Here, "X-rays" generally refer to soft and hard X-rays. A beamline collects, focuses, bends, and monochromates synchrotron radiation from the bending magnets or insertion devices, delivering radiation of suitable wavelengths to the experimental space where samples are located. In an X-ray beamline, we need to form images and focus the extreme ultraviolet or hard X-rays. So, we require optical systems significantly different from those used in the visible range. For X-rays, lenses similar to those in visible light cannot be used. Also, since the normal incidence reflectivity of mirrors is very low, total reflection or special optical systems are needed. Here, optical components for X-ray beamlines will be introduced, including mirrors, lens systems, X-ray windows, multilayers, and phase plates.
Refraction and Total Reflection of X-rays
One significant difference between X-ray and visible light optics is the significantly different refractive index. Generally, the refractive index is a function of wavelength. Figure 20 shows how the refractive index changes according to wavelength. There is a significant variation across the infrared, visible, ultraviolet, and X-ray regions, with particularly rapid changes in the resonant energy values in the near-infrared, near-ultraviolet, and X-ray regions. The refractive index of visible light is greater than 1, whereas in the vacuum ultraviolet and X-ray regions, it is very >203_word_end< to 1 but slightly less than 1, except near atomic resonance. Total reflection is the most efficient reflection regardless of the polarization of the incident X-rays.
Fig. 20. Changes in the refractive index in the infrared, visible light, ultraviolet, and X-ray regions.
Mirrors
The reflectivity of X-rays incident on a reflecting mirror at a large grazing angle (θ≫0) is almost zero, so total reflection should be used to achieve the desired effect in the X-ray region. When the grazing critical angle becomes too small, many inconveniences arise. First, alignment becomes difficult, and a very long mirror should be used to capture a large amount of incident X-rays. On the other hand, utilizing the fact that radiation below a particular wavelength hardly reflects at grazing angles above the critical angle, mirrors are sometimes used to filter out short-wavelength X-rays.
X-ray Multilayer Mirrors
One more notable optical component among soft and hard X-ray optical components is the efficient normal-incidence multilayer mirror. This mirror can reflect X-rays that are incident at right angles and acts as a soft X-ray lens with excellent resolution. It can be used in optical systems requiring extreme precision, such as holography or interferometry in the soft X-ray region. The multilayer plate is composed of multiple thin films, and each layer is a uniform surface substrate alternately coated with materials that either absorb X-rays well (e.g., high atomic number materials such as tungsten) or absorb X-rays less (e.g., low atomic number materials such as carbon or silicon). Examples include W/Si, W/B4C, Mo/Si, and Mo/B4C.
As multilayer thin films can be applied to both flat and curved surfaces, they are used as normal incidence lenses. They require highly smooth substrate surfaces with low roughness. Since they need to maintain the desired film thickness and very smooth interfaces, their fabrication requires high precision. >615_word_end< radiation is often linearly polarized. Therefore, mirrors should be used carefully in relation to synchrotron radiation because mirrors can alter polarization and polarization may reduce reflectivity. Generally, the electric field polarized parallel to the plane made by the incident and reflected rays is called π-polarization, while the one perpendicular to this plane is called σ-polarization. σ-polarization has less reflection loss and maintains a better degree of polarization than π-polarization.
As mentioned earlier, synchrotron radiation is often linearly polarized parallel to the electron orbit plane. Therefore, the axis of the mirror (perpendicular to the mirror surface) should be positioned to point in the perpendicular direction to the orbit plane. The shorter the wavelength, the higher the precision required for the optical components used. The quality of the X-ray mirror surface, i.e., flatness, curvature precision, and roughness, must be significantly better than that used for VUV with longer wavelengths. Materials suitable for such precision, such as glass, silicon, silica, and silicon carbide, are commonly used as substrates with appropriate coatings on. Like other optical components used in synchrotron radiation, mirrors also receive significant thermal loads from exposure to intense synchrotron radiation. If a precision mirror is even slightly distorted by heat, it will cause issues. Special attention is needed for the thermal load problems with high-brightness synchrotron radiation. A cooling system is needed to disperse and remove the generated heat, and the mirrors at the front end, in particular, need a very efficient cooling system because they bear the most thermal load.
X-ray Lens System
In synchrotron radiation experiments, focusing the X-rays onto the sample as small as possible is often necessary. In spectroscopy, diffraction, and imaging experiments, the beam must be focused down to microns or even smaller. For this purpose, methods utilizing mirrors, as discussed in the previous section, are available, and newly developed X-ray lenses can also be used.
Kirkpatrick-Baez Mirror
A Kirkpatrick–Baez mirror, or simply KB mirror, focuses X-ray beams by reflecting them at grazing incidence off a curved surface, usually coated with a layer of a heavy metal.
Fig. 21. K-B Mirror (source: DOI: 10.1021/ac035037r )
Schwarzschild Mirror
Using the multilayer mirrors described above, it is possible to form an X-ray normal incidence lens with high spatial resolution. It is called a Schwarzschild mirror. This lens consists of two precision-grade multilayer mirrors, one convex and one concave, coated with multiple layers. It is utilized as a lens in the soft X-ray range for applications such as X-ray microscopy and lithography.
Fig. 22. Schwarzschild mirror (source: DOI:10.5203/THESIS_FINDLAY_1 )
Fresnel Diffraction Zone Plate
This is also an X-ray lens that is capable of normal incidence and has excellent spatial resolution. It is highly regarded as one of the important X-ray optical components. As shown in Fig. 23 (a), the Fresnel zone plate consists of multiple concentric rings, where transparent and opaque rings to soft X-rays are alternating. It is made by forming thin concentric rings of heavy metals like gold (Au) on a thin film (thickness 1000Å) of materials like Si or SiN, which are highly transparent to soft X-rays. The soft X-rays that pass through the transparent rings are focused at a focal point due to diffraction. The Fresnel diffraction zone plate is widely used in X-ray microscopes. Since this lens is very small (with a diameter of about 0.2 mm), it can be damaged by excessively strong radiation and is also at risk of being easily lost, requiring special care in handling.
Bragg-Fresnel Lens: B-F Lens
The Bragg-Fresnel lens is designed for hard X-rays. Unlike the Fresnel diffraction zone plate described above, which focuses incoming X-rays by transmitting them through the zone plate, the B-F lens focuses the Bragg reflected beam. This lens consists of a series of linear or concentric regular grooves of constant depth etched or patterned by lithography using electrons or ions on a single crystal silicon or germanium wafer so that the groove bottoms and the high part strips alternately appear. Figure 23 (b), (c) shows figures of B-F lenses, respectively. X-ray beams incident on a single crystal Si (or Ge) wafer at certain angles are enhanced and mirror-reflected by diffraction at the wavelengths that satisfy the Bragg condition at the high part stripes.
Additionally, the groove depth was adjusted during production so that the Bragg reflection at the groove bottoms is amplitude-enhanced at the focus point of the high part stripes at the same wavelength. The groove depth is typically around 1 to 3 μm. The B-F lens has both focusing and monochromatization functions. By changing the incidence angle, the wavelength can be varied. So, the linear B-F lens can be used in a wide hard X-ray range of 6-100 keV. The linear B-F lens provides line focus. For point focus, the B-F lens made by arranging the K-B mirrors mentioned above or a cylindrical curved version is used. The circular B-F lens can be used for large angle incidence and achieve point focusing below 1 micron. In this case, too, the outermost strip width of the zone plate determines the resolution width. It can focus monochromatic X-ray beams to sizes of a few microns or less, making it useful for micro-diffraction or micro-probe experiments requiring large photon bunches.
Fig. 23. Frenel Zone Plate and on & off axis B-F lenses (source: DOI: 10.1063/1.1149082 )
X-ray Compound Refractive Lens
The lens systems examined above use mirror total reflection or diffraction. However, recently, a new focusing technique using refraction has been developed and is already used as a lens for hard X-rays. This lens, mainly used for hard X-ray beams with small divergence from undulators, has a very simple structure and is less sensitive to surface roughness and thermal load than mirrors. The refractive index (1-) for X-rays is extremely >203_word_end< to 1 but slightly less than 1, by around 10^-6. Since the refractive index is less than 1, the X-ray focusing lens should be concave, unlike convex lenses for focusing visible light. To prevent loss due to absorption when X-rays pass through the lens, materials with low atomic numbers are used, including Be, B, Mg, and Al. These materials can withstand severe thermal loads. However, a single concave lens does not provide sufficient refraction to achieve the desired focal length, so a compound lens consisting of multiple concave lenses is used.
Fig. 24. Schematic figure of X-ray Compound Refractive Lens
Windows and Filters
An X-ray window exists between the front end and the X-ray beamline to isolate the two parts because the vacuum level of the storage ring is 10^(-10) torr (during operation), whereas it is 10^(-7) torr in the X-ray beamline. Gases such as helium (He) show a relatively high transmittance at wavelengths longer than the absorption edge of 539Å (23eV). However, diatomic gases such as nitrogen or oxygen (or air) do not transmit vacuum ultraviolet below 2000Å. Therefore, the window serves to isolate both sides to send vacuum ultraviolet, soft, and hard X-rays into spaces filled with atmospheric pressure or gas. Materials for the window should have low absorption at the wavelengths intended for transmission. In the VUV range below 2000Å and approximately up to 1200Å, crystals like LiF, Mg2F, and CaF2 can be chosen.
On the other hand, for wavelengths below 1000Å, very thin metal films, such as 1000Å thick films of aluminum or germanium, can be good windows. However, such thin films are easily damaged and cannot be used as is, so they are installed behind narrow slits or small holes, or coated on fine mesh screens.
Aluminum (Al) can be used as a window in the range between 700Å and 170Å (L-absorption edge) (17.7eV～73eV), and carbon thin films can be used up to the K absorption edge of 43.6Å (284eV). Thin films of Be and Al are the most commonly used materials for short-wavelength windows. >869_word_end
X-ray Phase Plate
The polarization of synchrotron radiation is one of its essential characteristics for various applications. To obtain linear or elliptical polarization from the bending magnet radiations, appropriate measures are necessary. In the case of insertion devices, special designs of undulators or wigglers are required. However, there are times when it is necessary to adjust the polarization direction as needed, similar to optical experiments with visible lasers. For such purposes, X-ray phase plates are increasingly used.
Crystals exhibit birefringence near their Bragg diffraction angles. When X-ray beams are transmitted, the electric field vectors parallel and perpendicular to the scattering plane undergo birefringence, resulting in a phase difference between them. This phase difference is proportional to the crystal thickness and inversely proportional to the deviation from the Bragg angle. If we adjust this deviation of a crystal plate of a given thickness to create a π/2 phase difference between the two, it becomes a quarter-wave plate that converts linear polarization to circular polarization. If the phase difference is adjusted to be π, it becomes a half-wave plate that rotates the linear polarization direction by 90°.
Diamond crystals make excellent X-ray phase plates in the 4 to 17 keV photon energy range. Diamonds are perfect crystals with low absorption, high transmission, and excellent thermal dispersion, allowing them to withstand high thermal loads. For example, a well-collimated linearly polarized X-ray beam from an undulator can be converted to a circularly polarized beam using a diamond phase plate. Also, if the phase plate is made reciprocate so that the deviation from the Bragg angle rapidly changes and the phase difference alternates between +π/2 and -π/2, it is possible to obtain circular polarizations with alternating directions. M. Suzuki et al. achieved alternating circular polarizations by transmitting incident light through a 0.5 mm thick diamond (111) phase plate and using a phase retarder. They inclined the phase plate at 45° to the polarization plane of the incident beam and oscillated it at a frequency of 40 Hz using a piezoelectric driver (±300 arcseconds).
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.
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are included.
Therefore, spectral brightness is defined by
and
are the beam sizes in the x and y directions, respectively, and
and
are the angular divergences in the x and y directions, respectively. Emittances are global parameters of the storage ring, meaning that they are constant over the storage ring. The brightness of the synchrotron radiation increases as the emittance decreases, so storage rings, including PLSII, are designed with significant efforts to reduce emittance.
. For PLSII, E is 3.0 GeV, and since
mc2 is approximately 0.5 MeV for an electron, 
.
So, the spread angle is
rad.
Note that this angle is the vertical angular divergence of the divergence because the horizontal radiations emitted by the moving electrons add up to make the radiation spread as wide as the bending angle of the bending magnet. In PLSII, a thin fan-shaped beam with a spread of 0.262 rad is emitted from each of the 44 bending magnets, but only about 30 to 40 mrad of this is utilized, with the rest being blocked by photon stops.
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