversion efficiency reaches 3.4% for a pump energy as low as 2 µJ over a pulse duration of 15 ps at a repetition rate of 10 Hz. Strong agreements between theory and experiments for both phase-matching and conversion efficiency is obtained, which let us envision future triple photon generation quantum experiments.

Quasibirefringent phase-matching technique for third-harmonic pulse generation from multilayered metamaterials

A phase-matched third-harmonic (TH) generation from multilayered metamaterials (MMs) with a third-order nonlinearity is numerically investigated in the ultrashort pulse regime. To overcome the phase-mismatch problem due to natural material dispersion, we propose a solution based on engineered dispersion provided by MMs with hyperbolic dispersion, i.e., with anisotropic materials possessing a positive and negative dielectric permittivity. We analyzed selected material choices and demonstrated quasibirefringent phase-matched conditions for TH conversion, which could be achieved by optimizing the fill-factor of metamaterials. We study the conversion efficiencies of transmitted and reflected TH pulses as a function of incident angles and input fundamental-frequency intensity; the maximum efficiencies are obtained for optimal incident angles.

Dispersion tuning in sub-micron tapers for third-harmonic and photon triplet generation.

Precise control of the dispersion landscape is of crucial importance if optical fibers are to be successfully used for the generation of three-photon states of light-the inverse of third-harmonic generation (THG). Here we report gas-tuning of intermodal phase-matched THG in sub-micron-diameter tapered optical fiber. By adjusting the pressure of the surrounding argon gas up to 50bars, intermodally phase-matched third-harmonic light can be generated for pump wavelengths within a 15nm range around 1.38μm. We also measure the infrared fluorescence generated in the fiber when pumped in the visible and estimate that the accidental coincidence rate in this signal is lower than the predicted detection rate of photon triplets.

Enhancement of phase-matched third harmonic generation via soliton self-frequency shift cancellation in a fluorotellurite microstructured fiber

We report the enhancement of phase-matched third harmonic generation (THG) via soliton self-frequency shift cancellation (SSFSC) in a fluorotellurite microstructured fiber (FTMF) pumped by a 1560 nm femtosecond fiber laser. The FTMF has two zero-dispersion wavelengths of 891 and 2012 nm for its slow axis. As the pump laser is polarized along the slow axis of the FTMF, phase matched THG at 629 nm is observed in the FTMF when the Raman soliton red-shifts to 1913 nm and the effective index at 1913 nm for the fundamental propagation mode matches with that at 629 nm for the high order propagation mode for a pump power of ∼25.2 mW. Interestingly, the THG at 629 nm is enhanced very much when the Raman soliton meets the second zero-dispersion wavelength of the slow axis and further SSFSC occurs with increasing the pump power. Such an enhancement is due to the unchanged operating wavelength of the Raman soliton with an increase in the pump power when SSFSC occurs and the resulting increase in the interaction length between the Raman soliton and third harmonic. Our results show that high efficient THG with a designed wavelength can be obtained via SSFSC in dispersion engineered optical fibers.

Phase-matched third-harmonic generation via doubly resonant optical surface modes in 1D photonic crystals.

Efficient nonlinear conversion requires that interacting optical waves maintain a consistent phase relationship when traveling in a medium despite its dispersion. Birefringent phase-matching, which is often used to compensate for the dispersion, is not applicable to optically isotropic nonlinear materials. Here, we present a one-dimensional photonic crystal structure that allows the propagation of optical surface waves, both at the fundamental and third-harmonic frequencies, as an efficient medium for phase-matched third-harmonic generation. A unique advantage of this structure is that the effective refractive indices for the surface waves are similar to the refractive index of air at both frequencies. This allows phase-matching between the first and third harmonics, and a visible collinear beam of the third harmonic is produced at the prism-coupled output. Moreover, these optical surface waves propagate over long distances even if a lossy nonlinear nanofilm is deposited onto the photonic crystal surface. We provide experimental results for third-harmonic generation at a wavelength of 410 nm for a bare dielectric Ta2O5/SiO2 multilayer structure and for the same structure coated with a 15-nm GaAs film.

Multimode phase-matched third-harmonic generation in sub-micrometer-wide anatase TiO₂ waveguides.

Third-harmonic generation (THG) has applications ranging from wavelength conversion to pulse characterization, and has important implications for quantum sources of entangled photons. However, on-chip THG devices are nearly unexplored because bulk techniques are difficult to adapt to integrated photonic circuits. Using sub-micrometer-wide polycrystalline anatase TiO₂ waveguides, we demonstrate third-harmonic generation on a CMOS-compatible platform. We correlate higher conversion efficiencies with phase-matching between the fundamental pump mode and higher-order signal modes. Using scattered light, we estimate conversion efficiencies as high as 2.5% using femtosecond pulses, and thus demonstrate that multimode TiO₂ waveguides are promising for wideband wavelength conversion and new applications ranging from sensors to triplet-photon sources.

Highly Efficient Phase-Matched Third Harmonic Generation From Mid-IR to Near-IR Regions Using an Asymmetric Plasmonic Slot Waveguide

We theoretically propose an asymmetric plasmonic slot waveguide (APSW) with a thin silicon nanocrystal (Si-nc) layer and a thinner silicon layer that fills the bottom and the top of the metallic slot region to increase third-harmonic generation (THG) efficiency. The needed modal phase-matching condition is satisfied with properly mode dispersion engineering by exploiting the waveguide geometrical parameters. Combining the asymmetric waveguide structure and the high third-order susceptibility of the nonlinear materials, efficient phase-matched THG from mid-infrared (IR) to near-IR regions is realized. Then, the THG performance was further improved by increasing the silicon slot width wherein the THG nonlinear coefficient as large as 21452 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$\hbox{m}^{-1} \cdot \hbox{W}^{-1}$</tex-math></inline-formula> is achieved. The corresponding THG efficiency comes up to 0.5% at a waveguide length of 9.3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$\mu\hbox{m}$</tex-math></inline-formula> with a pump power of 1 W.

Phase-matched third-harmonic generation in highly germanium-doped fiber

Phase-matched third-harmonic generation is demonstrated in a germanium-doped optical fiber. Green light at 514.4 nm is generated in an LP(03) mode when a pump field at ~1543.3 nm is launched into the fiber in the fundamental LP(01) mode. The phase matching is achieved for a particular combination of the germanium doping concentration and the fiber core diameter.

Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber

We observe phase-matched third-harmonic generation at 355 nm in a low-order mode of a sub-micron diameter glass fiber. The third-harmonic signal exhibits a sharp resonance for a fiber diameter d = 0.49 ± 0.02 μm, in excellent agreement with the value d = 0.506 μm predicted by theory. The third-harmonic conversion efficiency is 2 × 10 −6, and is limited by the pump power (1 kW) and effective fiber length (100 μm).

Third-harmonic generation by Raman-shifted solitons in a photonic-crystal fiber

Raman-shifted solitons in a photonic-crystal fiber can serve as a pump field for phase-matched third-harmonic generation in a higher-order guided mode of the same fiber. Phase matching for this soliton-dispersive-wave mixing process differs in its physics and in its formal notation from the conventional phase matching for third-harmonic generation with a dispersive pump.

Phase-matched third-harmonic generation in anisotropically nanostructured silicon

A frequency-tunable laser system based on an optical parametric oscillator is used to implement phase-matched third-harmonic generation in porous silicon films with a strong form birefringence. Phase matching, orientation dependences, and the behavior of the third harmonic as a function of the thickness of an absorbing film are confirmed by calculations and linear-optical measurements.

Phase-matched third-harmonic generation from nematic liquid crystals

The type-II phase-matching condition of the direct third-harmonic generation originated from third-order nonlinearity (3ω=ω+ω+ω) is performed in nematic liquid crystals with a fundamental light at 1064 nm. Since the phase-matching condition can be achieved in normal incidence of the fundamental light, the walk-off angle is zero. Thus, the interaction length is equal to the thickness of the liquid crystal film. Although the conversion efficiency in the present system is still low, 9.1×10−8, it will become 10−2 as discussed in this letter.

Depth-resolved multiphoton polarization microscopy by third-harmonic generation.

We achieve depth-resolved polarization microscopy by measuring third-harmonic generation induced by a tightly focused circularly polarized beam. In crystals exhibiting strong birefringence this signal is dominated by positively phase-matched third-harmonic generation. This process occurs in only optically anisotropic media, in which the birefringence compensates for the phase mismatch between the fundamental and the third harmonic induced by dispersion. Both the intensity and the polarization of the emitted signal provide information on the local optical anisotropy. We demonstrate the technique by imaging biogenic crystals in sea urchin larval spicules.

Phase-matching conditions for nonlinear frequency conversion by use of aligned molecular gases.

Transient birefringence can be induced in a gas of anisotropic molecules by an intense polarized laser pulse. We propose to use this birefringence to phase match nonlinear optical frequency-conversion processes. The conditions for anisotropic phase matching are derived, and experimental conditions required for phase-matched third-harmonic generation in a gas-filled hollow-core fiber are presented. We show that these conditions are experimentally feasible over a significant parameter range, making possible a new type of nonlinear optics.

Phase-matched third-harmonic generation in mercury-(I)-chloride.

Using phase-matched third-harmonic generation we determine the effective nonlinear susceptibilities in Hg2Cl2 (Calomel) to /chi(3)eff,I/ = 4.5 x 10(-22) m2V(-2) and /chi(3)eff,II/ = 9.7 x 10(-22) m2V(-2) for type I and type II phase matching, respectively. The type III phase matching uses the same tensor components as type I and is deduced to be /chi(3)eff,III/ approximately equal to 1.5 x 10(-22) m2V(-2). The effective third-order susceptibilities of Hg2Cl2 are two orders of magnitude higher than those of CaCO3, and the tensor components chi11 - 3chi18 exceed the components of ADP by a factor of 5. These measurements demonstrate that Calomel might be a promising material to be used for nonlinear optical devices.

90° phase-matched third-harmonic generation of CO_2 laser frequencies in AgGa_1–xIn_xSe_2

AgGa(1-x) In(x)Se(2) with x=0.474 was found to be 90 degrees phase matchable for third-harmonic generation of CO(2) laser wavelengths 9.2714-10.5910 mum by means of temperature tuning. Sellmeier equations and the thermo-optic constant for this crystal are presented.

Phase-Matched Third-Harmonic Generation in a Nematic Liquid Crystal Cell

Liquid crystals (LCs) are known for their strong nonlinear optical properties. A large contribution to the nonlinearity originates from molecular reorientation, an effect that has been used to demonstrate many interesting optical phenomena, such as [1] wave mixing, self-phase modulation, self-focusing, optical bistability, and optical Freedericksz transitions. This nonlinear mechanism is effective even at relatively low optical powers, but is also relatively slow. Much faster is the electronic contribution to the nonlinearity of LCs, which leads to effects such as second and third harmonic generation. Second harmonic generation in most liquid crystals is only an interface effect because of symmetry requirements. Efficient third harmonic generation (THG) is difficult to achieve in the LC bulk because of phase mismatch. However, in cholesteric liquid crystals, phase matching can be achieved using the properties of the periodic medium [2]. In this paper, we present an observation of strong phase-matched THG from within a simple nematic LC cell which is one of the most widely used types of LCs. The nematic LC is composed of rodlike molecules with one molecular axis much longer than the other two. The long axis of the molecules tends to point along a common direction, the director, while they are free to move from one location to another. The phase-matched THG we present here resulted from the combination of two nonlinear processes of different origin. A tightly focused laser beam of femtosecond pulses is used, which slightly modifies the molecular orientation inside the LC cell, leading to the generation of phase-matched third harmonic from the focal point. The same laser beam that deforms the local molecular orientation is used to generate the third harmonic light. The experimental setup used to generate third harmonic light from a nematic LC is similar to the setup used in THG microscopy [3]. The laser source is a synchronously pumped optical parametric oscillator (SpectraPhysics Tzunami-Opal system) which provides 130 fs pulses at a wavelength of 1.5 mm with a repetition rate of 80 MHz. The laser beam was focused onto a LC cell at normal incidence, using 360, numerical aperture › 0.85 microscope objective, to a spot size of ,1 mm. The sample used for the experiment was a parallel-aligned E7 nematic LC with a thickness of 50 mm. The LC was held between two glass substrates. A rubbing material with a low pretilt angle was used (PI2555), to impose a high anchoring potential on the LC molecules at the cell surfaces. The depth of the focal point in the sample is controlled using a piezoelectric driven stage. The third-harmonic light at 0.5 mm is collected by a lens and measured by a photomultiplier after filtering out the fundamental wavelength. It was verified by spectral measurements that only third harmonic light was generated, while no second harmonics signal could be detected. The polarization of the input beam is controlled by a polarizer, ly4 and ly2 plates. The coordinate frame is chosen so that the top glass-LC interface is in the x-y plane while the director of the LC at this plane is pointed at the y axis. The electromagnetic field is therefore propagating along the positive z axis. Tightly focusing a Gaussian beam in a homogenous nonlinear medium usually results in no THG [4]. However, when the medium is not homogeneous or, more specifically, when there are variations of the nonlinear thirdorder susceptibility x s3d in the bulk, third harmonic light

Noncritically phase-matched frequency conversion in Gd_xY_1–xCa_4O(BO_3)_3 crystal

A nonlinear optical crystal YCa(4)O(BO(3))(3) (YCOB) is phase matchable for third-harmonic generation (THG) of a Nd:YAG laser by type I mixing between 1.064 and 0.532mum . By partial substitution of Gd for Y in YCOB, a solid solution Gd(x)Y(1-x)Ca(4)O(BO(3))(3) gradually changes the phase-matching angles of THG to (theta, ø)=(90( degrees ), 90 ( degrees )) . We present the properties of noncritically phase-matched THG in Gd(x) Y(1-x)Ca(4)O(BO(3))(3) (x=0.28) .

Phase-matched third-harmonic generation by nonlinear phase shift in a hollow fiber

W/cm2 are introduced into a 1.8-cm hollow fiber in room air. From the observation of the third-harmonic beam quality and spectra, it is clarified that the harmonics are pumped at the leading edge of the fundamental pulse. The model calculation accounting for the nonlinear refractive index change of air shows a quantitative agreement with the experimental results.