Main

In the past century, the range of useful wavelengths of coherent radiation was greatly extended from the infrared, visible and ultraviolet to the extreme ultraviolet (EUV), soft- and hard X-rays. Although in the optical range it is possible to effectively manipulate the spectral, temporal or spatial content of light using various passive (lenses, mirrors, diffraction gratings) and active (acousto- and electro-optic modulators, spatial light modulators (SLMs) and so on) elements, this becomes a challenging task for high-energy photon beams. Several approaches can be used to produce EUV and X-ray diffraction gratings, such as lithographic etching of thin-film transmission gratings1, or designing special multilayer blazed gratings2. However, the working spectral range of these devices is usually relatively narrow and their manufacturing is a technologically complicated task due to the need for precise control over the etching process.

Temporal modulation of the X-ray beam is usually performed by mechanically moving one or more optical elements in the beam path. Such an approach is cumbersome, has limited speed and precision, and is not always possible due to geometrical constraints. A miniature microelectromechanical system (MEMS) was presented recently, exhibiting a 350 MHz modulation frequency3. However, there are complications with the proposed device: its working frequency has to be matched to the repetition rate of the light source and it requires a beam with a small footprint, which might limit the total photon throughput. A new proof-of-principle device based on the phase-change material Ge2Sb2Te5 was proposed for a reflective SLM in the X-ray spectral range4. Although demonstrating a fast 'writing' speed and high stability, this device suffers from a rather large feature size, limited by the heat propagation effects and the thermal nature of the switching process.

Here we demonstrate a novel approach that can be used as a reflective SLM for the EUV or soft X-ray beams; this approach features ultrafast switching time and a sub-90-nm feature size. For the proof-of-principle demonstration, we use two crossed coherent EUV beams (write beams) to imprint a metastable periodic structure into the electronically ordered quantum material 1T-TaS2, in which the lifetime of the electronic state is controllable5 (Fig. 1a). This results in a diffraction grating, which efficiently deflects the short wavelength photons.

Fig. 1: Scheme of the experiment and properties of 1T-TaS2.
figure 1

a, The optical layout showing the EUV write beams (pumps 1 and 2) and the probe beam. CCD, charge-coupled device. b, The crystal structure of 1T-TaS2. c, A schematic representation of the electronic ordering in the thermodynamic commensurate (C) and nearly commensurate (NC) CDW states, and the photoinduced states H and A. d, The lattice expansion along the c-axis (after Sezermann et al.22) for cooling (blue) and heating (orange) cycles. e, An energy-level diagram showing the pump and probe transitions. The assignments are from Ettema and colleagues23.

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Transient gratings, which are formed by the interference of non-collinear pulsed visible or infrared laser beams interacting within a material, are commonly used to investigate carrier diffusion and lifetimes6,7,8, heat propagation effects9,10, acoustic waves11,12, phonon polaritons13,14, and electron-, vortex-15 and spin-dynamics16,17,18 in a wide range of materials. The EUV transient grating approach was recently demonstrated at the Fermi free electron laser (FEL) source19,20,21. Such gratings are transient as they are limited by the non-equilibrium lifetime of the intrinsic excitations created in the material by the laser pulses. Typically heat dissipation, carrier diffusion or the charge-carrier recombination processes limit the grating lifetime to short timescales, usually not exceeding the nanosecond range. This can be overcome by the use of a metastable electronic state in 1T-TaS2 with a tunable lifetime (from microseconds at 150 K to exceeding typical laboratory scales below 70 K; see ref. 5).

This material is a layered Van der Waals system (Fig. 1b) that exhibits a series of electronic ordering transitions and exotic metastable states in response to exposure to light. Under quasi-static thermodynamic conditions, the high-temperature metallic state develops an incommensurate charge density wave (CDW) at 550 K, which transforms to a unique 'nearly commensurate' state at 350 K that persists down to 180 K on cooling, whereupon it undergoes a first-order transition to a commensurate CDW. The nearly commensurate state is best thought of as a regular patchwork of commensurate domains separated by domain walls (Fig. 1c). A substantial change in lattice constants is associated with the nearly commensurate–commensurate transition22, namely, the out-of-plane expansion is particularly large and hysteretic (Fig. 1d).

Optical excitation of the commensurate state results in the formation of either a metastable chiral domain (H) state23 or an amorphous (A) Wigner glass state24, depending on the excitation parameters25 (Fig. 1c). The lifetime of the ‘hidden’ H state, which is superficially similar to a supercooled nearly commensurate order, can be conveniently controlled by temperature and strain5. The A state is more thermally robust than the H state and seems to exist on typical laboratory timescales up to at least 200 K (ref. 24).

In this work we show that the excitation of 1T-TaS2 with two crossed EUV beams at low temperatures creates a metastable diffraction grating that deflects EUV light with remarkable efficiency. We also demonstrate that the imprinted structure can be erased with a single EUV beam, resulting in a programmable modulator for coherent EUV radiation. The extraordinarily high diffraction efficiency of the device is caused by the lattice contraction in an out-of-plane direction associated with the electronic phase transition.

Results and discussion

We study the device operation in a typical transient grating experimental configuration, focusing on the evolution of the electronic order in 1T-TaS2 at two temperatures. First, we perform measurements at room temperature, where the ground state of the sample is a nearly commensurate CDW and no long-lived metastable state is expected. We observe a typical transient grating response on the picosecond timescale (Fig. 2a), which is driven by the nearly resonant pump with a photon energy of 31.1 eV, and probed away from any atomic transitions by 93.3 eV photons in backward diffraction geometry (Fig. 1a). The transient grating period was set to 87 nm. Typically for EUV, the signal consists of an exponential background with superimposed oscillations that originate from periodic modulation of lattice temperature26. This is also confirmed by the rise time of the signal (5.2 ± 1 ps), which matches with the electron-lattice thermalization time27. The relaxation rate, on the other hand, is given by the heat diffusion time in the system. The slower oscillation corresponds to the surface acoustic wave, with a frequency close to the transverse acoustic phonon (Fig. 2c), whereas the faster oscillation might be attributed to the surface skimming longitudinal wave with a frequency close to the longitudinal acoustic phonon. The transient grating signal almost completely disappears after 200 ps, signifying the thermal equilibration between the bright and dark grating fringes. The disappearance of the diffracted signal, however, does not necessarily mean the complete relaxation of the system to the ground (nearly commensurate) state. Earlier all-optical studies27 have revealed that at high excitation fluences the lattice might momentarily reach the incommensurate–nearly commensurate transition temperature, so it is plausible that the whole probed area of the sample is thermally converted into the high-temperature incommensurate state, which then relaxes back to the nearly commensurate state on a much longer timescale, once the heat is transported away. It is worth noting that due to non-resonant probe photon energy, we do not directly observe sub-picosecond change of electronic order28. By contrast, in all-optical transient grating experiment, the fast electronic component is about ten-times stronger than the slower lattice response (cyan trace in Fig. 2a).

Fig. 2: EUV transient grating measured at room temperature.
figure 2

a, The intensity of the probe beam diffracted from the EUV transient grating (TG) created by the write beams. The solid black line is the fit, the dashed lines are the separate components of the fit, and the solid blue line represents the optical pump–probe transient grating experiment. b, The footprint of the diffracted probe beam on the CCD detector. c, The acoustic phonon velocities deduced from the grating period and oscillation frequency are indicated by the lines. The data points are the longitudinal acoustic (LA) and transverse acoustic (TA) phonon frequencies from neutron scattering data40.

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We next perform a similar experiment at 100 K, in which the ground state of 1T-TaS2 is a commensurate CDW. At this temperature, the pulsed photoexcitation is known to create various metastable orders. Already after the first exposure to the crossed pump beams, a strong scattering appears on the detector at the wavevector of the transient grating. Remarkably, the scattering intensity was still present and almost constant even after the pump beams are blocked, revealing permanent imprinting of the periodic structure (Fig. 3), which does not relax for at least 750 s. After 750 s, the sample was excited by one of the EUV pump beams, which does not create an interference pattern in this case, but rather plays a role of a heating pulse. We show in Fig. 3b that this 'erases' the diffraction grating in 48 ± 3 s (exponential fit). After blocking the pump beam and allowing the sample to cool down, the whole process of semi-permanent switching can be repeated on the same spot of the sample, confirming that no degradation of the surface occurred.

Fig. 3: EUV diffraction observed at low temperature.
figure 3

a, A schematic diagram of the sample dilation along the c-axis caused by writing a grating onto the sample and the metastable periodic C/H structure. b, The intensity of the diffracted probe beam on the CCD as a function of time, with the timings of the write and erase pulses indicated above. c, The diffracted streaks recorded on the CCD at the numbered data points in b: (1) initial state; (2) immediately after switching (3); 750 s after switching; and (4) after erasing the grating with a single EUV beam.

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We attribute the strong scattering signal with a long lifetime to a photoinduced phase transition to a metastable hidden electronic order23,24,27 (Fig. 3a): while the bright illuminated stripes in the EUV grating are converted to the photoinduced state, the dark areas stay in the ground state. The diffraction efficiency of the imprinted structure is at least one order of magnitude higher than the transient grating at 300 K. Such a stabilized structure would not be possible in the event of a thermal phase transition, in which case the temperature of the bright and dark stripes would equilibrate on a sub-nanosecond timescale and thus the whole sample would end up in a single phase, either a nearly commensurate or commensurate CDW depending on the final lattice temperature. The existence of a photoinduced hidden state is therefore essential for such a long-lived effect to occur. Although we do not have direct information on the type of the final state from the current data, judging from the high stability of the structure at 100 K, it is plausible that the A phase, or a mixture of the A and H states, is reached.

We note that the EUV light used in this work is very different from the traditional optical or electrical excitations; thus, it might not be possible to define the type of the photoinduced state solely on the basis of existing excitation fluence values, and systematic study of the switching efficiencies at different wavelengths is required to elucidate the phenomenon. In our experiment, the fluence in the bright fringes of the crossed pump beams reached 15.2 mJ cm–2, which is much higher than the excitation fluences used in earlier optical switching experiments and—together with shorter absorption length of resonant EUV light—corresponds to ~30-times-higher energy density absorbed in the sample. On the other hand, the density of absorbed photons is comparable in the present case and earlier optical data.

Similarly to the room-temperature case, the diffraction signal at 100 K mainly originates from the periodic deformation of the lattice. The rather inhomogeneous shape of the diffracted signal observed in such a metastable configuration (Fig. 3c) can be attributed to a non-uniform heating and strain in partially cracked or detached flakes on the sample surface, which affects the stability of the photoinduced state29 and causes its partial relaxation.

Two pathways for thermal erasing of the semi-permanent periodic structure with a single pump beam can be envisaged. First, if the fluence of the pump beam is above the switching threshold, then each individual pulse causes the whole sample to be converted into the photoinduced state. This would cause immediate disappearance of the diffracted signal. At later time, due to excessive direct current heating from the long pulse train, the sample might recover to the ground state. Second, if the fluence of the single pump beam is below the switching threshold, then the direct current heating of the sample is the only necessary process to be considered. The erasing time would depend on the heat load and the resulting sample temperature5.

As the diffraction intensity drops with a relatively long time constant (48 ± 3 s) in our experiment with a 3.8 mJ cm–2 pump, we conclude that the second scenario is operative.

To understand the unexpectedly high diffraction efficiency of the metastable structure, we have to consider the evolution of the crystalline lattice, which accompanies the electronic phase transition. The commensurate state is characterized by the unique ordering of the CDWs in the neighbouring layers which, among others, causes a ~0.5% change of the out-of-plane lattice constant when cooling from the nearly commensurate state (Fig. 1d). As the photoinduced states are characterized by nearly commensurate-like stacking30,31,32, a jump of a similar magnitude can be expected also in the present case resulting in a real-space electronic and lattice modulation. This can be considered as a nearly sinusoidal reflective diffraction grating (Fig. 3a). Its efficiency can be estimated from33:

$$\eta =\frac{{I}_{\rm{d}}}{{I}_{0}}=R{J}_{1}^{2}\left\{\frac{a}{2}\right\},$$

where \({I}_{\rm{d}}\) and \({I}_{0}\) are diffracted and incident intensities, respectively, \(R\) is the reflectivity of the material, \(a\) is the peak-to-peak excursion of the phase, and \({J}_{1}\) is Bessel function of the first kind. In paraxial approximation \(a=\frac{4\uppi h}{\lambda }\), where \(h\) is the height of the surface modulation and λ is the photon wavelength. The resulting diffraction efficiency for 13.3 nm photons in our experimental geometry is \({\eta }_{\rm{calc}}={10}^{-7}\), which matches well the experimentally measured value of \({\eta }_{\exp }={9.5\times 10}^{-8}\). Here, tabulated optical constants34 were used for calculating the reflectivity of the sample and the thickness of the switched layer. Importantly, according to this simple modelling, by tuning the experimental geometry and impinging the laser beams at an oblique angle, it should be possible to enhance the efficiency of the grating by more than two orders of magnitude. The angular dependence of the diffraction efficiency for different photon energies is plotted in Fig. 4a. For shorter values of λ and at large incidence angles, the efficiency can be enhanced further, and for λ = 0.5 nm, the calculated value reaches \({\eta }_{\rm{calc}}=0.1 \%\). It is also worth noting that unlike the polished optical elements, the proposed device can be produced with an atomically flat surface owing to the layered structure of 1T-TaS2.

Fig. 4: Modelling the efficiency of a sinusoidal grating.
figure 4

a, Calculated diffraction efficiency of the sinusoidal grating as a function of the angle of incidence for different wavelengths in the 0.5–30 nm range. The bold red line represents the modelling for the probe wavelength (λ = 13.3 nm) used in the experiment, whereas the white star indicates the experimentally measured value. b, Calculated diffraction efficiency of the sinusoidal grating as a function of the angle of incidence for fixed wavelength (λ = 0.5 nm) and different modulation amplitudes in the 0.01–0.5 nm range.

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Here we estimate the amplitude of the grating to reach h = 0.1 nm, which is much larger than previously reported values for EUV transient grating35. This parameter is responsible for the high diffraction efficiency of the structure and is defined by the relative change of the unit cell at the phase transition and the attenuation length of the pump photons in the sample. By switching a thicker layer of the sample, it should be possible to reach \({\eta }_{\rm{calc}} > 1 \%\) (Fig. 4b) and thus approach the efficiencies of the state-of-the-art multilayer etched gratings (~5%)1. In general, it might be beneficial to use shorter wavelength photons due to their longer absorption length; however, further investigation into the switching process at different atomic resonances and with non-resonant excitation is required to optimize the wavelength. By optimizing the experimental conditions and fine-tuning the balance between thermal and non-thermal effects, it might be also possible to change the duty cycle and spatial profile of the imprinted structure, which can help to redistribute the intensity between different diffraction orders. We expect that the feature size of the grating can be further decreased approaching the intrinsic domain size in the hidden state (10–20 nm). The phase transition was already successfully triggered in a 60 nm device by current injection36.

Although we used bulk exfoliated crystals in this work, which is not a technologically scalable solution, recent developments in chemical vapour deposition37,38 molecular beam epitaxy39 growth of thin 1T-TaS2 might provide the prospects for industrial manufacturing of high-quality and large-area devices based on thin films.

Conclusion

We have created a programmable EUV and soft X-ray spatial light modulator in which the periodic structure can be written and erased on demand using short laser pulses. The unexpectedly large amplitude of the surface modulation arises from the large out-of-plane lattice contraction concurrent with the photoinduced phase transition. The stability of the structure is directly related to the long lifetime of the photoinduced hidden charge-ordered states in the material. The formation of the grating is not inherently limited to the present combination of wavelengths. An extension to other wavelengths would result in a wavelength-tunable and programmable grating for EUV and soft X-ray radiation.

Beyond the laser imprinting, which requires two crossed coherent EUV beams for 'writing the structure, a hybrid electro-optical device could be envisaged. In this case, the textured electronic structure could be created by current injection using an array of electrodes in a manner very similar to liquid-crystal-based SLMs. The presented tunable device can be also used as an intensity and spectral monitor, dispersing a small portion of the beam onto the reference detector. By varying the properties of the imprinted grating, it would be possible to tune the usable spectral range and/or the spectral resolution of a spectrometer without the need to replace or mechanically move any component of the system, adding much more flexibility in EUV and soft X-ray optical layouts.

Methods

Materials

The single-crystalline 1T-TaS2 samples were grown using the chemical vapour transport method from elemental tantalum and sulfur, with iodine as a transport agent27. The bulk crystals were exfoliated by the scotch tape technique and immediately inserted into the vacuum chamber to avoid oxidation. X-ray diffraction confirmed the high quality of the samples. Direct current transport measurements were performed for the initial characterization of the samples.

EUV transient grating experimental set-up

The experimental set-up is shown schematically in Fig. 1a. The transient grating experiments were performed at the EIS-TIMER beamline at the FERMI FEL facility (Triste) in backward diffraction geometry; ~50 fs EUV pulses from the FEL source were split by the wavefront division beam splitters into two pump beams and one probe beam. After spectral filtering, the beams were overlapped and focused on the sample, which was mounted on a cold finger cryostat. The angle between the two pump beams was set to 27.6°, resulting in an interference pattern on the sample surface with a period of 87 nm, taking into account the pump wavelength \({\lambda }_{\rm{pump}}\) = 39.9 nm. The state of the sample was then monitored as a function of the time delay between the pumps and the probe in a stroboscopic manner, by recording the intensity of diffracted probe beam (\({\lambda }_{\rm{probe}}\) = 13.3 nm) with the charge-coupled device camera. For studying metastable structures at low temperatures, the sample was excited by a train of ~50 pump pulses once (corresponding to 1 s illumination time), and then the slow dynamics was monitored in real time by repeatedly exposing the sample to the probe beam only. The incident fluence on the sample was 3.5 mJ cm–2 for the probe beam and 3.8 mJ cm–2 for each of the pump beams.

An energy-level diagram showing the pumping and probing transitions is illustrated in Fig. 1e. The pump photon energy \({\hslash \omega }_{\rm{pump}}\) = 31.1 eV is close to several electronic transitions in 1T-TaS2 (ref. 41) from initial states of tantalum, whose binding energies are 34.7 (2) eV (\({\rm{O}}_{3}\,\text{edge}\, 5{p}_{3/2}\)), 25.5 (1.7) eV \(({\rm{N}}_{6}\,\text{edge} \, 4{f}_{5/2})\) and 23.6 (1.2) eV \(({\rm{N}}_{7}\,\text{edge} \, 4{f}_{7/2})\) to tantalum \(5{d}_{{xy}}\), \(5{d}_{3{z}^{2}-1}\) final states (with bandwidth ≈ 2 eV) near the Fermi level; the full-width at half-maximum (in electron volts) are indicated in brackets. The probe wavelength \({\hslash \omega }_{\rm{probe}}\) = 93.3 eV is non-resonant and has at least a three-times-longer absorption length, which ensures that it does not disturb the grating despite the relatively high incident fluence used in the experiment.

The experiments were performed at room temperature (in the nearly commensurate state) and 100 K (in the commensurate ground state).

Fitting procedure

The room-temperature data was fitted as a superposition of exponential background and two damped oscillators:

$$\begin{array}{l}{I}_{{\rm{TG}}}\left(t\right)={I}_{0}{\rm{H}}\left(t\right)\left(1-{{\rm{e}}}^{t/{\tau }_{0}}\right)\left[{I}_{1}{{\rm{e}}}^{t/{\tau }_{1}}\sin \left({\omega }_{1}t+{\varphi }_{1}\right)\right.\\\left.\qquad\qquad+\,{I}_{2}{{\rm{e}}}^{t/{\tau }_{2}}\sin \left({\omega }_{2}t+{\varphi }_{2}\right)+{I}_{3}{{\rm{e}}}^{t/{\tau }_{3}}\,\right]\end{array}$$

where \({I}_{n}\) are amplitudes of individual components, \({\omega }_{\mathrm{1,2}}\), \({\varphi }_{\mathrm{1,2}}\), \({\tau }_{\mathrm{1,2}}\) are the frequencies, phases and damping constants of the oscillators. respectively, and \({\tau }_{3}\) is the relaxation time of the exponential background. Additional exponent with the characteristic time \({\tau }_{0}\) was used to account for the rise time of the signal. As the FEL pulse length is much shorter than the relevant timescales, we assumed instantaneous excitation, which was modelled by a Heaviside function \({\rm{H}}\left(t\right)\).