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Abstract
Circularly polarized light in the vacuum ultraviolet (VUV) region is important for probing the structural and electronic properties of matter. Moreover, a circularly polarized VUV coherent light enables one to observe the dynamics of biomolecules and electron spins in solids. The development of a table-top technology to directly generate circularly polarized VUV coherent light is of great value, owing to the limitation of polarization control elements for the VUV region. However, solid-state nonlinear media for this purpose, which simplifies the setup, have not been presented. Here, we demonstrate a solid-based method for the direct generation of circularly polarized VUV coherent light using third-harmonic generation in a dielectric square lattice photonic crystal nanomembrane (PCN). We found that the waveguide resonance of PCN with fourfold rotational symmetry, irradiated by a circularly polarized fundamental beam, generates circularly polarized third harmonic at 157 nm with sufficient intensity for VUV spectroscopic applications. The presented results suggest the possibility that the PCN can be used as a practical nonlinear medium for circularly polarized coherent VUV generation.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
Circular dichroism (CD) spectroscopy, which is light absorption spectroscopy that measures the difference of absorption of right (RCP) and left circularly polarized (LCP) light, is a well-established spectroscopic technique to prove the chirality, magnetization, and electron spin states in substances [1,2]. Recent laser technology has enabled the production of coherent circularly polarized light in vacuum ultraviolet (VUV) and extreme ultraviolet regions through high harmonic generation (HHG) in gases using a table-top setup [3,4], and thus the application of these light sources to CD measurements has been demonstrated [5]. Such CD measurements in the VUV and extreme ultraviolet region can be applied in various fields, including life science and solid-stage physics. In the field of life sciences, CD measurement is a powerful tool for investigating the structural conformation of biomolecules [6]. In particular, VUV CD measurement [7] can probe many important biomolecules, for example, amino acids [8] and saccharides [9]. Currently, VUV CD measurements are mainly performed using incoherent synchrotron radiation [8,9]. However, if coherent VUV light sources can be used, the advantages of focusing the beam in a size of wavelength-order and generating an ultrashort pulse can be realized. Therefore, it can be applied to label-free CD imaging [10], real-time observation of ultrafast intramolecular dynamics [11–13], and other advanced measurement techniques in the VUV region that might enable visualizing molecular distributions and ultrafast dynamics, which currently cannot be observed.
In the field of solid-state physics, a source of coherent circularly polarized VUV radiation contributes to the advancement of angle-resolved photoelectron spectroscopy (ARPES) [14] because a high-energy VUV photon can reach a wide momentum space in the band structure [15]. Circularly polarized VUV pulses are sensitive to the spin and orbital angular momentum of electrons and enable the observation of the dynamics of excited electronic states [16,17]. This enables the probing of nonequilibrium dynamics of electrons in topological insulators and superconductors, in which electron spin plays an important role in the emergence of unexpected physical properties [18,19].
The practical application of coherent circularly polarized VUV light remains difficult owing to the lack of polarization control elements. Bulky reflective elements [20] or photoelastic modulators [8,9] are currently used; however, they are difficult to handle and enlarge the size of the setup. The circularly polarized HHG technique for gases, which has been developed in recent years [3,4], may be applicable to the VUV region; however, it requires the advanced polarization control of pump lasers. If a solid-state nonlinear medium can directly generate circularly polarized VUV light irradiated by circularly polarized fundamental pump light, the experimental setup can be significantly simplified. In addition, it is advantageous that polarization modulation in the VUV region can be performed only by the polarization modulation of the visible fundamental wave. Thus, it is necessary for the solid-state nonlinear medium to have an appropriate symmetry that can directly generate circularly polarized light. A probable solution for this requirement is to use nonlinear metamaterials, which are artificial nanostructures with sizes comparable to or smaller than the light wavelength, which allows control of the nonlinear optical response by appropriately designed shapes [21]. Especially, it has been demonstrated that in metallic nanostructures with rotational symmetry, the polarization selection rules that decide the relation of polarization states between fundamental and harmonic waves permit the generation of circularly polarized second and third harmonics (THs) for a circularly polarized fundamental beam [22]. This phenomenon was discovered in bulk nonlinear media [23] and recently demonstrated in metallic metamaterials [24,25]. However, the very low damage threshold of metallic nanostructures [26] severely restricts their use because the damage threshold of practical light sources determines the upper limit of intensity. Therefore, dielectric metamaterials [27], which have been recently used to produce coherent radiation at 197 nm (6.2 eV) [28] and 185 nm (6.7 eV) [29] using the effect of Mie resonance, may offer a feasible solution owing to the high damage threshold of dielectrics. However, the radiation intensity has been still insufficient for use in VUV spectroscopic applications, and circularly polarized VUV radiation has not been achieved.
Recently, it has been clarified that a freestanding dielectric thin film (nanomembrane) with a thickness smaller than the fundamental wavelength can generate linearly polarized third-harmonic (TH) VUV light with sufficient intensity for spectroscopic applications despite the nonphase-matching condition [30]. That is because, in addition to the high laser damage threshold of dielectrics, the submicrometer thickness of the nonlinear medium suppresses the effect of nonlinear propagation of the fundamental beam, and its peak electric field intensity can be considerably increased. Considering the relationship between symmetry and polarization selection rule [22], circularly polarized third-harmonic generation (THG) is forbidden by symmetry when the nanomembrane is unstructured (i.e., isotropic); however, it is allowed if the nanomembrane has artificial structures with a fourfold rotational symmetry, as described above. We determined that conventional square lattice photonic crystals possess the required structure and can be used to generate circularly polarized VUV light. However, it has not yet been clarified whether the direct circularly polarized light generation is possible by utilizing the rotational symmetry of the dielectric artificial structure with photonic crystal waveguide (WG) resonance, although such a phenomenon is known to occur because of Mie resonance in an isolated dielectric nanostructure with rotational symmetry [31,32]. In addition, it has not been clarified whether such structured nanomembranes are still capable of providing a sufficient VUV intensity for practical spectroscopic application such as CD measurements and ARPES; therefore, these points were addressed in this study.
Here, we propose and demonstrate a method of generating directly circularly polarized VUV coherent light via collinear THG in a photonic crystal nanomembrane (PCN) that is a dielectric nanomembrane with a square periodic lattice of circular holes and can give fourfold rotational symmetry. This approach is based on the THG polarization selection rule that states a circularly polarized fundamental beam produces a TH beam with opposite helicity under fourfold rotational symmetry [22]. In the field of metamaterials, this concept has hitherto been applied to rotational symmetry in a unit cell of a nanostructure, but we demonstrate that it is also applicable to rotational symmetry of the arrangement of isotropic unit structures in periodic hole-array dielectric nanostructures, i.e., photonic crystals. Furthermore, this shows for the first time that directly generating circularly polarized light in the VUV region from an artificial nanostructure is possible by using the PCN. The circularly polarized VUV radiation is observed at 157 nm (7.9 eV) with as adequate intensity of applying VUV light sources for the probe beams associated with ARPES and CD spectroscopy measurements. We have also confirmed that these results are consistent with the results of numerical simulations. Our results show that practical method for solid-state-based circularly polarized coherent VUV generation can be developed by using PCNs.
2. POLARIZATION SELECTION RULE UNDER FOURFOLD ROTATIONAL SYMMETRY
First, we explain the THG polarization selection rule under fourfold rotational symmetry, which plays an important role in this study. The angular momentum conservation law forbids harmonic generation in an isotropic medium under excitation by circularly polarized light [33]. However, this restriction is lifted when the circularly polarized light propagates along an ${N}$-fold rotational symmetry axis. In such a case, the circularly polarized fundamental wave can be converted into the countercircularly polarized ($N - 1$)th-order harmonic [22]. For example, an RCP TH wave can be generated when an LCP fundamental wave propagates along the fourfold rotation axis of a metamaterial [25]. Such a circular polarization selection rule has been considered for bulk solid crystals [23]; however, in recent years, even in the case of a metamaterial whose structure size is comparable to a wavelength, the same selection rule has been clarified by considering the relation between the symmetry of the structure and nonlinear response tensor [34], which represents the relation between the electric fields of the fundamental wave and harmonic wave in the far field [22,24].
In a medium with fourfold rotational symmetry, the circular components ${E}^{\pm}$(${3}\omega$) of the generated TH wave with the superscript ${+}\;(-)$ corresponding to LCP (RCP) light can be expressed in the far field in the following form (see Supplement 1, Section 1):
where $\alpha$ and $\beta$ are constants. If the fundamental beam is circularly polarized, only the second term on the right-hand side of Eq. (1) remains, thereby generating a countercircularly polarized TH wave. Therefore, it is expected that in a nanomembrane with a square periodic lattice of holes that has fourfold rotational symmetry, an RCP TH wave will be generated by an LCP fundamental beam at normal incidence and vice versa, as shown in Fig. 1(a).
Fig. 1. PCN and transmission spectra. (a) Scheme of the circularly polarized VUV THG using a PCN; (b) scheme of the $\gamma \text{-} {\text{Al}_2}{\text{O}_3}$ PCN; (c) optical microscope image of the PCN (length of scale bar = 100 µm); (d) scanning electron microscope image of the 600-nm period PCN (length of scale bar = 1 µm); (e) transmission spectra of the PCNs with 600 (red) and 500 nm (blue, shifted by ${-}{0.1}$ for clarity) periods. The transmittance spectrum of the unstructured nanomembrane is also shown (black). The orange dotted line indicates a wavelength of 470 nm. (f) Comparison between experimental (red) and calculated (blue) transmission spectra of the 600-nm period PCN; (g) simulated electric field intensity distribution inside the PCNs with 600 nm (left) and 500 nm (right) periods excited at a wavelength of 470 nm at normal incidence.
3. PCN SAMPLE
The PCNs were fabricated using a 48 nm-thick $\gamma \text{-} {\text{Al}_2}{\text{O}_3}$ thin film epitaxially grown on a 525 µm-thick Si (100) substrate using chemical vapor deposition [35] because epitaxial $\gamma \text{-} {\text{Al}_2}{\text{O}_3}$ nanomembranes can be manufactured by using a conventional method and high-efficiency THG in the VUV region was observed from them [30]. In the epitaxial $\gamma \text{-} {\text{Al}_2}{\text{O}_3}$ the crystal axis perpendicular to the substrate is ordered, but the in-plane crystal axis is randomly oriented, which typical domain size is about several tens of nanameters [36]. Therefore, the optical response at normal incidence is isotropic. A square lattice of circular holes (diameter = 190 nm) was fabricated using electron beam lithography and dry etching of the epitaxial $\gamma \text{-} {\text{Al}_2}{\text{O}_3}$ film. The Si substrate was removed using photolithography and reactive ion etching (see Supplement 1, Section 2 for more details of the sample preparation). The periods of the square lattice hole fabricated on PCNs were 500 and 600 nm. The thickness, diameter, and periods were determined so that the WG resonance wavelength of the photonic crystal was 470 nm with THG at 157 nm in the VUV region, as will be described later. A scheme of the PCN and optical and scanning electron microscope images of the samples are shown in Figs. 1(b)–1(d). Note that buckling, which is commonly observed in conventional nanomembranes such as ${\text{SiO}_2}$ and Si nanomembranes [37], was not observed in the epitaxial $\gamma \text{-} {\text{Al}_2}{\text{O}_3}$ nanomembrane, even after the PCN fabrication process. This is crucial for the optical response of the PCN because thickness inhomogeneity of the nanomembrane caused by wrinkles suppresses photonic crystal WG resonances.
Fig. 2. Polarization dependence of VUV THG from PCNs. Excitation polarization dependence of the THG spectra from (a) unstructured nanomembrane, (b) 500-nm period PCN, and (c) 600-nm period PCN: RCP (blue) and LCP (red) excitation; linearly polarized excitation (black). Circularly polarized components of VUV THG from the PCN excited by (d) RCP and (e) LCP beams. Orange (green) is the LCP (RCP) component of THG.
4. RESULTS
A. Transmittance Spectra of the PCNs
To clarify the resonance wavelength of the PCNs, we measured and simulated their transmittance spectra (see Supplement 1, Section 3). Figure 1(e) shows the transmittance spectra of the fabricated PCNs and an unstructured $\gamma \text{-} {\text{Al}_2}{\text{O}_3}$ nanomembrane at normal incidence. The observation of several dips in the PCN transmission spectrum indicates the occurrence of quasi-WG mode resonances [38] that can couple the incident light to the WG modes of the photonic crystal. The WG resonances of the PCN with the 500 nm period are blueshifted with respect to those of the PCN with the 600-nm period because the resonance wavelength is inversely proportional to the hole period [38]. Figure 1(f) shows a comparison between the experimental and simulation results. The WG resonance wavelengths obtained in the experiment shown in Fig. 1(e) were well reproduced by the numerical simulation performed with the commercially available software CST MW STUDIO 2019 (Dassault Systems) using the measured refractive index of epitaxial $\gamma \text{-} {\text{Al}_2}{\text{O}_3}$ (see Supplement 1, Fig. S1). Note that the observed WG resonances were broader, and the nonresonant transmittance was lower than those obtained in the numerical simulation. Such broadening may have been caused by fluctuations in the hole shape and the period, and the nonresonant transmittance may have been suppressed by scattering from the roughness caused by the etching process. Figure 1(g) shows the simulated electric field intensity distribution inside the PCNs with 600 nm (left) and 500 nm (right) periods irradiated at 470 nm. We can see that the electric field inside the 600-nm period PCN was strongly enhanced because of the effect of the WG resonance.
B. Measurement of Circularly Polarized VUV THG from the PCN
In the VUV THG experiment, we used an optical parametric amplifier with a pulse duration of 100 fs at a repetition rate of 1 kHz, pumped by a regeneratively amplified femtosecond Ti:Sapphire laser (see Supplement 1, Section 4). Figure 2 shows the VUV radiation spectra obtained when the unstructured nanomembrane and PCNs were irradiated with fundamental beams at 470 nm with linear and circular polarizations. As seen in Fig. 1(e) (indicated by the orange line) and Fig. 1(g), 470 nm corresponds to the WG resonance wavelength for the 600-nm period PCN and is off-resonant for the 500-nm period PCN. Figure 2(a) shows that in the unstructured nanomembrane, the THG signal centered at 157 nm is observed only for the linearly polarized fundamental beam [30] because THG is forbidden under circularly polarized excitation [34]. Additionally, the LCP and RCP fundamental beams do not produce the TH beam under the off-resonant excitation of the 500-nm period PCN, as shown in Fig. 2(b), although THG is allowed in terms of the symmetry. Conversely, in the 600-nm period PCN, VUV THG signals are observed for both linearly and circularly polarized fundamental beams, as shown in Fig. 2(c). This result indicates that in the vicinity of the WG resonance, the third-order nonlinearity of the PCN is enhanced and can produce a circularly polarized VUV radiation of measurable intensity (the microscopic mechanism is discussed later). Additionally, it is found that the intensities of the TH waves generated with the linear and circularly polarized fundamental beams are nearly the same.
Next, clarifying the polarization state of the THG form of the 600-nm PCN is necessary to prove that circularly polarized VUV coherent light is generated. Figures 2(d) and 2(e) show that for the RCP fundamental beam, the LCP component dominates the TH wave generated in the 600-nm period PCN and vice versa; that is, the helicity of the TH wave is opposite to that of the fundamental wave. The observed degree of circular polarization $(I(3\omega)_{\text{LCP}}-I(3\omega)_{\text{RCP}})/(I(3\omega)_{\text{LCP}})+(I(3\omega)_{\text{RCP}})$, where ${I}{({3}\omega)_{\text{LCP}}}$ and ${I}{({3}\omega)_{\text{RCP}}}$ are the intensities of the LCP and RCP components of the THG, is as high as 68%, which corresponds to an ellipticity angle of 0.37 rad. This ellipticity indicates that while it is designed with fourfold symmetry, the PCN lattice becomes rectangular with twofold rotational symmetry, thereby allowing both RCP and LCP THG [22] (see Supplement 1, Section 1). The numerical simulation discussed below confirms that even an insignificant difference in the periodicity of the holes along the vertical and horizontal directions introduced in the fabrication process may remarkably influence the THG polarization selection rules for the PCN.
C. Numerical Simulation of Circularly Polarized VUV THG from the PCN
To understand the microscopic origin of the observed phenomena, we performed numerical simulations of the electric field distribution inside the PCN at the fundamental beam frequency $\omega$. Because the electric field inside the PCN along the propagation direction is almost uniform, for simplicity, we calculated the complex amplitude of the electric field ${\boldsymbol E}\!$(${\boldsymbol r}$, $\omega$), where $r$ is the lateral coordinate in the PCN plane, in the central cross section of the PCN situated 24 nm from both surfaces. In addition, the longitudinal component of the electric field, which is perpendicular to the plane, is negligible in comparison with the transversal in-plane components because the former is approximately 2 orders of magnitude smaller than the latter. Here, the calculation was performed for the PCN with a period of 600 nm from which the circularly polarized THG was observed. Figures 3(a) and 3(b) show the intensity distributions in the 600-nm period PCN at 483 nm (620 THz) and 500 nm (600 THz). The former corresponds to the WG resonance, and the latter corresponds to off-resonance, as shown in the transmittance spectra (top graph) of Fig. 3(g). It is found that the in-plane intensity distribution has a fourfold rotational symmetry in both cases, but the electric field strength is greatly enhanced when the WG resonance is involved [Fig. 3(a)].
Fig. 3. Numerical simulation of VUV THG from the 600-nm period (PCN). (a)–(b) Electric field intensity distribution of the fundamental beam in the PCN; (c)–(d) local ellipticity distribution of the fundamental beam in the PCN. Contours correspond to ${-}{0.6}$ (black) and ${+}{0.6}$ (blue) rad. (e)–(f) Third-order nonlinear polarization intensity distribution in the PCN. (a), (c), and (e) are excited at 484 nm (620 THz), and (b), (d), and (f) are excited at 500 nm (600 THz). Because there is no medium in the hole of the photonic crystal, the magnitude of the third-order nonlinear polarization is set to zero there. (g) Calculated transmittance, THG intensity, and ellipticity angle; (h) dependence of the calculated THG intensity and ellipticity angle spectra on the anisotropy of the periodicity of holes in the PCN; (i) calculated spectra of LCP and RCP components of the THG when the period in the horizontal direction is 610 nm and the fundamental frequency is 617 THz (486 nm). The values of the linewidth were set to those obtained from the experimental results in Fig. 2(e).
The nonzero third-order nonlinear susceptibility of the isotropic $\gamma \text{-} {\text{Al}_2}{\text{O}_3}$ results in the generation of the nonlinear polarization ${\boldsymbol P}$(${\boldsymbol r}$, ${3}\omega$) at the frequency ${3}\omega$, which can be described by the following equation (see Supplement 1, Section 5):
In order to understand the relationship between the amplitude of the third-order nonlinear polarization and the polarization state of the local field, Eq. (2) is modified as follows (see Supplement 1, Section 5):
The distribution of ${\boldsymbol P}({\boldsymbol r},\;3\omega)$, which can be calculated at any frequency in the same way as Figs. 3(d) and 3(f), allows the complex amplitude of the TH wave ${{\boldsymbol E}_{\text{far}}}({3}\omega)$ in the far field to be obtained by adding up the nonlinear polarization over the unit cell, ${{\boldsymbol E}_{\text{far}}}({{\boldsymbol r},3\omega}) \propto \sum\nolimits_{\text{unit\,cell}} {{\boldsymbol P}({{\boldsymbol r},3\omega})}$. By using this equation, we numerically calculated the intensity and ellipticity angle spectra of the TH wave in the far field generated from the PCN with a 600-nm period, as shown in Fig. 3(g). For reference purposes, part of the transmittance spectrum in the vicinity of the WG resonance is also shown. It can be seen that the THG intensity dramatically increases at the WG resonance frequency of 620 THz, but THG intensity is almost zero at the frequency of the off-resonant. This is consistent with the observation that THG was observed by circularly polarized excitation only when excited at the WG resonance wavelength, as shown in Fig. 2(c). THG spectra for the LCP and RCP fundamental beams are identical, which is also consistent with the experimental result shown in Fig. 2(c).
Regarding the polarization state of THG, in Fig. 3(g), the value of the THG ellipticity angle is equal to ${-}\pi /{4}$ (corresponding to LCP) for RCP excitation or ${+}\pi /{4}$ (corresponding to RCP) for LCP excitation at any fundamental frequency. These results indicate that a circularly polarized THG whose helicity is always opposite to that of the fundamental circularly polarized wave generated with the PCN with fourfold rotational symmetry.
As described at the last paragraph of the previous subsection, the in-plane anisotropy of the PCN affects the THG polarization state. To evaluate it by simulation, we calculated the intensity and ellipticity angle of the TH beam when the period of the holes in the horizontal direction was varied, while that in the vertical direction was maintained at 600 nm. The graph in the lower half of Fig. 3(h) shows that the increment of the period results in a redshift of the center frequency of the VUV THG intensity spectra and, as shown in the graph in upper half of Fig. 3(h), a remarkable decrease in the ellipticity angle around the center frequency caused by the introduced in-plane anisotropy. The calculated THG spectra of the LCP and RCP components presented in Fig. 3(i) agree very well with the experimental results shown in Fig. 2(e). As indicated by the green line in Fig. 3(h), the ellipticity angle decreases to 0.36 rad even with a 10 nm (1.6%) change in the hole period. This result indicates that a few-percent in-plane anisotropy inevitable in the real nanofabrication process results in the experimentally observed ellipticity of the TH wave generated in the PCN under a circularly polarized fundamental beam.
D. Intensity of VUV THG Generated from the PCN
To consider application as a practical VUV coherent light source, estimating the VUV intensity that can be generated by the presented method is important. Figure 4 shows that the THG peak intensity is proportional to the cube of the fundamental beam power for both the PCN and the unstructured nanomembrane. The THG signal sharply decreases when the excitation beam power exceeds the damage thresholds, which are 5.1 mW (${0.53}\;{\text{J/cm}^2}$) for the unstructured nanomembrane and 2.6 mW (${0.27}\;{\text{J/cm}^2}$) for the PCN. It indicates that the damage threshold of the PCN is comparable to that of the unstructured nanomembrane. This is very different from the case of a metallic nanostructure, whose damage threshold is drastically decreased by approximately 2 orders of magnitude by fabricating the nanostructure [26]. In artificial nanostructures, optical breakdown is triggered by defects that are usually created in the fabrication process and concentrated in the vicinity of the etched-away surface of the dielectric or metallic nanostructures. Because the electric field is greatly enhanced at such surfaces in metal nanostructures due to surface plasmon resonance, such surface defects strongly contribute to the optical breakdown. However, in the dielectric PCN, the electric field enhancement occurs mainly inside the membrane, as shown in Figs. 1(g), 3(a), and 3(b), so the effect of surface defects on the damage threshold is smaller than that on the metallic nanostructure. This is considered to be a reason that the damage threshold of the PCN is comparable to the damage threshold of the unstructured nanomembrane.
Fig. 4. Dependence of the VUV THG intensity on the excitation power. The PCN (red) and the unstructured nanomembrane (blue) are excited by a 470 nm linearly polarized fundamental beam. The solid line indicates cubic dependency.
Figure 4 also shows that the maximum THG signal from the PCN (maximum THG peak count: 133, indicated by the red arrow) is approximately 10 times lower than that of the unstructured nanomembrane (maximum THG peak count: 1137, indicated by the blue arrow), and we previously demonstrated that the PCN can produce ${8.0} \times {{10}^5}\;\text{photons}/\text{pulse}$ [30]. Therefore, the maximum photon number generated from the PCN is approximately ${8.0} \times {{10}^4}\;\text{photons}/\text{pulse}$, that is, ${8.0} \times {{10}^7}\;\text{photons}/\text{s}$. Note that in this experiment, the noise level was approximately ${{10}^{- 2}}$ when the THG signal from PCN was maximum (see Supplement 1, Section 6). The relevance of this result to the applications of the proposed approach is discussed in the next section.
5. DISCUSSION
Here, the possibility of applying the PCN to VUV CD spectroscopy and ARPES is discussed. As mentioned above, we estimated that the number of photons that can be produced by the PCN is ${8.0} \times {{10}^7}\;\text{photons}/\text{s}$. In VUV CD measurements, the typical value of the ellipticity angle exhibited by biomolecules in the VUV region is approximately 10 mdeg [8,9], which corresponds to a difference in the number of LCP and RCP photons of approximately 0.1%, that is, ${{10}^{- 3}}$. Thus, the achieved photon flux of approximately ${{10}^8}\;\text{photons}/\text{s}$, which shot-noise limit is ${{10}^{- 4}}$, is adequate to observe the signals in VUV CD measurements. The observed degree of polarization (68%) of the VUV beam results in a decrease of the CD signal to 69%, compared to a the perfectly circularly polarized probe (see Supplement 1, Section 7), but this does not prevent the CD measurements.
For practical use, however, an increase in photon flux is most likely necessary. As previously mentioned, the noise level in our experimental system is on the order of ${{10}^{- 2}}$. Furthermore, ARPES systems typically require ${{10}^9}\;\text{photons}/\text{s}$ [39]. To overcome this problem, it is necessary to further increase the VUV intensity. A simple approach to increase the photon flux in our method is to increase the spot size at the focal point of the fundamental wave while keeping the fluence constant. In this case, the VUV intensity increases with the spot size. For example, if the beam diameter is increased 10-fold, the VUV intensity will increase 100-fold. The photon flux in this case reaches approximately ${1} \times {{10}^{10}}\;\text{photons}/\text{s}$, more than sufficient for ARPES. For VUV CD, the noise level is on the order of ${{10}^{- 4}}$, and the shot-noise limit is ${{10}^{- 5}}$, which are both smaller than the order of the VUV CD signal (${{10}^{- 3}}$). That is, the VUV CD measurement becomes possible in our system as well.
To increase the spot size 10 times while keeping the fluence constant, the average power of the fundamental beam must be increased 100-fold. As shown in Fig. 4, the damage threshold of the PCN observed in this experiment is approximately 2.5 mW; this 100-fold increase in the average power corresponds to approximately 250 mW. This average power is well achievable using current commercially available lasers. Note that, in the case of femtosecond laser excitation with kilohertz-order repetition rate, the damage threshold is determined by the fluence rather than average power [30]; thus, it should be possible to achieve 250-mW excitation without damage. The beam diameter used in this experiment is approximately 35 µm, as described in the Supplement 1, Section 4; thus, a 10-fold increase in the beam diameter corresponds to approximately 350 µm. The size of the PCN used in this experiment is ${300}\;\unicode{x00B5}\text{m} \times {300}\;\unicode{x00B5}\text{m}$, so it needs to be enlarged to accommodate a 350-µm beam spot. PCNs with such dimensions can be achieved without difficulty by redesigning the back-side-opening sample pattern.
An alternative approach to increasing the VUV intensity is to use ${\text{SiO}_2}$ instead of $\gamma \text{-} {\text{Al}_2}{\text{O}_3}$ as a THG generation material. We have found that ${\text{SiO}_2}$ nanomembranes have higher laser damage thresholds and generate maximum VUV photon flux an order of magnitude higher than that from a $\gamma \text{-} {\text{Al}_2}{\text{O}_3}$ nanomembrane [30]. We recently also fabricated wrinkle-free ${\text{SiO}_2}$ nanomembranes with a size of approximately ${700}\;\unicode{x00B5}\text{m} \times {700}\;\unicode{x00B5}\text{m}$ [40]. If a PCN can be fabricated from ${\text{SiO}_2}$, higher intensity circularly polarized VUV generation can be expected.
The presented approach allows generating circularly polarized VUV coherent light conveniently using a commercially available femtosecond laser system and the standard THG setup. In addition, by switching the helicity of the circularly polarized fundamental beam for each pulse by, for example, using a photoelastic modulator [41], we can obtain circularly polarized VUV pulses with alternating helicity for each pulse, which are suitable for VUV CD spectroscopy, CD pump–probe spectroscopy, and time-resolved CD ARPES. Furthermore, the presented method enables the generation of VUV light of any polarization state by controlling the polarization state of the fundamental beam [24].
In the experiment, we demonstrated the generation of coherent radiation at 157 nm, which is conventionally used in laser ARPES through frequency conversion in a ${\text{KBe}_2}{\text{BO}_3}{\text{F}_2}$ crystal [42]. Such an achievement makes the PCN a viable alternative to the expensive ${\text{KBe}_2}{\text{BO}_3}{\text{F}_2}$ crystal, which can be used in virtually any laboratory.
6. CONCLUSION
In conclusion, we demonstrated a method to generate circularly polarized VUV coherent light via THG in a square lattice PNC. We observed circularly polarized THG at 157 nm is allowed by exciting the WG resonance of the PCN with fourfold rotational symmetry; its validity is also confirmed by numerical calculation. The VUV THG intensity is sufficient for VUV spectroscopic applications; therefore, it can be applicable for VUV CD measurement and time-resolved CD ARPES.
The wavelength of the VUV THG can be tuned according to the application by controlling the PCN period because the wavelength of the WG resonance is determined by it. Further shortening of the generated wavelength, where photoelastic modulators do not operate, can be possible if the HHG from the PCNs is realized. This is considered to be feasible because circularly polarized HHG from a crystal with rotational symmetry [43] and HHG in the extreme UV region from a nanomembrane [44] have been demonstrated. Artificial structures with a given rotational symmetry can thus be expected to enable control of the circular polarization in the HHG process.
Lastly, we comment on the general availability of the microfabrication process, which may be the technically demanding aspect of this work. In recent years, the rise of open platforms for nanofabrication is a worldwide trend, and it allows researchers (even in physics and optics) to access such microfabrication facilities [45]. In addition, because the process conditions have been clarified in this study, it should be possible to replicate such results without further trial and error. Therefore, we believe that the presented PCN should be available with reasonable effort for most researchers.
Dielectric nanomembranes have also recently attracted attention as tools for high-order harmonic generation [44] and electronic pulse control [46]. Therefore, the applications of the PCN are not limited to wavelength conversion, and PCNs may become a new platform for ultrafast light control devices.
Funding
Precursory Research for Embryonic Science and Technology (JPMJPR18G6); Japan Society for the Promotion of Science; KAKENHI (18H01147); Ministry of Education, Culture, Sports, Science and Technology; Nanotechnology Platform (JPMXP09A16UT0162, JPMXP09F19UT0013); Photon Frontier Network Program, Q-LEAP (JPMXS0118067246); Center of Innovation Program.
Acknowledgment
We thank Y. Svirko, H. Sakurai, Y. Arashida, D. Hirano, T. Ikemachi, and N. Kanda for helpful discussions. Additionally, we thank E. Lebrasseur, M. Fujiwara, and A. Mizushima for their support in fabricating the device. Fabrication of the samples was performed using the apparatus at the VLSI Design and Education Center (VDEC, currently d.lab) of the University of Tokyo.
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
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