Direct Third-harmonic Generation Research Articles

Laser processing of silicon with GHz burst pumped third harmonics for precise microfabrication.

Femtosecond laser processing has proved to be a valuable tool for various microfabrication applications. In order to further increase the quality and efficiency of femtosecond laser processing, processing with GHz burst mode lasers has gained attention in recent years, where packets of high-repetition rate pulses are used instead of single pulses at the fundamental repetition rate. However, the use of burst-pulses has mainly been limited to the fundamental wavelength of powerful regenerative amplifier systems, often near 1 micrometer wavelength. In this study, we explore the characteristics and potential benefits of further wavelength conversion of burst-pulses emitted at the near-infrared to the ultraviolet region via direct third-harmonic generation. We construct an in-line process evaluation setup with a chromatic confocal sensor, and evaluate the ablation characteristics of the burst-pumped and non-burst processing of silicon. We observe that burst-mode processing has significantly reduced surface roughness and debris, resulting in high-quality laser processing. To demonstrate the utility of such burst-pumped UV processing, we show the successful milling of a spherical structure enabled by in-line surface profile feedback, while similar processing with non-burst conditions did not work. We believe such results show the strong potential of burst laser sources for use in accurate microfabrication of structures with micrometer-scale resolution.

Investigation on the optical characteristic of calcite crystal and α-BBO crystal in direct third-harmonic generation process

Calcite crystal and α-BBO crystal of which the microstructure possesses symmetric center with delocalized π bond were selected to produce phase-matched direct third-harmonic. In order to obtain a high third-order nonlinear conversion efficiency, the parameters including the walk-off angles, phase-matching angles, acceptance angles, acceptance wavelengths and group-velocity index in calcite crystal and α-BBO crystal were calculated within I (ooo→e), II (ooe→e) and III (oee→e) phase-matching types. The tinier walk-off angle and the larger acceptance angle in α-BBO crystal may lead to a better third-order nonlinear interaction in UV region. The smaller phase-matching angle in calcite crystal makes it possible to produce third-harmonic with shorter wavelength even in deep UV region. In the experiment, phase-matching angles and phase-mismatching angles of type-II which was the most efficient phase-matching type were measured in calcite crystal and α-BBO crystal. The results may provide a reference for further study on direct third-harmonic generation.

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.

Free electron nonlinearities in heavily doped semiconductors plasmonics

Heavily doped semiconductors have emerged as tunable low-loss plasmonic materials at mid-infrared frequencies. In this article we investigate nonlinear optical phenomena associated with high concentration of free electrons. We use a hydrodynamic description to study free electron dynamics in heavily doped semiconductors up to third-order terms, which are usually negligible for noble metals. We find that cascaded third-harmonic generation due to second-harmonic signals can be as strong as direct third-harmonic generation contributions even when the second-harmonic generation efficiency is zero. Moreover, we show that when coupled with plasmonic enhancement free electron nonlinearities could be up to two orders of magnitude larger than conventional semiconductor nonlinearities. Our study might open a new route for nonlinear optical integrated devices at mid-infrared frequencies.

Third-order nonlinear optical properties of calcite crystal in UV region

Different from cascaded second-order nonlinear frequency conversion which is a common way to obtain ultraviolet (UV) laser only through noncentrosymmetric crystal, the optical properties of the phase-matched direct third-harmonic generation (THG) in the centrosymmetric calcite crystal was studied. A femtosecond laser was taken as the pumping source in the type-I (ooo→e) and type-II (ooe→e) phase-matched experiment, and a nanosecond laser was also used for comparison. Polarization angle ρ, phase-matching angle θ and azimuth angle φ in direct THG were determined and verified. Strong third-harmonic at 266 nm was observed in calcite crystal pumped by femtosecond laser. Compared with type-I phase-matched, Type-II was more efficient for energy conversion. The shortest harmonic wavelength obtained was about 213 nm, which was close to deep-UV region. The maximal output energy was 19.3 μJ (average power, ～19.3 mW) and the maximal conversion efficiency was 1.25% at 266 nm, which was the highest conversion efficiency at present. These results may indicate a wider application field for centrosymmetric crystals and another method to produce laser in UV and even deep-UV region.

Optimal third-harmonic generation in an optical microcavity with χ(2) and χ(3) nonlinearities.

Third-harmonic generation can be realized via both χ(3) and cascaded χ(2) nonlinear processes in a triply-resonant microcavity. It is still unknown how these processes interfere with each other and the optimization of the conversion efficiency still remains as a question. In this work, the interplay between the direct third-harmonic generation and the cascaded process combining of the second-harmonic generation and the sum-frequency generation are investigated. It is found that the interference effect between these two processes can be used to improve the conversion efficiency. By optimizing the cavity resonance and the external coupling conditions, the saturation of the nonlinear conversion is mitigated and the third-harmonic conversion efficiency is increased. A design rule is provided for achieving efficient third-harmonic generation in an optical microcavity, which can be generalized further to the high-order harmonic generations.

Efficient frequency conversion for cubic harmonic generation at 266 nm in centrosymmetric α-BBO crystal.

Direct third-harmonic generation (THG) is a third-order nonlinear process without the restriction to the symmetric characteristic of crystals. It is of great interest for setting up a χ(3) optical parametric oscillator which can be used in multiphoton quantum correlation. To obtain pure and strong THG, we proposed to elect the centrosymmetric crystal with delocalized π bond as the nonlinear media during the frequency conversion process. An unprecedented cubic harmonic energy 37.6μJ (average power ∼37.6 mW, conversion efficiency ∼2.5%) at 266nm was generated in α-BBO crystal (not the β-BBO), indicating direct THG in practical application. These results also demonstrated a succinct and efficient way to generate deep-UV laser and another development direction of nonlinear crystals in UV region.

Third-harmonic entanglement and Einstein-Podolsky-Rosen steering over a frequency range of more than an octave

The development of quantum technologies which use quantum states of the light field interacting with other systems creates a demand for such states over wide frequency ranges. In this work we compare the bipartite entanglement and Einstein-Podolsky-Rosen (EPR) -steering properties of the two different parametric schemes which produce third-harmonic optical fields from an input field at the fundamental frequency. The first scheme uses second harmonic cascaded with sum-frequency generation, while the second uses triply degenerate four- wave mixing, also known as direct third-harmonic generation. We find that both schemes produce continuous-variable bipartite entanglement and EPR steering over a frequency range which has previously been unobtainable. The direct scheme produces a greater degree of EPR steering, while the cascaded scheme allows for greater flexibility in having three available bipartitions, thus allowing for greater flexibility in the tailoring of light matter interfaces. There are also parameter regimes in both for which classical mean-field analyses fail to predict the mean-field solutions. Both schemes may be very useful for applications in quantum communication and computation networks, as well as providing for quantum interfaces between a wider range of light and atomic ensembles than is presently practicable.

Third-harmonic generation in relative-phase-controlled two-color laser field

We experimentally demonstrate third-harmonic generation (THG) by intense femtosecond laser pulse at a central wavelength of ∼800 nm superposed by its second harmonic in air. The third-harmonic signal shows a periodic modulation with a period of ∼0.67 fs when the delay between fundamental and second-harmonic wave is continuously changed. The periodic modulation of THG can be attributed to the interference of third-harmonic signals generated from a direct THG channel (3ω=ω+ω+ω) and a four-wave mixing (FWM) channel (3ω=2ω+2ω−ω). With high pump intensity, the fitting of the measured TH spectrum as a function of delay implies that the pump pulse undergoes a strong pulse splitting and self-phase modulation at the focus.

Direct third harmonic generation due to quadratic cascaded processes in periodically poled crystals

We report the first, according to our knowledge, experiment for direct third harmonic (TH) generation in periodically poled quadratic crystals. TH radiation of a diode array pumped and acousto-optically Q-switched Nd:YVO 4 laser is generated in a 25 mm long periodically poled lithium niobate (PPLN) crystal of period 7.0 μm. A theoretical model is developed that explains the experimental results. It predicts that the efficient phase-matched direct TH generation in periodically poled structures with duty factor 0.5 requires even order quasi-phase matching. In contrast to the similar experiments in bulk birefringence crystals, where direct phase matched TH signal is the sum of the contribution of both intrinsic and cascaded cubic nonlinearities, in periodically poled quadratic crystals only cascaded cubic nonlinearity contributes to the direct phase-matched TH signal.

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.

Optical harmonic generation in the Cantor-type dielectric superlattice

Second-harmonic (SH) and direct third-harmonic generation (THG) in a one-dimensional finite Cantor-type dielectric superlattice (DSL) can be treated exactly by using a transfer matrix method. Taking advantage of a numerical technique, we discuss the dependence of the SH and TH on the wavelength and the field amplitude variables of the fundamental wave as well as structural parameters of a Cantor-type DSL. Under typical structural parameters, high conversion efficiency of the SH and TH can be obtained at some special fundamental wavelength.

Highly efficient direct third-harmonic generation based on control of the electro-optic effect in quasi-periodic optical superlattices

We present a method for controlling the efficiency of direct third-harmonic generation in quasi-periodic optical superlattices by means of the electro-optic effect. The calculated results manifest that this method is extremely efficient for achieving high efficiency of direct third-harmonic generation in predesigned quasi-phase-matched coupled parametric processes and is feasible at any given fundamental intensity. In addition, we demonstrate that the electro-optic control approach is significantly better than the temperature-control method.

Microstructural design for phase-matching engineering

Superlattices have opened up a promising area for the development of new synthetic materials that are of interest for scientific and application purposes. Similar to energy-band engineering in semiconductor superlattices, phase-matching engineering can be used for efficient high-harmonic generation. As an example, a theoretical analysis is given of direct third-harmonic generation at any wavelength by means of the second-order nonlinearity.

Analytical Expression for the Fourier Spectrum of a Quasiperiodic Fibonacci Superlattice with k Components (k ? 3)

The two-component quasiperiodic optical superlattice has been proved useful to some coupled parametric processes such as the direct third-harmonic generation. In this paper a three-component quasiperiodic superlattice has been studied theoretically. Using the projection method, the analytical expression of its Fourier spectrum has been deduced. The results might be conducive to the design of nonlinear optical devices related to the coupled parametric processes, such as the fifth-harmonic generation.

Ultraviolet generation in a dual-periodic domain inverted structure in LiTaO3 crystal by frequency tripling a 1.064 μm laser

We demonstrate a coupled optical parametric process that is able to realize in a dual-period domain inverted structure in complex quasi-phase-matched scheme. As an example, we designed and fabricated a dual-periodic domain inverted structure in LiTaO3 for the first time. This structure couples second-harmonic generation and sum-frequency generation through two cascade quasi-phase-matched processes, therefore, a direct third-harmonic generation can be realized. The test verified that ultraviolet was generated in the optical superlattice through frequency tripling a 1.064 μm laser.

Three-component quasiperiodic superlattice and its Fourier spectrum

The domain-inverted ferroelectric materials, or simply the dielectric superlattice, can be patterned into different configurations. For example, there are the periodic, quasiperiodic, Thue-Morse and several other types. The periodic superlattice is widely used for the second-harmonic generation, sum-frequency generation and optical parametric oscillation, for which only one optical parametric process is involved. The two-components quasiperiodic superlattice has been proved useful to some coupled parametric processes such as the direct third-harmonic generation. In this paper a three-component quasiperiodic superlattice has been discussed theoretically. Using the projection method, the analytical expression of its Fourier spectrum has been derived. Relations with the periodic and two-components quasiperiodic superlattices has been given. The results might be useful to the design of nonlinear optical devices related to the coupled parametric processes.

Dielectric superlattices for nonlinear optical effects

Dielectric superlattices show a lot of new phenomena that are promising in applications, such as nonlinear optical frequency conversion and optical bistability. This paper reviews the main achievements in this field. Much has been focused on the work done in our Lab. Since 1980, we have extended the concept of superlattice from semiconductor to dielectrics. When quasi-phase-matching technique is introduced into a quasiperiodic dielectric superlattice, more interesting phenomena can occur. For example, multiwavelength second-harmonic generation and coupled parametric processes such as direct third-harmonic generation have been realized with high efficiency. A new mechanism for optical bistability in a 2-dimensional dielectric superlattice, i.e. a 2-dimensional nonlinear photonic crystal, has been proposed theoretically had proved experimentally.

Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice

Quasi-periodic structure can be introduced into nonlinear optical materials such as LiTaO 3 crystals. Such structures were used for quasi–phase-matching second-harmonic generation. These materials are now shown to be able to couple second-harmonic generation and sum-frequency generation through quasi–phase-matching. The approach led to a direct third-harmonic generation with high efficiency through a coupled parametric process. The result verifies that high-order harmonics may be generated in a quadric nonlinear medium by a number of quasi–phase-matching processes, and therefore, exhibits a possible important application of quasi-periodic structure materials in nonlinear optics.

Phase matching conditions for four-wave mixing in the principal planes of biaxial crystals

For general parametric collinear four-wave mixing (FWM) or direct third harmonic generation (THG) processes involving fields at four different frequencies, the determination of the phase matching (PM) directions becomes considerably difficult. But the situation may be greatly simplified when the incident waves propagate in one of the principal planes. In this case, we present here the criteria for determining whether PM can be satisfied for these processes. The explicit equations, even analytic expressions in some processes for obtaining the corresponding PM directions are presented. Data of PM directions for direct THG in several typical biaxial crystals are given.