Letter pubs.acs.org/journal/apchd5
Generation of Coherent Extreme-Ultraviolet Radiation from Bulk Sapphire Crystal Hyunwoong Kim,†,‡ Seunghwoi Han,†,‡ Yong Woo Kim,† Seungchul Kim,§ and Seung-Woo Kim*,† †
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea § Department of Optics and Mechatronics Engineering, College of Nanoscience and Nanotechnology, Pusan National University, 2 Busandaehak-ro 63beon-gil, Busan 46241, South Korea ABSTRACT: Coherent extreme-ultraviolet (EUV) radiation produced by means of high-order harmonics generation (HHG) from intense laser pulses is used for various ultrafast pump−probe experiments. In this study, we test bulk sapphire as to its HHG capability as a new solid EUV emitter operating with moderate nJ-energy laser pulses obtained directly from an oscillator. Specifically, the high bandgap of sapphire (∼9 eV) permits EUV harmonics at wavelengths up to ∼60 nm for laser intensities of 1.31 TW cm−2 when irradiated by 12 fs pulses at 800 nm. The EUV output exceeds 107 photons per second without causing drastic thermal damage due to the high heat dissipation capabilities of bulk sapphire. In addition, the freespace EUV propagation can be steered by shaping the bulk surface without requiring extra grazing incidence mirrors. All these experimental findings prove the feasibility of using bulk sapphire as a desktop EUV source for relevant metrological applications. KEYWORDS: extreme-ultraviolet radiation, high harmonic generation, bulk sapphire, ultrafast photonics, nonlinear optics
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range of 40−130 nm using a grating-based spectrometer through a toroidal refocusing mirror (Methods). Figure 1a shows the EUV spectra measured from the sapphire specimen when the incident laser is aligned normal to the C-plane with its polarization direction being perpendicular to the sapphire A-plane (112̅0). This irradiation condition corresponds to the Γ−K direction in the Brillouin zone of sapphire crystal (Figure 1d). The shorter wavelength side of the measured EUV spectra extends to the 13th harmonic (H13) that is centered at a wavelength of 61 nm. The maximum electric field induced inside the sapphire specimen reaches 0.236 V Å−1 when the incident laser intensity is increased to 1.31 TW cm−2 with 3.08 nJ per pulse. All observed harmonic peaks appear to have the Gaussian shape, being located at oddorder harmonic positions of the fundamental wavelength of 800 nm. The peak of each harmonic scales in a nonperturbative way with the incident laser intensity (Figure 1e): H7 to the power of 3.8, H9 to 6.0, H11 to 8.3, and H13 to 5.0, respectively. At the same time, the cutoff energy of the measured EUV spectra exhibits a linear increase, with the incident electric field induced inside the sapphire specimen (Figure 1f). Another important observation is that the detected EUV output appears highly sensitive to the lateral focal position of the incident laser within the sapphire specimen (Figure 1g). This phenomenon is attributable to the strong reabsorption of
oherent EUV and even X-ray radiation can be produced from various gaseous atoms when their electrons are driven into the continuum by quantum tunneling.1−4 In recent years, efforts have been made to exploit solids as HHG materials ever since the first report of HHG success with a ZnO bulk crystal.5 Subsequent investigations were made with various solid materials in the form of thin films,6−9 bulk crystals,10−13 solid phase atoms,14 or nanostructures.15 In contrast to the use of gaseous atoms, the HHG mechanisms that occur in crystalline solids can be explained in terms of the interband and intraband transitions of the electrons inside the band structure as they interact with the incident laser field.10,16−18 Accordingly, the solid-based HHG process is now being extensively investigated as a means of exploring attosecond physics7,19−22 and crystal band structures.23,24 Figure 1 illustrates the experimental setup used in this study to generate high harmonics from bulk sapphire. The specimen used in the experiment consists of a single crystal sapphire substrate with a thickness of 430 μm, cut along the C-plane (0001) or M-plane (101̅0). The sapphire specimen is installed on a 2-D stage for micropositioning control. The incident laser beam is produced from a Ti:sapphire oscillator that emits 12 fs pulses at a center wavelength of 800 nm at a 75 MHz repetition rate. The laser average power is tunable from 70 to 250 mW, equivalently from 0.366 to 1.31 TW cm−2 in terms of the peak pulse intensity. The pulse energy is a few nJ and focused on a 5 μm spot diameter inside the specimen. The EUV spectrum emanating from the specimen is monitored over the wavelength © XXXX American Chemical Society
Received: April 2, 2017 Published: June 28, 2017 A
DOI: 10.1021/acsphotonics.7b00350 ACS Photonics XXXX, XXX, XXX−XXX
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Figure 1. High harmonic generation from bulk sapphire. (a) Measured EUV spectra with increasing the field strength. (b) Experimental setup. (c) Sapphire crystal structure. (d) Brillouin zone of sapphire crystal. (e) Harmonic yield vs driving laser peak intensity. (f) Harmonic cutoff energy vs electric field inside crystal. (g) EUV output vs laser focal position. Negative sign is inside crystal. (h) Total photon flux vs exposure time.
to the internal structural modification of the specimen by the accumulated heat. Figure 2 shows how the overall harmonic yield depends on the crystallographic orientation, which was analyzed by rotating the specimen about the polarization direction of the incident laser field. In this experiment, the laser polarization direction was fixed stationary with respect to the spectrometer grating to maintain a consistent detection efficiency by avoiding polar-
EUV radiation by the solid specimen itself. The EUV output is detectable only when the pulse energy is concentrated within a few microns of the back surface of the specimen. Despite the reabsorption, the total photon flux of all the harmonics combined is measured to be more than 107 photons per second for a 1.31 TW cm−2 incident intensity (Methods). More importantly, the photon flux sustains strength for longer than 30 min (Figure 1h), with a slow gradual reduction observed due B
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Figure 2. Crystallographic orientation dependence of high harmonic generation from bulk sapphire. (a) Measured high harmonic spectra (in rectangular plot) by rotating the laser polarization direction about the C-plane. (b) The same spectra of the case a shown in a polar plot. (c) Measured high harmonic spectra (in rectangular plot) by rotating the laser polarization direction about the M-plane. (d) The same spectra of the case b shown in a polar plot. H7, H9, H11, and H13 are high harmonic peaks. Γ, A, K, and M are axis symbols in the Brillouin zone of sapphire crystal. For clarity, EUV intensities in the polar plots in (b) and (d) are normalized individually with respect to each harmonic maximum intensity.
Figure 3. Spatiotemporal coherence measurement of generated EUV harmonics. (a) Experimental setup arranged with a double-slit microstructure (SEM image, inset). (b) Observed interference patterns for the 7th harmonic (H7) and 9th harmonic (H9). (c) Visibility analysis using the interference intensity profile taken along the solid line (white) for each harmonic. MCP: microchannel plate, CCD: charge-coupled device camera, V: visibility.
and M-plane, which leads to a 6-fold hexagon and a 4-fold rectangle, respectively. The experimental data also shows that the 7th harmonic (H7) displays the least dependence on the crystallographic orientation on the C-plane, while the other harmonics (H9, H11, and H13) become strong in either the Γ−K or Γ−M direction in the Brillouin zone (Figure 1d). In addition, with the laser beam being normal to the M-plane, all of the harmonic components turn to similar variations being strong in both the
ization rotation. The measurement data reveals that when the laser is incident normal to the C-plane, the harmonic yield shows a 6-fold symmetry in terms of the rotation angle of the polarization direction (Figure 2a,b). In contrast, a 4-fold symmetry appears dominant when the laser is set normal to the M-plane (Figure 2c,d), indicating the strong dependence of the HHG process on the crystalline structure. The difference can intuitively be understood by considering the projection of the hexagonal unit cell of sapphire (Figure 1c) on to the C-plane C
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Figure 4. Propagation steering of EUV radiation from bulk sapphire. (a) Measured propagation profiles of EUV radiation from a flat sapphire surface. (b) Measured propagation profiles of EUV radiation from a sloped sapphire surface cut with a tilt angle of 30°. (c) Propagation geometry of the case (a); the driving infrared (IR) laser is focused normal to a flat sapphire surface with an incidence angle of 25°. The divergence angle of EUV radiation is measured 9°. (d) Refraction geometry of the case (b); EUV radiation is observed to refract with an angle of 63°, which is the same as the refraction angle of the driving IR laser calculated from the Snell’s law with its refractive index being 1.76 in bulk sapphire.
Γ−K and Γ−A directions. These observations indicate that each harmonic component has its own distinct dependence on the crystallographic orientation in connection with the interband polarization and intraband current within the electronic band structure. More physical explanation requires calculating the crystalline-dependence using comprehensive physical HHG models from solids, for which quite a few experimental and theoretical investigations are currently underway.16−18 In connection with the efforts, our experimental results may be exploited to identify the band structure23−25 as well as the physical HHG mechanism from sapphire crystal. Figure 3 illustrates the results of an experimental verification for the spatiotemporal coherence of the generated harmonics. In the experiment, a double-slit microstructure is placed between the specimen and spectrometer (Methods). The double-slit microstructure was fabricated using focused ion beam (FIB) milling on a silver foil of 10 μm thickness with two slits being equally 12 μm wide and separated by a 36 μm gap (Figure 3a). This arrangement permits the viewing of the double-slit interference pattern of each harmonic, separately and simultaneously, with a single spectrometer setup using a 2D microchannel plate as the detector. The interference pattern shown in Figure 3b is the result of sampling integrated over a period of 300 s. The fringe visibility was calculated as V = (Imax − Imin)/(Imax + Imin), where Imax is the maximum intensity of the center fringe peak and Imin is the minimum intensity of the next nearest fringe valley. The EUV radiation that emanated from the sapphire specimen was precisely aligned to be symmetrical about the center of the double-slit aperture. Hence, the measured visibility can be assumed to represent the modulus of the complex coherence factor, which can straightforwardly be
interpreted as the spatiotemporal coherence of the generated harmonics.26 The measured data shows that both the H7 and H9 harmonics exhibit high degrees of visibility of 0.83 and 0.76, respectively. This quantitative result is comparable to that for the case of gaseous atoms27,28 and proves that bulk sapphire is able to produce HHG signals of high spatiotemporal coherence. Unlike gaseous atoms, sapphire crystal is a dense periodic bulk solid that contains many electrons that can act as not only HHG emitters but also strong EUV absorbers. This implies that the EUV radiation produced by HHG is subsequently subject to strong reabsorption by the specimen material itself. Quantitatively, the transmission T of light through a bulk sapphire specimen of thickness d decays as T = exp(−αd) with α being the absorption coefficient that is found 0.115 nm−1 near the H7 wavelengths.29 Thus, the intensity of H7 is attenuated to merely 3% after traveling a short distance of 30 nm. This situation is not much different for other harmonics since the wavelengths of H9 to H13 are also subject to strong absorption in sapphire.29 Consequently, only the EUV radiation generated on the shallow exit-side skin layer of the specimen eventually contributes to the EUV output detected in free space outside the specimen. Figure 4 illustrates how the EUV radiation from the specimen propagates in free space (Methods). When emitted from a flat back surface of the specimen (Figure 4a), the EUV propagation has a divergence angle of 9°, which is much narrower than the convergence angle of 25° of the incident laser. The Gaussian beam waist of the EUV propagation is estimated to be ∼1 μm on the back surface of the specimen, whereas the incident laser is focused on a 5 μm diameter spot (Figure 4c). In addition, when the back surface of the specimen D
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index of sapphire (1.76), assuming the laser is incident normal to the specimen. Photon Flux Measurement. The EUV yield of Figure 1h was monitored using a Cu−BeO photomultiplier (R595, Hamamatsu) that responds to the EUV wavelength range of 30−150 nm. The photomultiplier was positioned 20 mm from the sapphire specimen, and the resulting photocurrent I was measured using a picoammeter (6485, Keithley). The photon flux N was estimated using N = I/(q × Q × G), where q denotes the electron charge (1.6 × 1019 C), Q is the quantum efficiency of the photocathode (0.07), and G is the amplification gain of the photomultiplier (4 × 105). Visibility Measurement. The experimental setup of Figure 3a consists of a double-slit microstructure, a line grating, and a detector unit. The double-slit microstructure was fabricated on a silver thin substrate of 10 μm thickness and located at a 10 mm distance from the sapphire specimen and 315 mm away from the line grating. The detector unit consists of a microchannel plate (BOS-40-6/CsI, Beam Imaging Solutions) combined with a phosphor screen and a CCD camera. The line grating is an aberration-corrected concave type (001−0464, Hitachi) of 1200 grooves per mm and a 500 mm radius of curvature, being able to project the double-slit interference of each harmonic separately from others. Free-Space Propagation Measurement. The experimental data of Figure 4 were monitored by varying the gap distance between the sapphire specimen and a microchannel plate responsive only to EUV radiation. No line grating was used in this experiment. The sapphire specimen was moved together with the focusing lens of the incident laser along the optical axis on a linear stage under automatic control. The divergence angle was quantified by analyzing the EUV propagation profiles consecutively measured with increasing the gap distance. The 30° tilted rear surface of the sapphire specimen was fabricated by the focused ion beam milling under numerical control.
is cut with a tilt angle (Figure 4b), the EUV propagation tends to have almost the same refraction angle as that of the incident laser without showing distinctive chromatic splitting. This is not consistent with Snell’s law because the refractive index of each EUV harmonic in sapphire is known to vary from 0.8 to 2.2, depending on its harmonic order, whereas that of the fundamental IR laser is 1.76 at 800 nm.30 The reason is that the EUV radiation in free space originates from a shallow layer of sapphire that is shorter than a single wavelength, thus, it remains in parallel all with the fundamental laser after refraction. This observation implies that the output EUV radiation can be steered simply by using a sloped surface without extra grazing reflective mirrors. Furthermore, if the specimen is patterned to have an appropriately curved shape, the EUV propagation may be brought possibly to a focal spot in free space without using reflective or diffractive optics. To conclude, our experiments performed in this investigation demonstrate bulk sapphire as an effective high bandgap emitter that produces coherent EUV harmonics at wavelengths up to ∼60 nm for laser intensities of 1.31 TW cm−2 with nJ-energy pulses emitted from a Ti:sapphire oscillator. The intensity level is one or two orders of magnitude lower compared to those values so far reported for solid materials having similar bandgaps of 9 eV. The net EUV output reaches more than 107 photons per second without causing severe thermal damage to the crystal structure. Owing to strong reabsorption, the net EUV flux emanating into free space is contributed mainly by the back crystal surface within an effective skin depth of ∼30 nm. Accordingly, by cutting the sapphire specimen with a tilt angle, output EUV harmonics can be steered without requiring extra grazing reflective optics. These experimental findings prove that bulk sapphire is a promising HHG emitter as coherent EUV sources for attosecond physics and various relevant applications.
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METHODS HHG Spectrum Measurement. The EUV spectrometer system shown in Figure 1b is comprised of a toroidal mirror, a line grating, and a detector unit. The toroidal mirror collects the EUV radiation from the sapphire specimen with an acceptance angle of 5° horizontal (8° vertical), refocusing it on to the entrance-slit aperture of the line grating with a grazing incidence angle of 84°. With 133.6 grooves per mm on a 20 × 25 mm2 concave surface (998 mm radius of curvature), the line grating receives the refocused light and subsequently spreads it by diffraction into a line spectrum. The detector unit is made of a microchannel plate (XUV-2040, Brightview Inc.) to which a charge-coupled device (CCD) camera (DH420A-FO-195, Andor) is attached for quantitative spectral analysis. The whole spectrometer system is contained in a vacuum environment of 10−6 Torr and its overall resolving power is estimated to be 0.1 nm in wavelength. Peak Intensity Calculation. The peak intensity Ip of the incident laser field is calculated as Ip = Pa/(Fr × Tp × Af); Pa is the average laser power (250 mW maximum), Fr is the pulse repetition rate (75 MHz), Tp is the pulse duration (12 fs), and Af is the focal area given by (π/4)D2 with D being the focal diameter (5 μm). The result is worked out to be 1.41 TW/cm2, which represents the peak intensity of the incident laser in vacuum. The peak intensity reduces to 1.31 TW/cm2 inside the sapphire specimen due to the reflection loss from the specimen surface by a factor of 4n/(n + 1)2, with n being the refractive
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Hyunwoong Kim: 0000-0002-7253-5114 Seung-Woo Kim: 0000-0003-0235-1739 Author Contributions ‡
These authors equally contributed to this work.
Author Contributions
The project was planned and overseen by S.-W.K. Experiments were performed and analyzed by H.K., S.H., Y.W.K., and S.K. All authors contributed to the manuscript preparation. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Research Foundation of the Republic of Korea (NRF-2012R1A3A1050386).
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