High-order harmonic generation (HHG) is a phenomenon that occurs under a strong laser field, and is explained using a three-step model in gaseous medium [1–4]. HHG occurs when an intense laser pulse is focused on a gas. When the electric field amplitude of the laser pulse is comparable to the electric field within the atoms, electrons can be detached from atoms by tunneling ionization. A detached electron is accelerated by the laser field and returned to its parent ion, under certain conditions. The collision between the electron and the parent ion yields emission of higher-order harmonics with higher photon energy. HHG emits coherent pulses, with a frequency spectrum corresponding to odd orders of the driving laser frequency. Broadband coherent pulses are widely used to measure ultrafast phenomena such as pump-probe methods [5, 6] and attophysics [7, 8]. HHG can implement extreme ultraviolet (EUV) and x-ray light in a tabletop setup; therefore, it is used for compact microscopy, spectroscopy, and lithography [9].

Chirped pulse amplification (CPA) has been used to reach a peak power intensity of over 10¹⁴ W/cm² in the driving laser to initiate HHG in a gaseous medium [10]. CPA features a complex optical system and relatively low pulse repetition rate, due to the reduction of the pulse repetition rate in the amplification stage.

Plasmonics [11] refers to coherent electron oscillations traveling along a metal-dielectric interface with an electromagnetic field. Owing to the plasmonic phenomenon, which can locally concentrate the electromagnetic field on the surface of a nanostructure, amplification exceeding 20 dB can be realized while maintaining the pulse repetition rate of a driving pulse oscillator. Research on HHG using plasmonics has been discussed for a decade. Plasmonic nanostructures consisting of two-dimensional metallic pattern arrays [12–14] and three-dimensional waveguides [15, 16], using a noble-gas medium, have been reported.

Since Ghimire et al. [17] opened the way to generate high-order harmonics from crystalline solids, many research groups have shown the dependence of solid-based HHG on the crystal direction [18], electron trajectory [19], bulk structure [20–22], and field intensity [23]. HHG in condensed systems is explained by the recollision three-step model, similar to the gaseous-medium case [24]. An intense laser field accelerates the excited electron from the valence band along the conduction band. The resulting carrier motion in the nonparabolic bands can lead to emission of harmonics via intraband transitions. At the same time, recombining the excited electron with frequencies corresponding to the instantaneous band gap emits harmonics, called interband transitions. In 2016, a metal-dielectric nanostructure with high HHG efficiency in a crystalline solid and plasmonic amplification helped to stably generate high-order harmonics in the EUV band, even under low driving-laser intensities [25].

In this study, we compare the plasmonic amplification in terms of the dimensions of gold-sapphire conical structures through theoretical calculations, and we investigate the effect of plasmonic amplification on HHG in the EUV band. In addition, the plasmonic nanostructure as a compact coherent light source is verified via damage analysis under various experimental conditions.

2.1. Sample Fabrication

The gold-sapphire conical structure acts as a driving-laser amplifier using surface plasmon polaritons and geometrical effects. The electromagnetic field of the incident femtosecond pulse propagates along the metal-dielectric interface, is reflected inside the conical structure, and is then enhanced at the apex of the cone. The enhanced femtosecond pulse initiates HHG at the sapphire tip [Fig. 1(a)]. The fabrication process for the nanostructure is shown in Fig. 1(b). First, the array of conical structures is patterned on a monocrystalline C-plane sapphire wafer with a thickness of 430 μm by plasma dry etching. Every sapphire cone has a height of 1.5 μm and a base diameter of 2.4 μm. The pattern of conic structures has a spacing of 0.6 μm. Second, a gold layer of 200 nm thickness is deposited via chemical vapor deposition. A chromium layer of 3 nm is used as an adhesion layer between the sapphire and gold layers. Finally, the tip of the gold-covered sapphire cone is milled using a focused ion beam. The diameter of the flattened Au-sapphire apex depends on the alignment of the focused ion beam; the outlet diameter of the flattened sapphire tip varies from 100 nm to 1 μm. Figure 1(c) shows a scanning electron microscopy (SEM) image of the fabrication results. The gold layer with high conductivity is bright, and the flattened sapphire tip with low conductivity is dark, in the SEM image.

Figure 1. Schematic and sample fabrication. (a) Concept of nanoscale extreme ultraviolet (EUV) pulse emitter via field enhancement of surface plasmon polaritons created along the Au-sapphire conical structure [25]. (b) Sample-fabrication processes in sequence: (1) conical patterning on the sapphire substrate via plasma dry etching, (2) deposition of a 200-nm gold layer via chemical vapor deposition, and (3) exit-aperture fabrication using a horizontally aligned focused ion beam. (c) scanning electron microscopy (SEM) image of Au-sapphire conical structures.

We fabricate gold-sapphire conical structures with different outlet diameters using the sample fabrication process; the diameters obtained are 200 and 400 nm. Figures 2(a) and 2(d) are top-view SEM images of each specimen. The bright area is gold-covered, and the dark region at the center is the sapphire surface. The different conductivities of sapphire and gold provide the contrast in the SEM images.

Figure 2. Magnified scanning electron microscopy (SEM) images of samples with (a)–(c) outlet diameters of 200 nm and (d)–(f) 400 nm: the Au-sapphire conical structure with an outlet diameter of 200 nm, (a) before laser exposure, (b) after laser exposure of 0.16 TW/cm2, and (c) after 0.37 TW/cm2; and the Au-sapphire conical structure with an outlet diameter of 400 nm, (d) before laser exposure, (e) after laser exposure of 0.16 TW/cm2, and (f) after 0.37 TW/cm2. The laser exposure time is 30 s.

2.2. Numerical Simulation

Finite-difference time-domain (FDTD) calculations using commercial software (Lumerical FDTD Solutions; Ansys, Canonsburg, USA) are performed to compare the intensity enhancement in these two specimens. The sapphire structure is assumed to be a truncated cone, and is modeled as if a 200-nm gold layer were uniformly applied to the surface of the structure. The incident laser is an 800-nm femtosecond pulse with a pulse width of 12 fs, and it starts from inside the sapphire and propagates along the z axis. The polarization direction is parallel to the x axis. For calculation, the mesh was set to 5 × 5 × 5 nm³ under perfectly matched layer boundary conditions.

The polarization direction is parallel to the x axis. For calculation, the mesh was set to 5 × 5 × 5 nm³ under perfectly matched layer boundary conditions.

Figures 3(a) and 3(b) show the enhanced intensity distribution at the flattened Au-sapphire apex of each structure in the xy plane. The intensity-enhancement factors have the largest values at the Au-sapphire interface around the x axis, parallel to the polarization direction of the incident laser pulse. The maximum intensity-enhancement factors at the surfaces of the structures are 100 and 78 for structures with outlet diameters of 200 and 400 nm respectively. The factor decreases from the interface to the center. The intensity-enhancement factors decreased to 11.8 and 3.8 at the centers of the apices. The intensity enhancement of the Au-sapphire conical structure is caused by surface plasmon polaritons and internal reflection. The high intensity enhancement at the interface between gold and sapphire can be explained by the plasmonic phenomenon that is observed at the metal-dielectric interface. The intensity enhancement corresponding to the plasmonic effect decreases sharply as the distance from the interface increases, for both structures. The intensity enhancement formed inside the sapphire conical structure has periodicity along the x and y axes, and the intensity enhancement factors and formed positions are similar for the two different gold-sapphire conical structures [Figs. 3(c) and 3(d)]. This shows that the overlap between the internally reflected and incident pulses contributes to the intensity enhancement.

Figure 3. Finite-difference time-domain (FDTD) calculation of two different Au-sapphire conical structures. (a), (b) Results for the enhanced intensity distribution over the xy plane on the sapphire tip of structures with outlet diameters of 200 nm and 400 nm respectively. In each case the white dotted circle indicates the exit aperture of the sapphire tip, which is an interface between the sapphire cone and gold layer. (c), (d) Results for the enhanced intensity distribution over the xz plane of structures with outlet diameters of 200 nm and 400 nm respectively. The white dotted lines show the edges of Au and sapphire regions.

2.3. Experimental Setup

The Au-sapphire conical structures are mounted on a three-axis picomotorized stage inside a vacuum chamber at the 10⁻⁶ mbar level. Femtosecond pulses from a Ti:sapphire oscillator are focused using an achromatic triplet lens of 6 mm focal length (OA046; Femtolasers Produktions GmbH, Vienna, Austria) into the bottom of the conical structures, with a focal spot size of 5 µm. Chirped mirrors (GSM007; Femtolasers Produktions GmbH) before the focusing lens help to optimize the chirp of the pulses; the pulse duration is 12 fs at the structure. The polarization direction of the pulses is parallel to the x axis of Fig. 1(a), which is parallel to the C plane and perpendicular to the A plane of the sapphire crystal structure. A toroidal mirror collects the generated EUV photons from the nanostructures with acceptance angles of 5° horizontal and 8° vertical. The collected EUV photons enter an EUV spectrometer with a grazing-incidence diffraction grating and are counted by a microchannel plate (MCP) coupled to a phosphor screen and optical charge-coupled device. The coating material of the MCP is cesium iodide (CsI), with a quantum efficiency of over 10% for wavelengths under 160 nm. The MCP is mounted on a stage moving along a Rowland circle of the grating, and the measurable spectral range is 40–130 nm. The spectrometer is spectrally aligned using Ar atomic emission lines. Among the fluorescence signals of the argon atoms, peaks having a strong signal in the EUV band are selected. The resolution of the spectrometer is about 0.1 nm in wavelength.

Figure 4 shows the EUV spectra from the Au-sapphire conical structures with outlet diameters of 200 and 400 nm. The EUV spectrum measured from a bulk sapphire surface is also included, for comparison. The intensity of the incident laser is 0.37 TW/cm², which means approximately 1.25 V/Å for the electric field inside the sapphire structures. Both the conical structures and the bulk sapphire generated high-order harmonic signals corresponding to the odd-order positions within the EUV band.

Figure 4. Measured high-order harmonic generation (HHG) spectra in the extreme ultraviolet band. The spectrum is low-pass filtered in the wavelength domain, with smoothing. The peak power intensity of the driving laser is 0.37 TW/cm2. Each spectrum is measured for 30 s.

The gold-sapphire conical structure with an outlet diameter of 400 nm has a higher harmonic yield from the 7^th to the 11^th order. However, the gold-sapphire conical structure with an outlet diameter of 200 nm has a higher cutoff harmonic order corresponding to approximately 60 nm, because the structure has a higher intensity-enhancement factor at the apex. The larger exit aperture of the gold-sapphire conical structure has a lower cutoff order, due to the lower field-enhancement effect. However, the total EUV flux increases as the number of molecules acting as EUV emitters increases.

Sapphire serves as an emitter of high-order harmonics, but can also be a strong absorber of EUV radiation. The transmittance of 7^th harmonics (~114 nm in wavelength) for 25 nm of sapphire is approximately 0.05; therefore, the EUV radiation induced by HHG inside the nanostructure is reabsorbed before propagating through the apex. The strong intensity enhancement deep inside the structures (induced by internal reflection) does not influence the measured HHG, but the intensity enhancement at the surface of the apex (caused by the plasmonic effect) affects the measured signal. A flat sapphire sample generates up to the 7^th-order harmonics under the same experimental conditions, indicating that the intensity enhancement of the gold-sapphire conical structures boosts the higher-order nonlinear phenomena.

The measured harmonic from flat sapphire follows perturbative scaling, given by I_HHG ∝ I ^N, where I_HHG is the measured intensity of the high-order harmonics, I is the intensity of the driving-laser pulse, and N is their order [23]. In this study the measured intensity of the harmonics depends on the area of the sapphire structure’s apex, corresponding to the number of emitters. The expected measured harmonic from the gold-sapphire conical structures is given by IHHG ∝ I ^N ∙ A, where A is the number of emitters at the structure’s end surface, under perturbative conditions. However, the measured spectra do not follow this scaling, due to the large divergence of the harmonic signals from the structures. The narrow apex areas of the structures, a few times the emitted harmonic’s wavelength across, induce large divergence. The structure with an outlet diameter of 200 nm has a larger divergence than the one with an outlet diameter of 400 nm. The small acceptance angle of the spectrometer also works as a spatial filter; therefore, the measured harmonic yield cannot easily be compared for different structures.

The spectra generated by both nanostructures have peaks between the 7^th and 9^th orders, and between the 9^th and 11^th orders. They are believed to be even-order harmonics generated by the steep variation of the enhanced laser field on the aperture surface of the structure [26]. The inhomogeneity of the local fields plays an essential role in the HHG process and leads to the generation of even-order harmonics. The quantum path difference and interference between the long and short trajectories of electron excursion can explain the spectral splitting of the even-order harmonics in the measured spectrum [27].

Figure 2 shows the SEM images of the Au-sapphire conical structures after laser exposure. Figures 2(b) and 2(e) show deformed apices of the structures under laser exposure at lower intensities, where high-order harmonic signals are not measured during the experiments. The exposure time is 30 s. The apex of the structure with an outlet diameter of 200 nm is deformed by melting of gold along the interface of the gold layer and the sapphire cone, where strong enhancement occurs [Figure 2(b)]. The structure with an outlet diameter of 400 nm is damaged by the deformation of the sapphire surface along the calculated strong-field-enhancement area [Figure 2(e)]. As the intensity of the incident laser increases, the structures are deformed by melting of the gold layer at the outlet and damage to the sapphire structures [Figs. 2(c) and 2(f)]. Significant thermal damage is accompanied by the sapphire surface cracks that form perpendicular to the direction of the incident field’s polarization, in the strong field enhancement of the structure with an outlet diameter of 200 nm [Fig. 2(c)] [28].

Each nanostructure is exposed to the fs laser pulses for 30 seconds in this study. As in the previous study [23], the efficiency of extreme-ultraviolet signal generation decreases with increasing damage. However, the structures continuously generate EUV signals even after theyare deformed. The number of EUV pulses generated, according to the principle of HHG is equal to the number of pulses of the driving laser. Therefore, extreme-ultraviolet pulses are generated with a pulse repetition rate of 75 MHz.

The gold-sapphire conical nanostructures with different dimensions devised in this study enable us to demonstrate efficient EUV radiation by intensity enhancement, and to understand the efficiency of HHG and sample damage according to theoretical calculations. Because the intensity enhancement and EUV yield can be adjusted according to the design of the metal-coated dielectric structure, a structure suitable for broadband light sources of higher-order cutoff or strong EUV radiation can be applied. Such a compact plasmonic EUV emitter can be used for fields that require nanoscale coherent light sources in the EUV band, such as lithography, spectroscopy, and microscopy.

The author declares no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the author upon reasonable request.

The author would like to thank the KAIST Analysis Center for Research Advancement (KARA) for help in fabricating the nanostructures for this work.

National Research Foundation of Korea (NRF) (No. 2021R1C1C100982511)