BNL-213673-2020-BOOK
Infrared Spectroscopy and spectro-microscopy with synchrotron radiation
P. Dumas, G. L. Carr
To be published in "Synchrotron Light Sources and Free-Electron Lasers"
January 2020
Photon Sciences Brookhaven National Laboratory
U.S. Department of Energy USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Notice: This manuscript has been authored by employees of Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 with the U.S. Department of Energy. The publisher by accepting the manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
INFRARED SPECTROSCOPY AND SPECTRO-MICROSCOPY WITH SYNCHROTRON RADIATION
Paul Dumas*a, Michael C. Martinb and G. Lawrence Carrc a SOLEIL Synchrotron, L’Orme des Merisiers, Saint Aubin, BP48- 91192- Gif Sur Yvette Cedex (France) b Advanced Light Source, 1 Cyclotron Road, Lawrence Berkeley National Laboratory, Berkeley CA 94720-8229 (USA) c National Synchrotron Light Source II, Bldg. 741, Brookhaven National Laboratory, Upton NY 11973-5000 (USA)
Contents Introduction Source Types and Characteristics Dipole Bend Radiation (conventional Synchrotron Radiation) Approximate Expressions Gaussian Beam Parameters Edge, Transition and Diffraction radiation Long Wavelength Cutoff Electron Bunching and Coherence Time-resolved Spectroscopy Coherent Emission Light Hazards, Optics and Instrumentation Light Hazards Optics First Mirror Beam Propagation Aberration-free Optical Designs Instrumentation Spectrometers Spectral Resolution Microscopes Detectors Beyond the Diffraction Limit: Towards Sub-Wavelength and Nanospectroscopy Array Detector Imaging and Oversampling Scanning Probe Systems Applications
1 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Spectroscopy using non-coherent far-IR synchrotron radiation Solid State Physics Gas Phase Surface Science Microscopy at diffraction-limited spot size Material Science Extreme Conditions Earth and Planetary Science Archaeology Biology Spectroscopy using Coherent Radiation Nanospectroscopy and Nanoimaging References
Abstract This chapter addresses the general properties of infrared radiation as produced at synchrotron light source facilities as well as the optical systems for extracting the light and matching it to various infrared instruments. As such, it can serve as a guide for understanding basic radiation properties as well as for the successful design of a beamline to perform infrared microspectroscopy. The bending magnets that steer the synchrotron electron beam into a circular orbit serve as the essential source of infrared emission, and simplified formulas are provided to allow calculating flux and brilliance for a particular beamline design. Various optical designs for collecting the infrared and efficiently propagating it to the measurement instruments are also presented, including a novel optical design for managing the large source depth. A wide range of measurement techniques and associated instrumentation have been reported over the last twenty-five years, and some of the more recently developed techniques are described here with examples. Spectroscopy and microscopy (especially in combination) are among the most prevalent techniques and continue to evolve via new instruments for near-field nanospectroscopy and tomography. Infrared detectors are a mostly well- developed technology so only a basic overview is provided here as guidance for the types commonly used with the synchrotron infrared source. An exception is the need for detectors to enable near-field nanospectroscopy across the entire far-infrared and 2D detector arrays for complete spectroscopic imaging.
Glossary • AFM Atomic Force Microscope • ALS Advanced Light Source (Berkeley, CA, USA) • BESSY Berliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung (Berlin, Germany) • CGS centimeter, grams, seconds and Gaussian unit system • CLS Canadian Light Source (Saskatoon, Canada) • CVD Chemical Vapor Deposition (for diamond) • ER Edge Radiation • ETH Eidgenössische Technische Hochschule (Swiss Federal Institute of Technology)
2 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
• FPA Focal Plane Array (2D detector array) • FTIR Fourier Transform InfraRed • FWHM Full Width at Half Maximum • IR Infrared • IRENI Infrared imaging beamline at the former SRC • LURE Laboratory for the Utilization of Radiation Electromagnetic at Univ. of Paris – Sud • MAX-Lab Accelerator and light source facility in Lund, Sweden • MCT Mercury Cadmium Telluride • NA Numerical Aperture ( = n sin for a focus half angle in a medium of refractive index n) • Nd:YAG Neodymium Yttrium Aluminum Garnet (laser) • NSLS National Synchrotron Light Source (Upton, NY, USA) • NSLS-II National Synchrotron Light Source II (Upton, NY, USA) • rad Radian (angular unit of measure) • RF Radio Frequency • RMS Root Mean Square • SI Système International (Int’l System of Units) • SLS Swiss Light Source (Paul Scherrer Inst., Switzerland) • sr Steradian (solid angle unit of measure) • SRC Synchrotron Radiation Center (Stoughton, WI, USA) • SOLEIL Synchrotron Soleil (Saint Aubin, France) • SOR Synchrotron Orbital Radiation (Okazaki, Japan) • SRW Synchrotron Radiation Workshop (software) • s-SNOM scattering-type Scanning Near-field Optical Microscopy • THz Terahertz • Ti:S Titanium Sapphire (laser) • UHV Ultra-High Vacuum
Introduction Interest in infrared synchrotron radiation began in the late 1970’s (Lagarde 1978; Stevenson and Cathcart 1980; Williams 1982; Duncan and Williams 1983), with the characteristics of the infrared synchrotron source being well-described. These include being highly polarized, pulsed, and having a spectrally broad emission. Most significantly, it is typically more than 1 thousand times more brilliant than the standard thermal source used for most infrared spectroscopy. Two of the earliest reports on infrared synchrotron radiation came from the original BESSY in Berlin, Germany (Schweizer 1985) and SOR facility in Okazaki, Japan (Nanba 1986). It has since developed into an important source for a variety of throughput-limited measurement techniques that have impacted many different scientific disciplines (e.g. biology & medicine, materials science, earth & space sciences, and catalysis). While spectro-microscopy has been the dominant measurement technique, the source has proved important for grazing incidence reflection/absorption spectroscopy (for surface studies), ellipsometry (for directly extracting optical response functions), and very high-resolution spectroscopy. The pulsed nature of the source has also been exploited for time-resolved spectroscopy. New techniques under development include near-field nano-spectroscopy and tomography. Though there are
3 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) many types of infrared sources based on electron accelerators (e.g. free electron lasers), the scope of this chapter is limited to high-energy electron synchrotron / storage ring type sources. Therefore, only the source types that produce a continuum of photon energies (frequencies) from millimeter waves through visible light — such as dipole bending magnet radiation — are considered here. The design of an optimized facility for infrared synchrotron radiation science must manage several constraints associated with the environment of a high energy electron accelerator and storage ring. As will be shown below, the requirements for large vertical and horizontal collection angles can be difficult to fulfill and tend to limit performance in the far-infrared to millimeter spectral ranges. The variety of measurement techniques have expanded in concert with improvements in beamline optical designs for matching the source to the instrumentation. These designs require a detailed knowledge of all characteristics of emitted radiation such as the intensity distribution, polarization and phase distribution. In the analysis to follow, it is assumed that the synchrotron source of interest is a storage ring employing high energy (>500 MeV) electrons such that all photon energies of interest — from a few eV down to below 1 meV — are far below the critical frequency for dipole bend sources defined as
3 c 3 C = {1} 4 where is the relativistic mass enhancement factor (for electrons, = 1957·E, where E is the particle’s energy 18 in GeV). Typical values for C are on the order of 10 Hz or photon energies of a few keV or greater. Thus, the entire infrared range (photon energies of 1 eV and below) corresponds to the long-wavelength limit. A similar assumption is that the upper frequency limit for either dipole edge or diffraction radiation sources is in the visible range or below so that the infrared properties are intrinsic to a sudden change in the electron’s field during the emission process. The SI system of units are used throughout this chapter, rather than the Gaussian system frequently used for electromagnetism. The responsivity of infrared detectors (especially for the far-infrared) is typically in units of Volts/Watt (V/W) or Amperes/Watt (A/W), so source properties are described in terms of power rather than number of photons per second. The most commonly used unit for infrared frequencies is the wavenumber, which is the number of wave cycles per centimeter distance. This is in contrast to frequency in wave cycles per second (Hertz). To distinguish the two, a Greek “nu” with a bar is used for wavenumber i.e. 휈̅ = 1/, in units of cm-1 while = c/ (= c휈̅ ) with the speed of light c in cm/s and in cm. As with frequency in Hz, the wavenumber unit has the advantage of being linear with photon energy, with 1 eV = 8065.6 cm-1. The infrared spectral range then extends from 10 cm-1 in the far-infrared to just over 10,000 cm-1 in the near-infrared, with the visible spectral range from 14,300 to 25,000 cm-1 (wavelengths between 700 nm and 400 nm). Note that some graph axes are labeled as “Frequency [cm-1]” and others as “Wavenumber [cm-1]”. These are entirely equivalent Source Types and Characteristics: This section concerns the characteristics of infrared synchrotron radiation as a source and its basic propagation. The most commonly used source of infrared synchrotron radiation is the emission from the dipole magnets that horizontally bend the electron beam around into a closed orbit. Other source types result from a sudden change in the electron’s orbit or electromagnetic environment and include edge radiation, where the electron crosses the boundary between regions of different magnetic field (i.e., the edge
4 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) at the entrance or exit of a dipole bend magnet field). Transition and diffraction radiation, where a change in the dielectric properties along the electron’s trajectory affect its Coulomb field, have not received much consideration as sources of infrared in storage rings. Transition radiation, where the electron is incident on a medium fully inserted into the beam, is not normally encountered in an electron storage ring due to the negative effect on the electron beam itself. It shares a number of characteristics with dipole edge radiation, with the exception that the latter blends into dipole bend radiation. Diffraction radiation occurs when only a portion of the Coulomb field intercepts a different medium. This can include the changing interior dimensions found in the vacuum chambers of most electron storage rings. Other common synchrotron radiation source types for producing x-rays, i.e. devices with periodic magnetic structures such as undulators and wigglers, are not useful for producing long wavelengths on high energy storage rings due to the impractically large length scale that would be required. The same issue applies to specialized structures, such as metal gratings for Smith Purcell radiation. These devices involve the superposition of multiple, sequential source points where the electron falls behind its previously emitted electromagnetic wave component by (or /2 for a sequence of sources having opposite phase) to yield constructive interference. Using the standard definition v/c as the ratio of the electron velocity v to the speed of light c, an electron in a 3 GeV storage ring has a mass enhancement factor of = 5871 so that = √1 − (1/훾)2 = 0.9999999855. Even after traveling a distance of 10 meters, an electron would be only 0.15 m behind a photon, which is negligible relative to the wavelength of an infrared photon. This difference increases for an electron on an undulating trajectory, but not enough to allow for constructive interference in the infrared. It should be noted that many of these other source types are very useful in lower energy electron accelerators – especially linear accelerators where the electron beam quality after the radiator is not an issue and is not so close to unity. The most important characteristic of infrared synchrotron radiation is its very high radiance (or brilliance), which is used to overcome the low throughput of many spectroscopic techniques such as microspectroscopy. While x-ray brilliance is described in units of photons per second per 0.1% spectral bandwidth, the analogous but more practical spectral radiance with units of W/m2/sr/Hz [or W/cm2/rad2/cm-1] is used here. Likewise, spectral flux is used to describe the overall radiated power per spectral range in units of W/Hz or W/cm-1 and spectral intensity for the radiated power per spectral range per solid angle (comparable to spectral brightness). Note that the angles of interest here are small compared to 1 radian, so the product of two orthogonal angles in radians is equivalent to the solid angle in steradians. For convenience, units of rad2 are used here rather than sr. Table 1 lists the various radiometric quantities, their definitions and the units employed in this chapter. Table I – Radiometric Quantities and Units for Infrared Quantity Name Symbol Units Radiant Flux W -1 Spectral Flux , W/cm Radiant Intensity 2 W/rad2 I = , Spectral Intensity 2 W/rad2/cm-1 I = Radiance 2 W/rad2/cm2 L = I A = A
5 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Spectral Radiance 2 3 W/rad2/cm2/cm-1 L = I A = A Each source type has an intrinsic polarization that can be exploited for some measurement techniques. This also affects the characteristic intensity profile at a focus. In most situations, the linearly polarized component of the source is extracted and other specific polarization states generated from that using polarization optics. Dipole Bend Radiation (Conventional Synchrotron Radiation) A standard source of infrared synchrotron radiation is from the electrons as they orbit through the dipole bending magnets. The typical geometry is shown in Figure 1. The continuous transverse acceleration results in a constant emission tangential to the orbit such that the collected flux is proportional to the angular extent coll of the first optic or aperture collecting the light. Details of this emission were originally determined by Schwinger (1949). Expressions for the infrared intensity and spectral dependence can be found in the work 3 7 -1 of Duncan and Williams (1983). In the low frequency limit (i.e. 휈̅ << 휈̅C /4 2x10 cm for NSLS-II), the spectral intensity at a point precisely in the orbit plane for beam current i in amperes (see eqn. 14 in Duncan and Williams, 1983) can be written
2 3 I | = 5.1810−7 i ( ) 2 -1 =0 [W/rad /cm ] {2} where is the angle measured transverse to the synchrotron’s orbit plane (i.e. vertically for a horizontal orbit). Note that, for a constant bending radius, there is no explicit dependence on the horizontal angle defined as .
Figure 1. Geometry for describing dipole synchrotron radiation from an electron on a circular orbit (green arc) of bending radius , with an observer viewing the radiation emitted from orbit tangent point P. The dipole bend radiation forms a smooth swath of light in the orbit plane along the direction . The emission in the vertical direction falls off away from the orbit plane.
The -dependent radiant intensity varies according to the function
2 2 2 I()/I( = ) F∥() + F⊥() = (1+ X ) K ( ) + X (1+ X )K ( ) {3} 2 3 1 3 2 3 2 where X = () , = 2 C (1+ X ) and the Kj/3 are modified Bessel functions. The two terms on the right describe, respectively, the horizontally and vertically polarized emission fractions. For convenience, approximate expressions are provided in a subsequent section (see below).
6 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Integrating I() over the vertical angle in combination with eqn. 2 yields the spectral flux (power per frequency 휈̅) as collected in a horizontal angle coll, i.e.
( ) −7 1 -1 = 8.6410 i ( ) 3 [W/cm ] {4} coll where i is the current (amperes), coll is the horizontal angular collection (radians), and is the bending radius in cm. This expression assumes that the full emission above and below the orbit plane is collected. Figure 2 displays the calculated spectral flux for infrared beamlines at three synchrotron light source facilities when each one is operated with 100 mA of electron current. Note that this is not the radiance, which turns out to 1/3 be independent of the bending radius. The curves differ only according to the value of coll· . Here, coll is the collected horizontal angle as determined by the physical limitations imposed by other components of the specific storage ring. Note that the effects of limited vertical angular collection and the cutoff from the metal vacuum chamber for the electron beam are not included here. Also, many of the medium (~ 3 GeV) energy synchrotron light sources operate with electron beam currents closer to 500 mA. The “⅓” power in eqn. 4 is ubiquitous for bending magnet radiation and stems from the source geometry. Each electron radiates continuously along an orbit of curvature , with the electron falling behind its emission an amount 3/6 per distance along the orbit arc. The radiated wave therefore falls out of phase with the previously emitted radiation such that further emission begins to contribute to a distinctly separate radiation mode. Setting this distance equal to the RMS value of a cosine [over the segment from 0 to (/2)·, serving as the cutoff point] yields 3/6 ≈ /9 so that ≈ 7/8 ()1/3 = 7/8 ( ·휈̅)-1/3. This is one approximate derivation of the far-field angular emission for dipole synchrotron radiation in terms of the electric field strength.
Figure 2. Ideal spectral flux as calculated using Eqn. {1} for the constant field (dipole bend) source, assuming 100 mA of electron current and for the angular collection at three different synchrotron light sources having
bending radii ALS = 4.95 m,
CLS = 7.14 m and NSLS-II = 25 m.
7 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
It is interesting to compare the infrared spectral flux provided by the synchrotron radiation source with that emitted from an isotropic and perfect blackbody at temperature T [in K]. From the Planck formula, the spectral radiance is
3 L 2h 1 2 = 2 [W/m /sr/Hz] {5a} BB c exp h kT −1 ( ) where h is Planck’s constant, k is Boltzmann’s constant and c is the speed of light (in m/s). Rewriting this in wavenumbers 휈̅ (in cm-1) and radians; L = 9.354x10−13 3 exp 1.439 T −1 −1 2 2 -1 {5b} ( ) [W/cm /rad /cm ] BB where the angular area is assumed to be small. In the low frequency limit, this becomes L = 6.5x10−13 2T T 2 2 -1 {5c} [W/cm /rad /cm ] BB In a common laboratory infrared spectrometer, the source is collected and imaged onto the sample using an f/4 optic (i.e. a parabolic mirror of 150 mm focal length and 38 mm diameter), corresponding to a cone with half angle of about 0.125 rad. The usable source area is about 6 mm diameter. For this geometry, the spectral flux is =1.32x10−15 3exp(1.439 T )−1−1 [W/cm-1] {6} BB
Figure 3. Comparison of the calculated radiated flux for the NSLS-II dipole bend synchrotron radiation source with thermal sources at two typical operating temperatures (2000 K and 5000 K), plus the T = 295 K ambient. Note units of W.
This spectral flux can be calculated for a typical spectrometer source temperature of T = 2000 K (mid-IR type) or T = 5000 K (far-IR Hg arc lamp). Figure 3 shows a comparison of such thermal sources with NSLS-II,
8 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
-1 assuming coll = 50 mrad and i = 500 mA. Note that the Hg arc lamp is shown as a dashed line above 300 cm where its quartz envelope becomes opaque. Here it can be seen that the ideal synchrotron radiation source outperforms thermal sources in the far- infrared when considering only power (not considering spectral radiance or brilliance). It will be shown later that the ideal case is not necessarily realized at long wavelengths, but a significant flux advantage still exists. The T = 295 K curve illustrates that the thermal background is a significant source that a detector will sense, even when no intended source or spectrometer is present. Approximate expressions The far-field intensity includes both horizontally and vertically polarized components, and the detailed distribution of this intensity as a function of vertical angle involves rather complicated (and somewhat inconvenient) mathematical expressions (cf. eq {3}). Fortunately, simple approximations exist that provide sufficient accuracy for most applications involving the design of an infrared beamline. One such approximate expression for the intensity distribution of the dominant horizontally polarized component takes the form of a Fermi function,
I0 F∥() 1+ expa( − b) {7} where is the angle (in radians) measured above or below the horizontal orbit plane, a = 8.6, b = 0.62, I0 is the peak intensity (eqn. 2) in the orbit plane where = 0, and ()1/3. A comparison between the exact result and this approximation is shown in Figure 4. Also note that the vertically polarized component F⊥() can be fairly well described by a Gaussian (for both above and below the orbit plane, see red-dashed curve in Figure3).
Figure 4: Far-field radiant intensity distribution of dipole bend radiation (solid curves) measured vertically from the orbit plane at = 0 along with results from the approximate expressions (dashed curves). The vertically polarized component (red) has been fit with a simple Gaussian function. Relative Angle in units of ()1/3.
9 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Due to the phase difference between the vertically polarized components as viewed above and below the orbit plane, they interfere destructively when brought to a focus where the predominant horizontal intensity yields a maximum. As such, the vertical polarization does not contribute significantly for measurements where the throughput is diffraction-limited. For this reason, discussions concerning the useful brightness concentrate on the horizontal component alone. Since the intent is to focus this emission to a small illumination area on a sample, the Fourier transform of this function is of interest, and also provides a measure of the source’s effective size. This is more readily seen in the angular distribution measured vertically, as the horizontal consists of a source continuum. Gaussian beam parameters This Fourier transform of the electric field strength’s angular distribution yields a function that is not much different from a Gaussian, which allows us to provide approximate Gaussian beam parameters that can be used for estimating the effective source size and beam propagation through an optical system (Figure 5).
Figure 5. Diagram for a Gaussian beam focus showing definitions of the waist
W0 at a focus, the far-field angle 0 and the Rayleigh range ZR. The waist W(z) represents the point where the electric field E has fallen to 1/e (and intensity to 1/e2) of its value directly on the axis of propagation (the z axis).
Values for these parameters that provide a good approximation for dipole bend radiation are:
1 1 3 1 2 2 4 1 2 W 3 Z 3 {8a} 0 ( ) 0 R ( ) 5 5 2 where W0 is the beam waist through a focus, 0 is the far-field angular divergence and ZR is the Rayleigh range, defined in the standard way. These expressions give the electric field 1/e points to within 10% accuracy and are consistent with the usual relationships for a Gaussian beam, i.e.
2 W0 W0 = 0 = Z = {8b} W R 0 0
1/3 Other definitions for the far-field angular intensity distribution are for the RMS value RMS = (3/4) () 1/3 (Hoffmann 1978) or the full angle needed for collecting 95% of the emission, e.g. full = 1.66() (Duncan 2 and Williams 1983), which is consistent with the beam’s full width = 2W0 as defined by the 1/e points for the intensity in eqn. 8a. This last definition is useful for determining the dimensions of an opto-mechanical system for efficiently extracting and propagating the light. The beam waist in eqn. 8a also provides a measure
10 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) of the transverse size of the electron’s Coulomb field radiating at a given wavelength, which is helpful for understanding the effects of a metal vacuum chamber on the emission at long wavelengths. Since each diffraction-limited source segment of the orbit radiates into a full angle ~ 1.6()1/3 = 1.6(휈̅)-1/3, one can calculate from eqn. 4 the spectral flux per such a segment as
−6 -1 =1.3810 i [W/cm ] {9} diffraction segment In this sense, for each diffraction-limited source segment, the long wavelength flux is spectrally flat and depends only on the electron beam current. Multiplying by the electron charge e yields the spectral energy per electron, per diffraction-limited source segment;
Q −25 = 2.210 [J/cm-1] {10} one electron
The expressions in eqns. 9 and 10 allow for simple performance comparisons with other source radiation mechanisms. Lastly, expressions for the peak on-axis spectral radiance can be determined using the spectral flux from eqn. 9 and the approximate source dimensions (i.e., 2 times the RMS values from eqn. 8) to yield
L −6 2 2 2 -1 3.3810 i [W/rad /cm /cm ] {11} Note that the spectral radiance increases as frequency squared, which is the same dependence found for long wavelength blackbody radiation in eqn. 5c. In the long wavelength limit, the relative brightness of the synchrotron source to the blackbody source becomes 5.2x106 i/T with i in amperes and T in Kelvin. Thus, the infrared spectral radiance of a synchrotron storage ring with 500 mA current is equivalent to a 3x106 K blackbody. Edge, Transition and Diffraction radiation Edge radiation (ER) occurs where an electron crosses a boundary between two different magnetic field strengths. The most common example is where an electron enters or exits the dipole field of a bending magnet. Here, the Coulomb field of the electron moving in a straight line is replaced with the field of an electron on a curved orbit. This abrupt change results in radiation that propagates in the forward direction, i.e. parallel to the electron’s velocity as it crosses the field’s edge. Transition and diffraction radiation are types of sources in which some, or all, of the electron’s Coulomb field is modified due to the presence of a medium having a different electromagnetic response. Transition radiation refers to the situation where the entire Coulomb field is affected (e.g. due to being incident onto an object such as a metallic mirror), whereas diffraction radiation occurs when a portion is affected (e.g. passing near to an object). These two types of sources are usually considered only for accelerators other than storage rings, due to the major disruption of the electron’s trajectory resulting in beam loss. However, they can be useful sources for diagnosing beams in linear accelerators and injection systems. For transition radiation from an electron crossing from vacuum to a good conductor, the entire Coulomb field of a charge moving at a constant velocity is abruptly removed. The opposite occurs for an electron emerging from a conductor into vacuum. This time-dependent Coulomb field exhibits the same behavior as for edge
11 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) radiation where an electron enters or exits a dipole field, and the expressions for the emitted radiation are the same. However, since edge radiation sources are directly connected to dipole bends, the far-field emission is a superposition of the two, and aspects of their emission can be difficult to distinguish experimentally. This can be seen in results from computer codes for calculating synchrotron radiation, such as SRW (Chubar et al. 2002, Chubar et al. 2007). To understand edge and transition radiation, one begins with the Coulomb field of a relativistic electron moving at a constant velocity, which is highly compressed in the direction transverse to the electron’s velocity. The cross-section of this field in the direction of motion (Jackson 2007) increases with distance from the electron, having a half-width at half maximum of 2b/, where b is the distance from the electron (defined in the same manner as an impact factor). The 1/e distance for radiating at wavelength defines the source waist W0 = /4. However, the transverse electric field and intensity for edge and transition radiation fall- off much more slowly with distance than a Gaussian, so the usual relationships between Gaussian beam parameters are not accurate or appropriate. Additionally, the orientation of the Coulomb field results in a radially polarization emission similar to the L01* “doughnut” mode, which is the superposition of two orthogonally polarized L01 modes, each having a quality factor of M 2 = 3 (Herman et al. 1998). In practice, the 1/e point of the electric field (1/e2 for the intensity) relative to the maximum intensity at an angle = 1/ defines a far-field half-angle 0 5/. The RMS value is about 3 times larger, suggesting an M 2 closer to 3.7. The far-field angular distribution of radiated spectral energy per electron, is given by [Ginzburg and Frank, 1945, Happek et al, 1999] dQ(,) e2 2 sin2 = 3 2 2 2 [J//rad/(rad/s)] {12} d 4 0c (1− cos ) where = v/c is the electron’s speed relative to light, 0 is the permittivity of free space and the frequency is in radians/sec. Here, the angle is measured as a polar angle from the direction of motion (to distinguish from the definitions of and as used for dipole bend radiation). Note that the source emission is independent of frequency, up to a cutoff frequency determined by details of the magnet’s fringe field (for edge radiation) or the conductor’s plasma frequency (for transition radiation from a metal). Integrating eqn. 11 over all angles yields the total spectral energy 2 dQ() e 2 = 2 ln −1 [J/rad/s] {13a} d 4 0c 1− or, in wavenumber units
dQ( ) −26 2 = 4.6210 ln −1 [J/cm-1] {13b} d 1− Assuming a 3 GeV electron, the factor in square brackets is about 17.7 such that the energy per wavenumber becomes 8.1x10-25 J/cm-1. Note that this is a factor of nearly 4 greater than for the dipole bend source (cf. eqn. 10). However, there is not a significant benefit in spectral radiance (brilliance) due to the larger M2 of transition radiation (and edge radiation). Therefore, the choice of source type for developing an infrared facility is more dependent on other considerations such as the mechanical constraints of the accelerator system itself.
12 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
For a beam of current i the spectral flux is then
d −7 2 = 3.310 i ln −1 = 5.1x10-6 i [W/cm-1] {13c} d 1− Thus, the total power for a beam current of 0.5A at 3 GeV and the spectral range extending up through the visible (25,000 cm-1) is about 63 mW. Note that this is for a single source. In practice, dipole edges occur in pairs, i.e. the exit point from one dipole magnet is followed by a straight section that connects to the entrance point of the next dipole magnet. The light reaching an observer comes from both sources. This is illustrated in Figure 5, showing one source where the electron enters the dipole field plus a second source where it exits the upstream dipole. Since the effective accelerations for the two edges are opposite, the intrinsic phase difference for the two sources is , resulting in destructive interference directly on-axis (the velocity difference for the electron and photon is negligible, as noted above). For an off-axis observer, the geometric path difference for the two sources results in a series of ring-like intensity fringes for a given wavelength. The observability of these fringes depends on having light from both sources reaching the observer (no obscuring obstructions), an ideal electron trajectory that has both sources accurately aligned, and a sufficiently narrow spectral bandwidth.
Figure 6: Intensity (or irradiance) profile for a single infrared wavelength through a rectangular aperture located downstream of two sequential dipole bend magnets. The continuum of light extending to the left is the dipole bend radiation from the nearest (downstream) dipole. The ring-shaped intensity fringes are due to interference between the two edge sources. Calculation using SRW code. The discussion here on diffraction radiation is brief as details of the source emission depend heavily on the shape and location of the radiating interface relative to the electron beam. The process is still related to the interaction of an electron’s Coulomb field with an object, with the time-dependence determined by the proximity to the electron itself, as discussed earlier. Based on this, the short wavelength limit for the emission is expected to obey
13 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
4 b diff {14} where b is the minimum distance between the edge of the radiator and the electron beam. For a typical 3 GeV electron beam and a minimum distance of 2 cm, the emission is limited to wavelengths longer than about 40 m (250 cm-1), i.e. the source would be strictly for long wavelengths in the far-infrared. Long wavelength cutoff With few exceptions, an electron accelerator serving as a light source has the electron beam contained in a metallic vacuum chamber that imposes a long wavelength limit for producing radiation. For a detailed analysis and discussion on this topic, the reader is referred to the work of R.A. Bosch (Bosch 2002). The effect can be visualized as the superposition of multiple radiating sources consisting of the actual electron plus a set of image charges that satisfy the boundary conditions at the conducting walls. For the discussion here, the radiating portion of the Coulomb field for each particle is characterized by the beam waist W0, which increases with wavelength . The waists for the negative electron and the nearest positive image charges overlap substantially when W0 becomes equal to the chamber height h. Since the charges are opposite, this becomes destructive and results in zero emission beyond a cutoff wavelength C. Calculation results for the dipole bend source (Bosch 2002) are shown in Figure7a. Note the strong cutoff for wavelengths longer than C where (2h)3 . {15} C
-1 Typical values for h are ~2 cm and ~ 10 m, such that C ~ 0.25 cm (4 cm ) for dipole bend sources. An interesting feature of the Bosch calculation result is an enhanced radiated intensity for the vertically polarized component as the wavelength increases toward the cutoff, as shown Figure 7a, which is due to a constructive overlap of the radiating field vertical components. (a) (b)
Figure 7. Calculated flux between two infinite conducting sheets placed a distance h/2 above and below the electron beam for (a) dipole bend radiation and (b) edge radiation. Note the predicted flux enhancement as the wavelength nears the cutoff value, especially for the vertically polarized dipole bend source (from Bosch, 2002).
14 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Edge radiation can be considered in a similar manner. Setting the effective source waist equal to the chamber height identifies a cutoff wavelength due to shielding from a metal vacuum beam pipe 4h . {16} C Comparing this to a detailed calculation in Figure 7b (Bosch 2002) shows good correspondence to the point where the emitted intensity has dropped to ½ of the unshielded value and where it is falling most rapidly as a function of increasing wavelength. To date, little experimental data exists to confirm the calculations for the edge source.
Applying eqn. 12 to case of 3 GeV electrons inside a metal beam pipe having 2.5 cm interior dimension, one expects the emission of edge radiation to be reduced significantly for wavelengths greater than ~53 m, or for frequencies below ~187 cm-1. This suggests edge radiation is not a useful source for reaching deep into the far-infrared. Additionally, for all types of sources, the far-field emission tends to fill much greater angles as the wavelength increases toward the cutoff (Bosch 2002), further challenging the ability to collect it efficiently. In general, these wavelength cutoff values serve as semi-quantitative guides since they are calculated for an ideal geometry of two conducting planes. The chamber walls of actual storage rings have more complicated geometries, including curved surfaces.
Figure 8. Comparison of calculated spectral radiance (brilliance) for several infrared synchrotron radiation facilities over the spectral range from the millimeter wavelengths to the near-IR. Calculations include both waveguide cutoff and limitations on vertical angular collection. For comparison, the ideal dipole bend source at 500 mA beam current is shown. NSLS-II has two types of dipole bending magnets, one with a large gap (LG) and the other with a standard gap (SG). Also shown is the radiance for a T=2000 K ideal blackbody (BB) source (dashed curve).
At this point one can consider all of the issues that limit the infrared spectral radiance for the dipole bend emission at a typical synchrotron radiation facility. Beam current is the principal factor in determining the spectral radiance, and values up to 500 mA are now common. At short wavelengths, the size of the electron beam (emittance) can be larger than the diffraction-limit, resulting in a decrease relative to the ideal. At longer wavelengths, limitations on the angular extraction actual (as determined by mechanical constraints) cause a slow decrease in radiance as the intrinsic opening angle 0 (see eqn. 8) increases beyond actual. Lastly,
15 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) a rapid loss in radiance occurs as the wavelength increases beyond cutoff. These effects can be visualized from the calculated spectral radiance for a number of synchrotron light sources, as shown in Figure 8. Electron Bunching and Coherence All of the discussion to this point assumes a continuum of electrons having uncorrelated longitudinal positions with the emitted flux directly proportional to the beam current. Since the radiated energy of the electrons is restored by the electric field in a radio frequency (RF) cavity, the electrons must arrive at the correct instantaneous cavity voltage and therefore orbit in bunches rather than as a continuum. The resulting emission is pulsed, with durations in the 10s to 100s of picoseconds, depending on the RF frequency and voltage as well as the energy spread of the electrons in combination with the storage ring’s dispersion. A typical storage ring operates with a cavity frequency significantly larger than the orbital frequency. The ratio of these two is known as the ring’s harmonic number, which must necessarily be an integer. At NSLS-II, the RF cavity frequency is 500 MHz while the orbital frequency is 378,788 Hz, resulting in a harmonic number h = 1320. Since the correct instantaneous cavity voltage occurs 1320 times for one orbit, electron bunches can be located at any of 1320 equally spaced locations, each referred to as an “RF bucket”. When each sequential bucket has an electron bunch, the synchrotron radiation is emitted as a 500 MHz pulse train. Time-resolved spectroscopy The pulsed aspect is not unique to the infrared but applies to the entire radiated spectrum, and can be exploited for a number of time-resolved methods, often as a spectroscopic probe of a system that has been excited (pumped) by a mechanism such as photoexcitation using a pulsed laser incident onto, or an electrical transient through, the sample system being investigated. This approach is especially useful for when fast and sensitive detectors are unavailable over the spectral range of interest, and the beam itself cannot be modulated by another method (e.g. using a fast shutter). A typical arrangement has a mode-locked laser or electronic pulse generator synchronized to the storage ring’s pulses, including a variable time delay between the two. The very high pulse repetition rate for modern storage ring light sources (500 MHz) is usually not practical due to the limited time between pulses (2 ns) for the sample system to relax plus limitations on the pump source. More commonly, a pulse repetition rate of 100 MHz or less is utilized, down to a single electron bunch orbiting in the entire ring. The available pulse repetition rates for the synchrotron source are limited to fRF/ai where fRF is the RF frequency and the ai are from the set of integer factors of the storage ring’s harmonic number h. For NSLS-II with h=1320, the ai values include any combination of factors in the set {1, 2, 2, 2, 3, 5, & 11}. Thus, available symmetric bunch fill patterns include 500 MHz (500/1), 250 MHz (500/2), 167 MHz (500/3), 125 MHz (500/2·2), 100 MHz (500/5), 83.3 MHz (500/2·3), 41.7 MHz (500/2·2·2), etc., down to the orbital frequency of 500/2·2·2·3·5·11 = 500/1320 = 379 kHz. This provides sufficient flexibility for matching to a number of mode-locked laser pulse repetition frequencies (e.g. Ti:S, Er fiber, Nd:YAG). Example studies of laser-pump and synchrotron infrared probe can be found in the work of Lobo et al (Lobo, 2002). In most cases, the laser pulse is shorter than the synchrotron bunch length such that the limiting time resolution is determined by the RMS electron bunch length. Of the parameters that control the bunch length, the overall dispersion of the storage is most often used. The integrated dispersion around the ring is described by the momentum compaction, usually labeled as “” and the storage ring operating mode for short bunches described as “low “ (Wiedemann 1993). Other effects associated with low and short electron bunches are described in the section on coherent emission (below).
16 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
When a modest degree of detector gating is available, hybrid modes can be used where the nominal train of electron bunches has a large gap where a single bunch (usually with a larger number of electrons) is placed. Such a pattern is sometimes described as a “cam-shaft mode”. The hybrid fill pattern allows for a reasonably large overall beam current − useful for non-timing experiments − in combination with a strong pulse for timing experiments. Coherent emission In a typical storage ring, each bunch contains about 5x109 electrons, randomly distributed with an approximately Gaussian longitudinal density distribution. Their relative distance, scaled by the wavelength of interest, determines the phase difference for their emission. When considering wavelengths smaller than the bunch length, the random positions lead to an incoherent superposition of each electron’s emitted waveform. The result is a longitudinally incoherent waveform where the intensity scales linearly with the number of electrons, i.e. the instantaneous beam current. For wavelengths longer than the bunch, the relative phase difference for each electron’s emission is small, and the radiating fields add coherently. The result is a waveform where the electric field amplitude is proportion to the number of electrons N and, hence, the intensity scales as N2. In general, the on-axis spectral intensity dI/d휈̅ for multiple particles where the phase differences are only due to the longitudinal distribution is (Nodvick and Saxon 1954)
dI(N) dI(1) = N + N(N −1)f ( ) {17} d d where N is the total number of particles, dI()/d휈̅ is the spectral intensity for a single particle, and the function f(휈̅) is a longitudinal form factor defined as
2 i z f ( ) = e S(z) dz {18} − where S(z) is the longitudinal probability density for finding an electron in the orbit segment between z and z+dz, with z in the direction of propagation such that f( ) is dimensionless. Since N >> 1, the N (N-1) factor in {13} becomes N 2 and dominates the factor of N when f( ) is not zero. Thus the intensity scales as the square of the beam current (assuming f( ) is independent of the current). Note that f( ) is essentially a Fourier transform of the bunch longitudinal density. In a storage ring under typical operating conditions, this longitudinal density can be described as a Gaussian with RMS length . In this case, the resulting form factor is: 2 {19} f ( ) = exp − (2 ) where is in units of cm. Reducing the bunch length favors coherent emission to higher frequencies. Since the normal operating conditions for most storage rings result in RMS bunch lengths greater than 0.03 cm (10 ps), the spectral range for coherent emission is below = 1 cm-1 ( = 30 GHz or wavelengths >1 cm). This is typically beyond the cutoff limit determined by the electron beam’s metal vacuum chamber (see section Long Wavelength cutoff) so is typically not produced or observed. Also, note that this is distinct from transverse coherence as determined by the transverse dimensions of the electron beam and angular range of emission. In other words, the emission can have transverse coherence but lack longitudinal coherence.
17 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
As noted previously, the bunch length in a synchrotron storage ring is determined by a number of factors, one due to the energy spread that describes the distribution of electrons energies around the nominal value, e.g. E = 3 GeV E where E/E 10-3. Electrons of different energies (and momentum) travel on orbits of different circumference, causing the electrons to disperse longitudinally. The dispersion on a closed orbit is characterized by a factor known as the momentum compaction (Wiedemann 1993), with lower yielding a reduced bunch length. This dispersion is crucial to the stable operation of a synchrotron as it functions in combination with the voltage gradient in the RF accelerating cavity to correct longitudinal deviations and restore energy to the electrons. Achieving shorter bunches through a reduced is more practical than via other parameters, such as reducing the energy spread or increasing the RF gradient. Under special operating conditions, shorter electron bunches, or ones with a longitudinal density modulation, can develop and produce coherent radiation at wavelengths shorter than the chamber cut-off (Carr et al. 2001, Abo-Bakr et al. 2002). More recently, the use of a “low ” mode has allowed the production of stable coherent synchrotron radiation up to about 30 cm-1 (1 THz). In practice, due to the strong interaction between the electrons themselves, reducing and the bunch length eventually leads to instabilities that limit the allowable electron density and the overall current that the storage ring can support. For this reason, low operation periods of a storage ring source are typically limited to a few weeks each year. Facilities that have managed stable coherent emission are BESSY II, the Metrology Light Source (Berlin, Germany), the Canadian Light Source (CLS, Saskatoon) and Synchrotron SOLEIL (Saint Aubin, France) (Barros et al. 2013).
Figure 9: Spectral Flux including coherent enhancement at low frequencies for various RMS bunch lengths and with peak particle density held constant. Other
parameters are coll = 50 mrad and bend radius = 495 cm. The dashed line shows the incoherent (long bunch) flux for 500 mA beam current. Dotted curves are measurement results from the BESSY II facility (Abo-Bakr, 2002).
Some example calculation results for the spectral flux, based on a Gaussian distribution of varying bunch lengths, are shown in Figure 9. Limitations on collection angle or waveguide cutoff effects are not included here. Also shown is the measured flux for BESSY II when operated with low current and low . To account for the instabilities that can arise when the bunch density exceeds a critical value, the calculations were done with the peak density held constant by varying the overall current according to I/L = 300 A/mm. Assuming 5 6 a 500 MHz RF system, this corresponds to about 10 electrons in a bunch for L = 25 m and 2x10 electrons
18 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
for L = 500 m. As can be seen, decreasing the bunch length favors a more extended spectral range for coherent emission, reaching well into the THz range when the RMS bunch length is less than 0.3 mm (< 1 ps). Even with the reduced charge in a bunch, the emitted flux in the coherent spectral range can be orders of magnitude higher compared to high current incoherent emission. Coherent emission has also been observed as a consequence of “laser slicing” (Byrd 2005, Shimida 2007), where the energy of electrons in a sub-picosecond section of a longer electron bunch is modulated by interaction with a strong optical laser pulse. The ring’s dispersion causes these electrons to shift longitudinally from their normal location in the bunch, leaving a very short “hole” in the otherwise relatively smooth negative background of the other electrons in the bunch. Light Hazards, Optics and Instrumentation The previous sections concerned only the low energy radiation to be collected and transported to various infrared instruments. The synchrotron radiation spectrum extends to much higher photon energies, which presents both safety and engineering challenges that an infrared beamline must manage. Light Hazards Compared to an x-ray beamline the construction of an infrared beamline is easier because conventional mirror optics can be used for collecting and transporting the light from inside the accelerator shielding to a location where infrared instruments can be operated. The reflectance from a mirror with a simple metal coating can be very high even when used to change the beam direction by 90 degrees. Therefore, a typical infrared beamline delivers its light around the fixed shielding of the accelerator to a location where no ionizing radiation is present. This does not necessarily eliminate all potential source hazards because the light itself can have sufficient intensity to fall into one of the laser hazard categories, requiring that the beam be controlled inside a contained environment. The hazard can be greatest in the blue and UV spectral ranges, for which filter materials can be used (e.g. a Kapton film). Optics First Mirror The first optical component of an infrared beamline is, for all the existing ones so far, a flat mirror. This mirror is used to deviate the emitted radiation either vertically or horizontally out of the bending magnet environment to the position of a second optical element, either a flat mirror again or a first focusing mirror. This first mirror, often called the extraction mirror, is one of the most delicate components of the beamline and requires both precise positioning and very high mechanical stability. Constraints on the design of this 1st mirror include: - A potentially complicated location sharing the UHV environment and vacuum chamber as the stored electron beam itself. This may be within the dipole vacuum chamber that, in turn, is constrained by the pole faces of the bending magnet, or in the narrow space between storage ring magnets (the dipole, quadrupoles, sextupoles, etc.) - If possible, it be retractable with an isolation valve to allow mirror maintenance without the need to vent a significant portion of the synchrotron storage ring itself. - Protection against damage from the very large power density of x-rays that are generated along
19 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
with the infrared. This includes during periods of storage ring accelerator studies or other situations where the electron beam is displaced from the standard orbit, and typically involves partially retracting the mirror. - If movable, it must be capable of precise repositioning for collecting the radiated photons. The most critical parameter to cope with when inserting such a mirror, is the power density of the impinging photons emitted from the bending magnet. In contrast to the previous sections where only the infrared was considered, here the full spectrum up through the critical photon energy must be included, e.g. x-rays that would be absorbed in the first component intercepting the radiated intensity. The radiation power generated from a dipole magnet is uniform in the plane of the orbiting particles (i.e. the horizontal plane). For the dominant emission having polarization in the horizontal orbit plane, the bending magnet power has an approximately Gaussian profile, peaked in the horizontal plane. The bending magnet power angular distribution per milliampere can also be expressed as (Khounsary and Lai 1992) d 2P 1.4410−18 = 5 F() {20} d d where is the bending radius (in meters) of the electron beam through the dipole magnet and is the electron relativistic mass enhancement factor (as described earlier), yielding the power density in [W/mrad2/mA]. The angular position of the observer is given by (the “azimuthal” angle around the orbit) and (“polar” angle, but measured from the horizontal plane where = 0). This power density is independent of through the dipole magnet, with the angular dependence due solely to and contained with the factor F(), i.e.
2 2 −5 2 2 2 7 5 F() = (1+ ) + 2 2 {21} 16 16 1+ ( ) +∞ 2 Integrating {21} over all , and noting that ∫ 퐹(훾휑)푑(훾휑) = , one arrives at the total power −∞ 3 produced by a 1 mA current per horizontal mrad of orbit: dP 4 = 0.9610−15 W/mrad/mA {22} d Where is in meters. For NSLS-II with = 25 m and a maximum beam current of 500 mA, the power per horizontal mrad is 22.8 watts. For a first mirror intercepting 50 mrad horizontally, the absorbed power to be managed would be more than 1 kW. Substituting = 0 into {20} and {21} yields a power density in the orbit plane of
2 5 d P −18 = 0.6310 2 d d W/mrad /mA {23} =0 For NSLS-II at 500 mA, the power per mrad2 is about 88 watts and the density on a 1st mirror located 1 meter from a dipole bend source point is 88 W/mm2. Even higher values occur at synchrotron facilities where the bending radius is smaller, due to the higher critical energy. It should be noted that the expressions {20-23} do not consider the emittance of the electron beam, so represent a maximum value.
20 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
More accurate results that include emittance, and for a source produced by an arbitrary magnetic field, can be computed using the SRW code. Since the natural vertical opening angle increases with decreasing energy (or increasing wavelength), the highest power density is concentrated close to the orbit plane (Figure 10) while the infrared and longer wavelengths extend much farther above and below that plane.
Figure 10: Flux density as a function of vertical angle from the orbit plane, assuming a horizontal aperture of 40 mrad, and for E=3 GeV, B=1.42T, and I=100 mA, yielding a critical photon energy of about 8 keV. The curves are for a selection of photon energies in the UV and x-ray range or for various wavelengths in the infrared. The greatest flux density is for the high energy photons (x-rays), that are mostly limited to a narrow angular range ( 1/ < 1 mrad) above and below the orbit plane.
At many facilities, infrared photons are collected from both edge radiation and dipole bend (constant field) sources. An example result for the far-field spatial intensity profile in the mid-infrared for such a case is shown in the top panel of Figure 11. The observation plane is located about 1 meter distance from where the electrons enter the dipole field. The ring-shaped intensity fringes that result from the interference between the near and upstream dipole edges are not observed in a typical measurement where the light is focused and spans a broad spectral range. The bottom panel of Figure 11 shows the full power density (integrated across all wavelengths) in the orbit plane along the same horizontal axis. This intensity is dominated by x-rays near the critical energy. The profile of that intensity near the straight axis angle depends on the magnetic field profile at the dipole edge (due to the dependence of the critical photon energy on the bend radius). Also note the x-ray intensity extending in the negative angle direction (beyond the straight axis) produced in the upstream dipole bend magnet. This intensity is less due to the much larger source-viewer distance (a typical distance between dipole magnets is more than 3 meters). Going back to the positive angle side, the intensity increases with angle due to the viewing geometry, i.e. as the distance between the source tangent point and viewing screen decreases.
21 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 11: (Top panel) Intensity profile at a single wavelength of 10 m (mid- infrared), as would be sensed over a surface normal to the optic axis, subtending 60(H) by 20(V) mrad2. Both edge radiation (ER) centered on straight
section axis and dipole bending magnet (BM) radiation can be seen. (Bottom panel) Total intensity (including dominant x-rays) directly on the orbit plane, spanning the same horizontal extent as the top panel. Note that the optical axis (center of the viewing screen) is shifted by ~13 mrad relative to the straight section axis. Calculation for E = 3 GeV, B = 1.42T, I = 400 mA.
The absorbed power density in the first mirror optic can be very high and typically must be managed to avoid mirror surface distortion and even permanent damage. The proximity of other accelerator components typically prevents placing this first mirror at a distance sufficient to reduce the intensity. Therefore, this optical component is typically designed with either a horizontal slot (to allow the x-ray flux to pass to an absorber located behind the mirror, or a water-cooled mask for absorbing the x-rays before reaching the mirror. Since a mask or slot is detrimental to the collection of infrared light, it is desirable to keep its vertical size as small as practical, with the dimension chosen relative to the accuracy by which the electron beam orbit can be controlled (a few millimeters being typical). This accuracy has improved greatly in 3rd generation synchrotron light sources (Lerch et al. 2012), as required for the narrow vertical gaps of state-of-the-art x-ray source insertion devices. A mask absorber requires considerable cooling which can lead to mechanical vibrations and a moving “shadow” on the 1st mirror appearing as intensity fluctuations (beam noise). Therefore, a mirror slot is used more often than a mask. Figure 12 shows the relative vertical-angular profiles of the x-ray, near-IR ( = 2m) and mid-IR ( = 10m) intensity. The effect of a slot or mask for x-rays becomes less and less detrimental with increasing infrared wavelength. Note that the results in the figure have been scaled to the same maximum - in reality, the x-ray intensity is many orders of magnitude greater. Since a slot or mask may not eliminate all of the x-ray flux reaching the first mirror, some degree of cooling is usually included in the design. When an incompressible fluid such as water is used, care must be taken to avoid turbulence and pressure fluctuations that mechanically couple to the mirror itself and introduce noise in the infrared beam. Other fluids, such as nitrogen gas, have been used successfully (L. Vaccari, private communication).
22 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 12: Power density (intensity) distribution along the vertical angle from the orbit plane as dominated by the flux of x-rays (black line) along with the profiles for wavelengths of 10 m (red dashes) and 2 m (blue dots). The simulation has been carried out with E = 3 GeV and B = 1.4T and the results scaled to the same maximum value.
Beam Propagation The previous sections describe features of the synchrotron infrared source and the thermo-mechanical issues for intercepting the infrared while managing the x-ray flux. From here, the propagation of the infrared light follows the standard principles of an optical system, with the goal of efficient transport while maintaining the intrinsic brightness of the source. The general design consists of mirror optics for collecting and relaying the infrared out from the storage ring environment to a location where it can be used with conventional infrared instruments. Mirrors are used almost exclusively rather than lens (dioptic) elements due to the extremely broad spectral range used in the majority of infrared techniques and the lack of fully transparent materials, as well as to avoid chromatic aberrations. The first mirror is commonly made with a metal substrate (e.g. copper or aluminum) to allow for any cooling that may be needed, the remaining mirror elements are made by conventional metallic vapor deposition onto a polished silicate glass or ceramic substrate. Mirror coatings are usually gold (for better near-IR performance) or aluminum (for better visible and near-UV performance). The calculated reflectances for both materials are shown in Figure 13. As can be seen, the reflectance is mostly independent of the polarization across most of the infrared and THz spectral ranges. These mirrors should have no additional dielectric coating to protect the surface or enhance the reflectance in certain spectral ranges as these coatings produce undesirable absorption features in the mid-infrared.
23 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 13: Calculated Infrared reflectance for aluminum and gold at 45° angle of incidence and for both s and p polarized light.
The typical infrared instrument operates with either a purged (1 Bar pressure) or rough vacuum (1 mBar) environment. In either case, a window is required for separating the instrument from the storage ring’s UHV. Diamond (CVD type) is the most widely used window material, being both sturdy and UHV compatible, while having a transmission of about 71% (due to reflection losses) over most of the visible and infrared spectral range (see Figure 14). In practice, a gradual decrease in transmission for frequencies above 5000 cm-1 can occur due to scattering losses from grain boundaries in polycrystalline CVD material. Transmission at higher frequencies becomes limited by the bandgap for diamond (indirect near 5.5 eV, direct near 7 eV). The transmittance of the predominant horizontal polarization of dipole bend radiation could be improved by orienting the window at Brewster’s angle, but this has not been implemented since it requires a larger window and greater thickness. In general, the window thickness should not be greater than about 0.5 mm to avoid excessive absorption between 1600 cm-1 and 2400 cm-1. For a window able to reliably sustain a 1 Bar pressure difference, this thickness constraint limits the overall clear aperture to about 15 mm. Therefore, this window is placed at a focus (beam waist), meaning that at least one mirror optic along the UHV portion of the beam transport systems needs to be a focusing element (e.g. an ellipsoidal or toroidal mirror, or combination of cylindrical mirrors). Typical diamond windows have about 15 mm diameter clear aperture and thickness around 0.35 mm, including a small wedge angle of ½ to 1 degree between the two optical surfaces for avoiding spectral interference fringing (Fabry-Perot effect).
24 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 14: Transmission for an ideal, 0.38 mm thick diamond window. The structure in the 2000 to 3000 cm-1 spectral range is due to intrinsic 2-phonon absorption processes.
After the infrared beam emerges from the window focus it is normally transported under rough vacuum to the various spectrometer endstations. The relaxed vacuum requirements allow for significant flexibility in the design of this portion of the optical transport system. When the distances are not too large, or the spectral range of interest does not extend to wavelengths greater than 50 m, beam divergence from diffraction is not a serious issue and the beam can be collimated for transport. This can be accomplished with a simple spherical or parabolic mirror when only a portion of the source needs to be focused onto the sample to be measured. For infrared beamline extractions where the horizontal angular collection is much greater than the vertical, a pair of cylindrical mirrors (one tangential and one sagittal) can be used to collimate while reshaping the beam to an adequate size for filling the entrance pupil of the spectrometer. Optical designs for the focusing the majority of the extended source into one plane are discussed later in this section.
An example of a basic infrared extraction and optical transport system is shown schematically in Figure 15. It consists of a first plane mirror with a horizontal slot to allow x-rays to pass while collecting the infrared, a focusing optical element (ellipsoidal or toroidal) that shifts the beam vertically away from the synchrotron orbit plane and re-image the source at a focus near the CVD diamond window, followed by a set of cylindrical mirrors for shaping and collimating the beam so that it matches the entrance aperture (acceptance) of a FTIR- type infrared spectrometer. Additional plane mirrors are included to provide beam steering. Not shown is the synchrotron storage ring’s shield wall, which must have a penetration for the infrared beam to be brought out for use. This penetration (hole) is usually located well above or below the synchrotron orbit plane to minimize ionizing radiation emerging. Additional shielding is usually place around the penetration such that no additional radiological protection, such as a steel or lead-lined hutch, is required.
25 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 15: A typical optical design for an infrared beamline, starting from where the electrons emit from the storage ring orbit,
through a CVD diamond window and then being shaped and collimated for delivery to a conventional spectrometer.
Since the relevant infrared spectral range can span several decades in frequency, the opening angle for the dipole bend source varies considerable such that a single arrangement for the collimating optics optimally matches the spectrometer. The situation is different for pure edge radiation where the opening angle dependence on wavelength is minimal. However, there are few cases where pure edge radiation serves as the infrared source. In practice, the optics are usually optimized for the long wavelengths where intensity is weakest. However, this choice is not consistent with the optical components used for mid-infrared microspectroscopy for which a different optical arrangement is employed.
Nowadays, optical modeling software is commonly used for designing the optical extraction and transport system. This has the benefit for determining required accuracy for mirror surfaces as well as the tolerance to mis-alignment. These software packages may be solely for ray tracing or may have varying degrees of physical optics and wavefront propagation included. Examples include ZEMAX™, SpotX, Shadow and SRW. Note that most commercial optical design software packages do not include calculations of the synchrotron source itself, requiring it be appropriately modeled by the user. SRW develops the source using electron beam parameters relevant to the specific synchrotron radiation facility. This includes edge radiation for which the evolution of the source electric fields from the near-zone to the far-zone occurs over a length scale greater than the distance to the first mirror optic. The following example illustrates some of the different results obtained by conventional ray tracing (i.e. Spot X; Moreno and Idir 2001) and wavefront propagation (i.e. SRW) calculations as applied to an optical system for collecting and focusing 10 m wavelength dipole bend radiation. The following parameters have been used: electron beam energy =2.9 GeV, bend radius ρ= 7.14m and collected angular aperture of 55h x 38v mrad2 as defined by a plane mirror located 1.1 meters from the source. Note that the orbit arc serving as the source is 0.393 m long (deep), so the 1.1 m distance is measured from the mirror to the central point of the source arc. The collected light is focused using a toroidal mirror having tangential radius=3.54m and sagittal radius= 1.77m. When placed an effective distance of 2.31 m from the source arc center, that central segment is focused to a point 2.9 m from source. The Spot X and SRW calculated intensity profiles at the first mirror
26 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) and at the first focus are displayed in Figure 16 and show good agreement except for the well-focused segment (bright region) where diffraction becomes important.
Figure 16: Intensity profiles of a 10 m wavelength beam (1000 cm-1 frequency) at the first aperture (far-field, top panels) and the focus (lower panels). Left – Simulation using Spot X ; Right- Simulation using SRW.
In both calculations, the coma-like intensity extending to the right of the focused spot is a consequence of the extended source (the 0.393 m deep curved arc). Note that an ideal lens (paraxial approximation) would produce a replica image of the curved source arc, also oriented mostly parallel to the direction of propagation, with only one segment of the source being focused correctly onto an image plane oriented normal to the direction of propagation. Source segments nearer the lens will be converging toward a focus beyond the image plane while source segments farther from the lens will have passed through a focus before the image plane, in both cases giving the appearance of coma. This is equivalent to having a very limited depth-of-field. Now a real toroidal optical element is less than ideal and, under most conditions, will display true spherical aberration and coma, also yielding out-of-focus rays. Though imperfect focusing at an image plane would be due to both depth-of-field and true aberration effects, the term “aberration” will be used here to describe both. Note that this aberration effect increases as the square of the horizontal beamline aperture (see Figure 17).
27 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 17: Increased geometrical aberrations observed at the secondary source (first focalization) for different horizontal angles of collection caused by the extended curved source. The simulations have been carried out with SpotX, with a vertical collection angle of 30 mrad, and for a wavelength of 10 m. Note that the image has been scaled to match the angular collection. This large source depth makes it very difficult to properly collimate the entire beam, causing inefficient propagation and poor coupling with the instruments; shape and collimation are hardly maintained for beams propagating at several meters away from the last optical element, as is generally the case in almost all synchrotron facilities (Figure 18). This is less of an issue for microscopy at the diffraction-limit since only a small portion of the source arc can be focused to one spot. However, for techniques where an extended source is beneficial, delivering the light from the full source arc to a common focal plane is desirable. The next section describes some optical designs for managing this.
Figure 18: Intensity profile of a 10 m wavelength beam as sensed at various distances along its collimated beam path, starting from the last mirror in the optical system. Note the significant change in the illumination profile with distance. (Horizontal opening angle= 80 mrad).
Aberration-free optical designs: The photon source size results from the convolution of three terms: the geometrical aberrations produced by the circular shape of the electron trajectory (synchrotron radiation mode) as well as true aberrations of the optical system, plus the electron beam size and diffraction (Hecht and Zajac 1987). When the geometrical
28 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) aberrations are small, for example, for restricted beamline apertures or for very large wavelengths as in the far IR, the horizontal and vertical profiles of the photon source can be treated as Gaussian (see section 1 above), whereas for large extraction apertures the geometrical aberrations prevail and the profiles maintain the aberrations of the source shape. In this case, the horizontal profile of the source emission resembles the one obtained from reflection through a cylindrical mirror and retains the aberrations resulting from the circular shape of the bending magnet source. In the vertical direction, the profile is Lorentzian and is formed by the overlapping of all the vertical emissions produced at each point in the electron trajectory. Compensating for the dipole source’s curvature and depth was first addressed by Lopez and Schwarc (Lopez et al, 1976; Schwarc, 1977) in a design concept sometimes referred to as an isochronous mirror or “magic mirror”. This type of mirror was first realized (Kimura et al. 2001) in the optical design of an infrared beamline at the SPRing-8 synchrotron light source (Hyogo, Japan). This facility has a 39.3 m dipole bend radius such that a beamline with acceptance angles of 36.5 x 12.6 mrad2 (HxV) yields a 1.44 m long (deep) source. The resulting optical performance is in very good agreement with the simulations. It should be noted that the mirror’s surface profile is very complex, being non-spherical and lacking typical symmetries, requiring computerized machinery to produce. One of the drawbacks of such mirrors is the cost for fabrication and sensitivity to positioning and optical alignment. More recently, T. Moreno (Moreno 2015) has provided another solution consisting of a two-mirror system, one being cylindrical and the other conical. The two mirrors independently focus the horizontal and the vertical emission, with the conical mirror’s varying radius and focal length compensating for the large source depth. The mathematical details are summarized here, but can be found in (Moreno 2015) . Figure 19 shows the geometry for a source arc of length 2d with bending radius .
Figure 19: Geometry for horizontally focusing the a bending magnet source arc using a cylindrical mirror, as viewed from above (Moreno 2015).
Similar to the analysis of Lopez and Schwarc, the method consists of minimizing the path distance between two rays, one ray emitted tangentially from the center of the curved source, reaching the center of the cylindrical mirror where it is reflected to the image plane. The second ray is emitted from another tangent point along the source arc to reach the same image point after reflection from a mirror surface. In the figure this ray starts at a distance d from the central source point, and forms an angle relative to the central ray.
29 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
푝 By setting 푢 = , the value of the ratio source-to-mirror (p) and mirror-to-image (q ) can be determined by 푞 solving : 3p u(3u −1)− (1−u 2 )(1−u) = 0 {24} 2
The coma coefficient (for 휃 ≠ 휋/2), which should be null, provides the value of the grazing incidence(휃)
1 2 2 tan q = p 1− 3p {25}
and the radius of curvature is determined by
p2 1 1 2 + − = 0 {26} 2 p q Rsin Equation 24 has two solutions depending whether the curvatures of the mirror and the source trajectory are oriented in the same way ( > 0 and 푞 > 푝) like in Figure 18 or opposite ( and 푞 < 푝). As an illustration of an aberration-corrected optical system, considering the following case based on the Advanced Light Source (ALS), which is a 1.9 GeV synchrotron light source with 1.27 T dipole bend magnets (yielding a 4.95 m bend radius). An infrared beamline planned for collecting 69 mrad (H) and 17 mrad (V) would have a 0.343 m long dipole bend source. An additional constraint imposed by the storage ring’s mechanical design is that the horizontal focusing mirror (a cylinder used at angle-of-incidence much greater than 45°) need to be located at p= 2.2 m from the source. With these parameters, eqn. 24 yields: 32.2 u(3u −1)− (1−u2 )(1−u) = 0 {27a} 24.99 or
2 u(3u −1)− 0.666(1−u )(1−u) = 0 {27b} 푝 The behavior of the 푓(푢) versus 푢 = is shown in Figure 20, indicating two solutions: u = 0.45 and 3.4. 푞 Having the source and the mirror curvature oriented in the same direction requires 푢 < 1 and the solution 푢 = 0.45. This gives a value of q = 4.888 m for the distance of the cylindrical mirror to the focus point. The angle-of-incidence is found to be 휃 = 28°. Though the vertical aberration has not been corrected at this point, it is instructive to compare the performance against a more traditional toroidal optical system with a 45° angle-of-incidence (for the central ray) to yield a 90° reflection. For the same extraction geometry, a toroid with curvature radii of p = 2.2 m and q = 4.888 m would be used. The results for both are shown in Figure 21, clearly showing that most of the horizontal aberration has been removed with the toroidal mirror at 28° grazing incidence. Still, one can see the elongated shape of the first focus point, which is due to the uncorrected vertical aberration at this point.
30 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 20: f(u) versus u for the case of a bending magnet radius of 4.95 m and a first distance of the cylindrical mirror to the source of 2.2 m.
Figure 21: First focus point profile for a wavelength of 10 mm, considering a toroidal mirror with grazing incidence of 45°, p = 2.2 m, q = 4.9 m, (left) and a toroidal mirror at the same position but with a grazing incidence angle of 28° (right). Simulation performed using SPOTX software (courtesy T. Moreno).
Figure 22: Vertical source aberration scheme (left) and cone-shape mirror schematic (right), with the parameters accounted for in the reported formula.
This vertical aberration can be corrected using a cone-shaped mirror is proposed in (Moreno 2015).(Figure 22). In the above example, the position of the polynomial mirror to remove the vertical aberration has been
31 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) constrained due to the space availability at the beamline, due to the location of the various components inside the storage ring. One could only position such a mirror at 1.4 m from the source with a grazing incidence of 휋/2. A saggital cylindrical mirror with p = 1.4 m and q = 5.7 m in order to fulfill the relation p + q = 7.1 m (horizontal and vertical focusing at the first focus point) would have a radius of R0 = 3.179 m. To compensate the vertical aberration, a conical mirror has been calculated with a radius 푅(푥) = 푅0 ± 퐴 · 푥 · 푅0 where R(x) is the radius of curvature at a distance x from the center of the mirror. In the above example, A = 2.04x10-3 mm-1. Figure 23 provides a comparison of the intensity image produced at the first focus point for both the uncorrected vertical aberration case and for the fully aberration corrected case using a combination of cylindrical and conical mirror. Both are for a wavelength of 10 µm that determines the angular emission from the source itself. Note that diffraction effects are not included here.
Figure 23: First focus point profile, for a wavelength of 10 m, considering a toroidal mirror with grazing incidence of 28°, p=2.2m, q=4.9 m, (left) and a combination of tangential cylindrical mirror à 28° grazing incidence and a conical mirror located at 1.4 m from the source (right). The optimization of the conical shape has been achieved using SpotX software.
Such an optical arrangement has been applied successfully, for the first time, at the Brazilian light source (Moreno 2013, Freitas et al. 2018) using the optical design shown on Figure 24.
Figure 24: Optical design schematic installed at LNLS Infrared beamline. One cylindrical mirror and one conical mirror have been calculated and optimized for producing an aberration-free beam. The distance of each optical component from the source is given in millimeters.
The simulated beam profile and beam propagation have been calculated, and are shown on Figure 25. Note the performance improvement relative to the same set of illumination profiles shown in Figure 18.
32 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 25: Simulation of the intensity profile for a 10 µm wavelength at various locations along the collimated beam path. The corrected optics maintain a constant illumination profile following the last cylindrical mirror (M6 -- see Figure 24), and at several meters away from this last mirror. The experimental measurements are in very satisfactory agreement with these simulations (R.O.Freitas et al. 2018; Moreno et al, 2013)
Instrumentation Since the basic synchrotron source is spectrally “white”, nearly all applications involve a spectrometer system. The majority of such instruments are interferometers, commonly referred to as “Fourier Transform InfraRed” (or FTIR) spectrometers (Stuart 2004; Günzler & Gremlich 2002; Steele 2002). Commercial instruments are well-suited for use with the synchrotron source and their operation is effectively the same as for conventional thermal sources. This simplifies greatly the development and the operation of infrared synchrotron radiation beamlines. Spectrometers Spectroscopic interferometers have mostly superseded dispersive-type grating monochromators for broad- band infrared spectroscopy since the early 1980s. In an interferometer, the light intensity is measured as a function of the interferometer’s optical path difference, with a Fourier transform converting this to intensity versus wavelength or frequency. As a result, the technique is commonly referred to as “Fourier Transform InfraRed” (FTIR) spectroscopy and the instrument known as an “FTIR spectrometer”. Commercially available instruments are highly optimized and well-suited to use with the synchrotron infrared source. A general discussion of FTIR instruments is provided here. More details can be found in other references (see Griffiths and De Haseth 1986, Stuart 2004). A typical spectrometer is composed of an internal source (typically a thermal-type emitter), a Michelson-type interferometer, a sample compartment and a detector (Figure 26). Many also include components for introducing an external source into the optical path and for sending the light to an external experiment setup. The Michelson interferometer has a beamsplitter for separating the incident light into two separate “arms” where the light in each is retro-reflected back to the beamsplitter and recombined, resulting in interference. That interference affects whether the light continues on to the detector or is returned to the source, with the interference condition affected by the optical path difference d between the two arms. When d is zero, all wavelengths interfere constructively to yield an intensity maximum at the detector.
33 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 26: Schematic of a standard Fourier Transform Infrared (FTIR) spectrometer. External port is used to input the synchrotron beam. Analysis can be done inside the sample compartment, but the beam, after the interferometer, can also be directed outside for a sampling technique which requires more space, or towards an infrared microscope. In such a case, the detector is located outside the spectrometer.
With the reflecting mirror in one arm movable, d can be varied such that the intensity reaching the detector experiences a sinusoidal intensity dependence with period d/ or d·휈̅ . The recorded intensity signal as a function of path difference is known as an interferogram. The light entering the interferometer is typically not monochromatic, so the interference is a linear superposition of a continuum of frequencies. A Fourier transform of the interferogram signal converts the intensity versus path difference into intensity versus wavenumber. In practice, the movable mirror is continuously and repetitively scanned at a velocity on the order of 0.5 cm/s (for a path difference varying at 1 cm/s) such that intensity at 1000 cm-1 yields an interference modulation at 1 kHz, which is compatible with high performance, low noise AC amplifiers and detector systems. Another benefit of this modulation with the moving mirror is that the signal from the detector can be electronically filtered to reduce noise and control the spectral range of interest, e.g. for a mirror velocity where the optical path difference is changing at 1 cm/s, a band-pass filter with a low frequency cutoff of 100 Hz and a high frequency cutoff of 2 kHz would produce a spectrum with intensity limited to between 100 cm-1 and 2000 cm-1. Most commercial interferometers allow for a variety of mirror velocities such that the modulation frequencies can be adjusted to avoid other noise signals. This can be particularly beneficial for synchrotron storage ring sources where the mechanical and electrical environment may not be as controllable as in a research laboratory environment. Instabilities and other properties of the electron beam in the storage ring may also exist and result in noise at specific frequencies. With careful choice of the scanner velocity and electronic filters, the effects of such noise can be minimized. As indicated in Figure 2, a sample at T = 295K is also an emitter of infrared light. Therefore, except in cases where that emission is to be measured, the sample is placed between the spectrometer’s interferometer and the detector. Though the thermal emission still reaches the detector, it is not modulated and therefore does not appear in the spectral signal.
34 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Since the synchrotron source is truly broadband, it can be used for spectroscopy from the UV through the visible, infrared and into the millimeter wavelength range. An FTIR spectrometer is not automatically capable of spanning this very wide spectral range due to the optical performance of the beam splitter and sensitivity of the detector, so these are designed to be interchangeable. For beamsplitters, a thin partially reflecting coating on a transparent substrate is typical for the UV, visible, near and mid-infrared. A thin layer of Ge on KBr is the most common beamsplitter for the mid-infrared. Free-standing mylar films can be used for the far- infrared as well as high dielectric materials such as Si and Ge. These are almost always provided by the spectrometer manufacturer. A variation of the Michelson design for improved performance at long wavelengths is the Martin-Puplett interferometer (Martin & Puplett 1970). A polarizer serves as an efficient beamsplitter in combination with roof mirrors at the end of each interferometer arm for rotating the polarization by 90 degrees, directing more of the light toward the detector when recombined at the beamsplitter. Such instruments have been used at UVSOR-III and previously at NSLS-VUV for both studies in condensed matter physics and coherent synchrotron radiation. Other interferometer types have been used with synchrotron radiation, including the lamellar grating type (Henry and Tanner, 1979). Spectral Resolution In contrast to a monochromator where optical slits are used to control the spectral resolution, this quantity is determined by the interferometer’s maximum path difference. This can be visualized using two monochromatic sources of light at frequencies 휈̅ and 휈̅+훿휈̅ , each yielding a sinusoidal intensity signal at the interferometer’s detector. In order to discriminate the two, the path difference must reach 1/훿휈̅. Instruments capable of 10 meters (or more) maximum path difference are commercially available, achieving a basic spectroscopic resolution of 훿휈̅ = 0.001 cm-1 (0.124 eV). An additional requirement is that light rays from different source points not result in path differences that would disrupt the required interference contrast. This issue is resolved by a source aperture known as the Jacquinot stop (Jacquinot 1954, 1960). To achieve a resolution of 훿휈̅ at 휈̅, the diameter d of this aperture must fulfill 2 d 2 f {28} where f is the focal length of the spectrometer’s source collimating optic. Assuming a 40 cm focal length optic and a far-infrared frequency of 휈̅ = 100 cm-1, the aperture requirement for a resolution of 훿휈̅ = 0.001 cm-1 is an aperture diameter of d 0.36 cm, which is only a factor of 2 larger than the diffraction limit for f/8 optics. This illustrates how high-resolution infrared and far-infrared spectroscopy is a throughput-limited technique that benefits from the very high spectral radiance (brilliance) of the synchrotron infrared source. High spectral resolution spectrometers are mandatory instruments for accurate measurements of the rotational and vibrational modes (and their combinations) of molecules in the gas phase where many narrow spectral features exist in close proximity to each other. A long arm for the moving mirror of the interferometer achieves the high resolution for which a few commercial instruments are available. A resolution of 0.00053 cm-1 has been achieved at the Swiss Light Source by a group from ETH, using a prototype Bruker IFS-125 interferometric spectrometer (Quack & Merk 2011). Because the synchrotron source is pulsed (cf. section on Electron Bunching), the spectral output is not necessarily a true continuum. For a single electron of fixed energy traveling on precisely the same orbit, the
35 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) light is emitted in pulses at the orbit frequency and the resulting spectrum would be a frequency comb up to the critical photon energy. However, each electron in a bunch moves longitudinally on a length scale given by the bunch length, which is much larger than most wavelengths of interest, thus disrupting the perfect periodicity and resulting in a continuum source. When the bunch length itself is smaller than the wavelength of interest, the periodicity is recovered. This is the same criteria as for coherent emission, i.e. unless the entire bunch is moving relative to its neighbors, coherent emission is usually accompanied by a frequency comb. When such a comb exists, performing high resolution spectroscopy is affected and potentially exploited. Spectromicroscopy Of all the techniques where the high brilliance of the synchrotron source is exploited, mid-infrared spectromicroscopy (or microspectroscopy) is the most prevalent. In its typical configuration, the IR microspectrometer is an FTIR spectrometer system followed by an infrared compatible microscope and detector. Figure 27 shows a schematic for a standard configuration with the microscope design based on a conventional optical microscope. In order to avoid chromatic aberrations across the entire infrared spectral range, all-mirror (catoptric) objectives and condensers, based on the Schwarzschild design, are used. These objectives provide diffraction-limited performance in the infrared and perform sufficiently well at visible wavelengths to provide useful viewing and navigating around the sample of interest. For this, the microscope instrument includes either switchable optics (between visible viewing and infrared measurement) or dichroic optics that allow simultaneous viewing and measuring.
Figure 27 : Schematic for a scanning infrared micro- spectrometer system using a single-element detector and the possibility for confocal operation where aperturing is used both before and after the sample. (adapted from Carr, Chubar & Dumas 2007)
The Schwarzschild objectives are available in a wide range of magnifications (up to 74X) and at high numerical apertures (up to NA = 0.71), the latter being important for achieving the best spatial resolution since the diffraction-limited spotsize is proportional to /NA. The choice of objective is usually determined by
36 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) constraints on working distance as needed to accommodate windowed sample cells or other experimental components such as cryostats. In the mid-IR, these objectives deliver diffraction-limited performance over an area extending 100–200 μm from the optic axis. The design causes the central portion of the objective’s aperture to be obscured, losing up to 25% of the optic’s effective area. This obscuration leads to significant diffraction effects when compared with the Airy pattern for a full-aperture conventional microscope objective, as illustrated in Figure 27 (Carr et al. 2007). Though the central maximum for the Schwarzschild (lower left) is narrower than for Airy (upper left), there is a substantial ring-shaped first-order diffraction maximum that reduces contrast and can lead to imaging artifacts. When diffraction-limiting apertures are placed at focal points before the condenser and after the objective, the optical system is considered “confocal”, improving both the spatial resolution and contrast (right side diagrams in Figure 28). Achieving these intensity profiles mandates that the objective’s entrance aperture (“pupil”) be fully and homogeneously illuminated. Underfilling causes the diffraction peak to broaden while the effect of the central obscuration becomes more important. Overfilling results in a loss of intensity. For mid-infrared molecular spectroscopy (as used for chemical identification) the so-called “fingerprint” spectral range around 1200 cm-1 is most important, so the optical system is usually optimized for that range. As noted earlier, moving the specimen through a micro-focused IR beam in a raster-like fashion performs microspectroscopic imaging with a single-element detector. In particular, a complete spectrum is collected individually at each point of the specimen to be imaged, with the spot size controlled by apertures in combination with diffraction and the wavelength. The sampling step size is usually set such that the spots overlap.
Figure 28 : Calculated detection profiles, based on optical point
spread functions, comparing full aperture (Airy, top row) and Airy Schwarzschild type (bottom row) objectives for the same wavelength and numerical
aperture (NA). A 25% central
obscuration was assumed for the Schwarzschild. Both the single
aperture (left) and confocal aperture (right) cases are shown, assuming matched optics. Note the large first-order diffraction ring for the single Schwarzschild
Schwarzschild relative to the Airy pattern and
also the confocal improvement.
Single Confocal
Desirable characteristics of the resulting image are: (1) high signal to noise at each pixel, (2) good lateral spatial resolution and (3) good contrast fidelity (Carr et al. 2007) (i.e. the observed change in a particular spectral intensity from point to point accurately matches the specimen’s actual composition). The spatial
37 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) resolution is diffraction-limited as has been discussed by (Carr 2001).The measured resolving power has been shown to be in good agreement with diffraction theory, including a 30% improvement for a confocal optical arrangement. Carr (Carr 2001) has also shown that confocal setup leads to better image contrast. The diffraction limit is achieved when the instrument’s apertures define a region having dimensions equal to the wavelength of interest. In the case of the confocal arrangement, i.e. apertures at the conjugate focii of both objective and condenser, the diffraction limit is close to /2. Imaging Microspectroscopy The process of single-point, raster scanning of a material to produce an infrared spectroscopic image becomes impractical for regions much larger than about 25 by 25 pixels due to the overall scanning time (on the order of 10 hours assuming a 1 minute measurement time per pixel). Starting in the mid 2000’s, mid-infrared array detectors based on MCT (Hg1-xCdxTe) photodiodes with 128 by 128 pixels became available to the research community. These detector arrays are often referred to as “focal plane arrays” (FPAs) or “staring arrays”, the latter indicating that each pixel collects light over some finite period of time, after which the resulting signal for each is read-out by appropriate multiplexing electronics. The full array must be read out for each interferometer path difference, which requires significantly slower mirror velocities. Additionally, the spectral range has been limited to above 850 cm-1 by the Other detector array technologies are discussed later in this chapter.
Figure 29: Schematic for an imaging infrared micro- spectrometer system using a focal plane array (FPA) detection system. Note that the small apertures for limiting the field-of- view are either opened or simply removed so that infrared illuminates the full area to be imaged. (Adapted from Carr, Chubar & Dumas 2007)
The schematic in Figure 29 shows a simplified layout for an IR microspectrometer based on such an infrared array detection system. As before, the optical system uses Schwarzschild objectives, but the apertures for constraining the microscope’s sensitive location are left open, that is, they do not provide any spatial discrimination. Thus, the microscope’s first objective illuminates a rather large area, and this illuminated
38 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) region is then imaged onto the FPA detector by the second Schwarzschild objective. Spatial discrimination is provided by the individual pixels of the detector, each one serving as its own ‘aperture’. Note that there are no field-defining apertures so this system is not the confocal in the sense described in the previous section. Assuming optical aberrations and other issues are not an issue, the infrared from a point in the specimen Therefore, when imaged onto the detector’s elements (pixels), each point in the specimen produces the diffraction pattern shown in the lower-left panel of Figure 28. Though the images obtained with FPA systems are of high quality, they are not an exact representation of the specimen’s properties. Instead, the images are degraded due to limitations of the optical system and other factors (detector fidelity, phase correction, apodization, etc.) (Carr et al. 2007). The most significant limitation for high spatial resolution imaging, however, is the diffraction of light, and it is discussed in more However, the large number of pixels (128 by 128 being typical) allows the specimen’s infrared image to be spatially oversampled with high signal- to-noise so that mathematical deconvolution can be applied to correct some of the diffraction effects. Detectors This section focuses on the detector types currently in use for synchrotron infrared and also identified some specific applications where new detector systems will be needed. In contrast to other spectral ranges, detector technology for infrared is well developed and extensive information on this subject can be found in the literature (see Rogalski 2003; Rogalski 2002). The ideal detector has a perfectly linear response, zero intrinsic noise, an arbitrarily fast response time, and responds over the full spectral range of interest. Such a detector does not exist, but one can select from a large variety of well-developed infrared detector technologies to fulfill particular measurement requirements in most cases. Since the power levels to be detected are not substantially different from those of the thermal sources in conventional infrared spectrometers, the same types of detectors are typically used. In general, detectors for the near-IR, visible and near UV are photodiodes (photovoltaic) based on III-V (e.g., GaP, In1-xGaxAs, InSb) or silicon semiconductors. In the mid-IR, photoconductive and photovoltaic Hg1-xCdxTe (“MCT” or “HCT”) detectors are the most common. All of these have a low-frequency cutoff determined by the material’s semiconductor band gap which, for the alloy systems, can be tuned by varying the composition (within limits, e.g. when the detector is made as a thin structure grown on a bulk substrate requiring lattice matching). For MCT used in mid-infrared spectroscopy, a value of x slightly less than 0.2 yields a low-frequency cut-off near 600 cm-1. Detector types change from photovoltaic and photoconductive in the near and mid-infrared to thermal for the far-IR. In the millimeter spectral range, which includes coherent emission, devices that sense the electric field such as Schottky diodes or electro-optic sensing can also be employed. In order for the detector to perform optimally, thermal excitations need to be minimized. This is achieved by operating the detector at a temperature such that kT << hc휈̅cutoff. i.e. keeping thermal energies below the lowest detectable photon energy. This naturally implies that detectors for the far-infrared require operating at cryogenic temperatures (T = 4.2K or less). The detectivity D* is the main parameter characterizing the signal to noise performance of a detector type, and more details can be found in the article of Rogalski (Rogalski 2003). The detectivity of several infrared detector types are shown in Figure 30. A particular challenge for mid and far-infrared detectors is to manage the T=300K background as an unintended source (see Fig 3). The intrinsic thermal fluctuations of this background represent a source of noise that sets a fundamental limit on a detector’s performance. This limit
39 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) is indicated by the dashed curves in Figure 30. Another useful indicator of a detector’s performance is the Noise Equivalent Power (NEP), which is defined as the power that yields a signal-to-noise ratio of 1 when measured at a 1 Hz rate. Values for NEP range from 10-11 W/Hz1/2 to below 10-14 W/Hz1/2, depending on the detector’s operating temperature and spectral filtering to limit background noise.
Figure 30: Comparison of the detectivity D* of various commercially available infrared detectors when operated at the indicated temperature. Chopping frequency is 1000 Hz for all detectors except the thermopile (10 Hz), thermocouple (10 Hz), thermistor bolometer (10 Hz), Golay cell (10 Hz) and pyroelectric detector (10 Hz). Each detector is assumed to view a hemispherical surrounding at a temperature of 300 K. Theoretical curves for the background-limited D* (dashed lines) for ideal photovoltaic and photoconductive detectors and thermal detectors are also shown. PC—photoconductive detector, PV—photovoltaic detector, and PEM—photoelectromagnetic detector. From (Rogalski 2003) with permission.
In synchrotron infrared facilities, especially for the mid-infrared region, the most widely used detector is the II-VI semiconductor alloy Hg1-xCdxTe, operated as either a photoconductor or in a photodiode configuration (for improved speed of response and linearity). Somewhat lower frequencies (to about 320 cm-1) can be reached using boron doped silicon extrinsic photoconductors (Norton 1991). When signal-to-noise and a slow response time are not a limitation, pyroelectric detectors such as deuterated triglycine sulfate (DTGS) offer a very convenient solution that can perform over a very broad spectral range. For long wavelength spectroscopy, commonly called the far-Infrared or THz, thermal detectors such as the liquid helium cooled bolometer are used. These detectors can achieve background limited performance when
40 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) the input spectral range is properly filtered. The long wavelength limit is usually determined by the finite size of the detector’s input aperture and internal optics. These detectors operate based on the temperature- dependent resistance of a heavily doped semiconductor or a superconductor within its transition region. The absorbed far-infrared causes a temperature increase that changes the detector’s resistance. That resistance change is then sensed as a voltage under bias. Typical semiconductors are doped silicon or germanium. Most bolometers are designed for a response time of a few milliseconds. Faster response can be achieved using superconductors (Shurakov & Lobanov 2015) or InSb where the far-infrared is absorbed initially into the electron system, yielding a fast response that occurs before the heat is thermalized to the atomic lattice as phonons. The above discussion concerns single-element detectors as used for conventional spectroscopy or microscopic imaging over limited areas via raster scanning of the specimen through a focus. In those cases, infrared detectors exist for all spectral ranges of interest. This is not the case for spectral imaging using commercially available 2D detector arrays that reach into the far-infrared, i.e. below 800 cm-1. Some technology does exist in the astronomy communities, but these are often high-cost, custom devices built for specific installations. Beyond the Diffraction Limit: Towards Sub-Wavelength and Nanospectroscopy The chemical specificity that FTIR techniques provide serves as a powerful probe, but has been constrained by diffraction and the wavelength of infrared photons ( 10 microns). The challenge is to bring this power to the nanometer scale i.e., well beyond the diffraction limit. Such a capability for sensing chemical and physical properties with nanoscale spatial resolution is important for gaining fundamental insights into both natural and engineered heterogeneous materials and systems. The fundamental properties of life occur at the sub-micron scale where chemical signals and macromolecular conformational changes are ultimately in charge of how life progresses at the whole organism level across the biosphere. Similarly, nanoscale differences engineered into materials can change critical parameters in charge of superconductivity, band gaps, magnetism and other key macroscopic uses of these materials. And the nanoscale porosity of naturally occurring minerals greatly affects their properties in the sub-earth environment and play important roles related to oil and gas extraction and carbon sequestration. The next few sections describe various developments that use the intrinsically high brightness of the synchrotron IR source to overcome the diffraction limit while pushing the frontiers of imaging science. Some exciting scientific applications enabled by these technical developments are described later in this chapter. Array Detector Imaging and Oversampling Recently, the development of commercially available focal plane array (FPA) detectors has enabled rapid FTIR imaging over larger fields of view. The originally proposed design (Carr, 2007) was exploited in the IRENI beamline setup at the Wisconsin SRC by using 12 synchrotron IR beams to fully cover the entire array and enable high s/n imaging with fields of view greater than 100 x 100 m2 (Nasse et al. 2011). A schematic of the beamline layout is shown in Figure 31.
41 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 31: (a) Schematic of the IRENI setup. M1–M4 are mirror sets. (b) A full 128 × 128 pixel FPA image with 12 overlapping beams illuminating an area of ∼50 μm × 50 μm. Scale bar, 40 μm. (c) A visible-light photograph of the 12 beams projected on a screen in the beam path (dashed box in a). Scale bar, 1.5 cm. The footprint of the each “beamlet” exhibits a shadow cast by a cooling tube upstream, which is not shown in a. (d) Long-exposure photograph showing the combination of the 12 individual beams into the beam bundle by mirrors M3 and M4. Scale bar, 20 cm. (Nasse 2011).
The use of an FPA detector also allows using higher numerical apertures in the IR microscope to yield a projected pixel resolution of less than 1 x 1 m2, which is beyond the diffraction limit for all mid-IR wavelengths. Use of a measured point spread function (PSF) and deconvolution of an image acquired with oversampled resolution allows a marginal improvement in resolution beyond the Abbe limit (Mattson 2012, Stavitski 2013). Figure 32 shows the resolution enhancement achieved on test samples at IRENI (Mattson 2012) and Figure 33 shows a biological tissue samples imaged with an FPA illuminated with 4 beams at the NSLS from reference (Stavitski 2013). Figure 32: Three polystyrene beads dispersed in a 10 micron thick polyurethane film imaged with the IRENI beamline. On the right is the original unprocessed image of the 3020 cm-1 aromatic CH stretching peak showing two beads close together and a third near the bottom of the image. Right image is the deconvoluted image showing clearly better spatial resolution. From Mattson 2012.
42 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 33: FTIR imaging with a globar vs multiple synchrotron beams. (a) Optical micrograph of the mouse spinal cord cross-section stained with eosin Y. Scale bar is 100 μm. (b) FTIR images showing the ratio of integrated absorbance for the C–H stretch (3000– 2800 cm–1) spectral regions acquired with the globar and linear array detector (6.25 × 6.25 μm size); (c) the same data set as in panel (b) interpolated onto a mesh with 0.54 μm spacing; and (d) same area scanned using synchrotron and FPA instrument (0.54 × 0.54 μm pixel size) showing much more fidelity. Note that panels b–d are plotted on the same color scale. (From Stavitski 2013).
Scanning Probe systems The combination of scanning probe systems such as Atomic Force Microscopy (AFM), which have tip-based imaging resolutions in the nanometer scale based on the physical size of the tips, with the chemometric process of synchrotron-based FTIR spectroscopy is a powerful combination and new imaging and spectroscopy modality on a truly nanometer scale. There have been several approaches to accomplish this combination. One that has worked particularly well with the broad spectral bandwidth and high brightness of a synchrotron IR source is scattering-type Scanning Near-Field Optical Microscopy (s-SNOM). In s-SNOM free space IR light is focused and scattered by a conducting AFM tip and is detected in the far-field with a standard IR detector. This technique provides spatial resolution equivalent to the tip apex radius, often around 10 nm, independent of the wavelength of light (Knoll 1999, Keilmann 2004, Muller 2015). It can therefore function in the microwave, IR and visible by using appropriate tip materials and detectors. Another technique uses photothermal imaging in the near field, and is known as AFM-IR. It provides a direct coupling of the thermal absorption of the incoming IR light pulse and an AFM tip which measures the amount of thermal expansion (Dazzi 2005). The spatial resolution of this technique is tied to both the tip apex size and the thermal diffusions within the sample, so it is typically better than 100 nm (Feng 2014). These new scanning probe methods improve the spatial resolution of infrared imaging and spectroscopy by 100 to 1000-fold beyond the diffraction limit. The signals from these nano-scale techniques, however, are weak with large backgrounds that need suppression and therefore these near-field techniques are often limited by the IR source characteristics. For broadband infrared spectroscopy covering a typical mid-IR FTIR spectrometer spectral range, the high brightness of a synchrotron IR beamline enables these near-field techniques to be truly broadband spectral tools providing chemical insights at the nanometer scale. Synchrotron IR light in combination with a scanning probe began in 2002 using a photothermal probe and specially designed AFM head at the Daresbury Synchrotron Light Source (UK) (Bozec 2002). They obtained improved spectral contrast on a polypropylene/polycarbonate sample compared to a thermal IR source. In 2004, Schade et al. (Schade 2004) demonstrated near-field THz spectroscopy and imaging using coherent synchrotron radiation at the BESSY synchrotron in Germany. Using a tapered cone optic with an antenna to avoid cutoff effects, they were able to achieve /12 at 12 cm-1, and performed imaging of biological tissues with this sub-diffraction resolution (Schade 2005). These pioneering measurements were among the first to
43 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) exceed the diffraction-limit and demonstrated that the design of the probe was important to obtain sufficient signal throughput. In 2012, Ikemoto et al. (Ikemoto 2012) achieved 300 nm resolution at 1000 cm-1 on a gold/silicon test structure using a scattering type near field setup, s-SNOM. In 2013, Herman et al (Herman 2013) used the Metrology Light Source in Germany with an asymmetric Michelson interferometer and a commercial s-SNOM instrument (Neaspec Gmbh) to achieve better than 100 nm spatial resolution. D’Archangel et al (Archangel 2013) used a modified Veeco/Bruker Inova AFM in combination with infrared at the Advanced Light Source to measure meta-structures with better than 100 nm spatial resolution. After incorporating a commercial FTIR (Thermo-Scientific) with this AFM, custom modified to run in asymmetric Michelson configuration, Bechtel et al. demonstrated a spatial resolution of better than 40 nm (Bechtel and Muller 2014), and coined the term Synchrotron Infrared Nano Spectroscopy (SINS). Near-field IR techniques have been demonstrated more recently at Synchrotron SOLEIL (Peragut 2014) and the National Laboratory for Synchrotron Light (LNLS) in Campinas, Brazil (Pollard 2016, Freitas 2017). Several more near-field nanospectroscopy instruments are planned for other synchrotron facilities worldwide. Figure 34 shows a generic schematic of a SINS experimental setup, and has been implemented with commercial instruments (Hermann 2013, Freitas 2018) or by customizing individual components (Bechtel 2014). In SINS, the incident synchrotron IR light is focused onto a conductive AFM tip which is in tapping mode in nanometer proximity to the sample. The conductive tip effectively acts as an optical antenna and its nanoscale tip apex becomes the source of scattering the light from the far-field into the sample and back out. To first approximation, the spatial resolution of the technique is independent of wavelength and is only limited by the tip apex radius, which can be 10 nm.
Figure 34: A schematic of a SINS experiment. Synchrotron light from an IR beamline enters an asymmetric Michelson interferometer where a beamsplitter (BS) directs half of the light to the tip of an AFM and the other half to the moving mirror. The light scattered back from the tip is recombined with the light from the moving mirror at the beamsplitter and is then sent to the IR detector. A lock-in amplifier demodulates the signal using a
harmonic of the tapping frequency, νt. Resultant interferograms as a function of moving mirror position can be converted into the real and imaginary parts of the sample spectrum. In order to extract the weak signal from where the tip apex and sample are interacting locally while suppressing the large background signal due to light reflecting from the overall tip and sample, a modulation technique is used. The AFM is operated in tapping mode, or non-contact mode, such that the tip-to-sample distance oscillates at a frequency t. The dependence of the near-field interaction on this distance is highly non-linear, resulting in harmonics of t being generated. The scattered signal intensity is demodulated using
44 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) a lock-in amplifier at one of the harmonics (for example at 2t, 3t, etc.), with higher harmonics yielding improved contrast of spatial variations, albeit at the expense of total signal strength. Secondly, by placing the s-SNOM setup within an asymmetrical Michelson interferometer setup, one benefits from heterodyne amplification of the weaker scattered near-field signal with the stronger reference arm beam (Huth 2011, Huth 2012). The self-homodyne signal is constant for a single AFM tip position, so by AC coupling via modulating the tip to sample distance in tapping mode, this self-homodyne signal is removed and the result is an interferogram that can be Fourier-transformed to obtain the complex near-field spectrum. The asymmetric configuration allows determination of both the amplitude and phase components of the sample response. For molecular resonances the amplitude response shows dispersive line shapes whereas the phase response yields Lorentzian-like line shapes. By properly modeling the tip-sample interaction, on can extract the complete dielectric response without the need for Kramers-Kronig transformations (McLeod 2014, Govyadinov 2013, Cvitkovic 2007). To a good approximation the imaginary component of the scattered signal, Im[, is proportional to the absorption coefficient of thin molecular films (Huth 2012), meaning they can be directly compared to far-field transmission spectra including FTIR spectral libraries. The spectral range that’s covered by a SINS experiment is limited by the choice of beamsplitter and detector, not by the source since synchrotron bend magnets cover from the far-IR to x-rays. Most mid-IR applications use a germanium coated KBr or ZnSe beamsplitter that have low-frequency cutoffs around 400 and 500 cm-1, respectively. An MCT photoconductive detector with a low-frequency cutoff around 700 cm-1 gives the highest sensitivity, but a lower sensitivity wide-band MCT can be employed to reach to 500 cm-1. For far-IR measurements, a different beamsplitter and detector combination must be employed. Beamsplitters made of KRS-5 can extend the spectral coverage down to about 200 cm-1, and a Si beamsplitter functions to below 10 cm-1. Typical far-IR detectors, such as liquid helium cooled bolometers, typically have too slow a response time (bandwidths around 1 KHz) to respond to the tip modulation frequencies used in SINS. Khatib et al. (Khatib 2018) have demonstrated using a liquid helium cooled Ge:Cu detector with a low- frequency cutoff around 330 cm-1 (Figure 35). Other impurity doped germanium detectors and advances in speeding up bolometer response times offer the possibility of extending the range of applications further into the far-IR. Development efforts are presently underway to incorporate higher speed bolometer-type systems into AFM-based near-field far-IR nanospectrometers to extend the spectral range to below 100 cm-1.
Figure 35: The measured second harmonic signal in a SINS setup at the ALS with a typical mid-IR setup (black line) and an extended far-IR choice of detector and beamsplitter (red line). The signal magnitudes have been scaled to the same maximum value for comparison. From Khatib 2018.
45 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Applications Spectroscopy using Non-Coherent Far-IR Synchrotron Radiation Solid State Physics Synchrotron infrared beamlines have been used for studying a number of exciting condensed matter systems from high temperature superconductors, to VO2, to semiconductors, and to graphene. Several studies have been carried out and are on-going in facilites where the far-IR capabilities are thoroughly exploited by appropriate detectors, spectrometers including beamsplitters, and sample environment. Examples are the terahertz reflectivity measurements on SrTiO3 crystals (Nucara et al. 2016) and the determination of a band structure asymmetry of bilayer graphene (Li et al. 2009). Optical conductivity has been studied using far- infrared ( THz) synchrotron reflectivity (Lo Vecchio et al. 2014; Autore et al. 2014; Mirri et al. 2012; Pellicer- Porres et al. 2013; Pellicer-Porres et al. 2011) among others. There exists a vast literature of the far-IR spectroscopy for solid states physics. Gas phase Among the first usages of the synchrotron brightness advantage, high spatial resolution spectroscopy of condensed-phase samples was exploited. MAX-Lab in Sweden (Nelander & Sablinskas 1995; Nelander 1993) and LURE in France (Roy et al. 1993) pioneered high-resolution gas-phase IR spectroscopy , since the highly collimated source provides a marked advantage for high resolution spectroscopy. The synchrotron source has been found to replace the usual thermal source in a Fourier transform IR spectrometer, giving an increase of up to two (or even more) orders of magnitude in signal at very high-resolution. This is due to the fact that Fourier transform spectrometers which are based on the Michelson interferometer principle, need smaller entrance apertures for higher resolution, just as grating spectrometers need narrower slits. The quality of a spectrum depends on the spectrometer, not the source, and it is already possible to obtain excellent results using conventional thermal sources. It is worth noting that excellent results can be obtained by using specifically dedicated spectrometers, e.g. using very long travelling distance of the moving arm of the interferometer for much higher resolution (≤ 0.004 cm-1). It is only at very high resolution that the synchrotron source becomes really advantageous (Carr, 2008). For most infrared spectroscopy studies, the achievable resolution is limited by the Doppler width of the sample molecules. Three facilities have dedicated gas-phase infrared beamlines : Canadian Light Source (May 2004), Australian Synchrotron (Creagh et al. 2006) and SOLEIL (Roy et al. 2006). McKellar has summarized the advantage of using the synchrotron source for high resolution spectroscopy in gas phase, as well as the most important highlights in this field in a recent article (McKellar 2010). Several gas cells are made available at infrared synchrotron high-resolution stations and are constantly upgraded ; for example, an elegant cryogenic long path cell with variable optical path lengths (Kwabia Tchana et al. 2013) and temperature control in the region around 165K. Doppler-limited spectra of the Nu3+Nu5 combination of bands of SF6 have been obtained recently (Faye 2018). Nuclear Spin 1 16 Symmetry Conservation in H2 O was investigated by Direct Absorption FTIR Spectroscopy of Water Vapor Cooled Down in Supersonic Expansion (Georges et al. 2017; Cirtog et al. 2011).
46 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Surface Science Bonding between adsorbed molecules and substrates has been at the heart of the identified potential of far- IR spectroscopy using synchrotron light sources. Most of the vibrational bands associated with these bonds lie in the far-IR region of the electromagnetic spectrum. Accessing such informations in this spectral region was very difficult (Engström & Ryberg 2001) due to the weakness of the thermal source and its low brightness, which is needed because grazing incidence geometry is mandatory in order to amplify the electric field at the surface of the metallic substrate. The main initial objective at the beginning of the exploitation of synchrotron far- infrared photon beams was to study the bonding between adsorbates and substrate (mainly metallic).Thorough studies have been performed on Cu and Pt surfaces (Hirschmugl et al. 1990; Dumas et al. 1997; Surman et al. 2002; Baily et al. 2003). Other studies identified the bonding nature of organic molecules on metallic surface (Humblot et al. 2003) . Vibrational dynamic studies are possible only by using the synchrotron light source. At the beginning of the 90’s, the interest of the study of the low energy modes was renewed when Persson suggested that frustrated translational modes of molecules or atoms are the key to the frictional force induced by the adsorbate on the metallic surface (Persson 1994). A direct relation with resistivity change was suggested and verified experimentally with the synchrotron far infrared source by simultaneous measurements of d.c. resistivity and IR reflectivity changes on the CO/Cu system (Hein et al. 2000; Hein et al. 1999; Dumas et al. 1999). There is currently no beamline dedicated to surface science, although a science proposal has been developed to include this capability at NSLS-II. Far-Infrared Spectroscopic Ellipsometry Far-infrared ellipsometry is another throughput limited measurement method that benefits from the high brightness of the infrared synchrotron radiation source (Kircher 1997). The method is used for directly extracting the optical response functions for a material through analysis of the reflected signal at angles of incidence near to Brewster’s angle. An advanced version, based on the Mueller-matrix formalism, was developed and implemented at NSLS (Stanislavchuk 2013) for the study of multiferroic and other materials where the optical response can contain both electric () and magnetic () contributions to the refractive index. Microscopy at limited diffraction spot size Material science Some interesting ways in which the properties of infrared synchrotron radiation have been used for studying samples important to solid state physics, materials science, catalysis, and soft matter such as polymer science as been reviewed in (Martin & Dumas 2012).Since then, materials science research continues to be a strong player both pushing technical developments and generating exciting and high-profile results, not only in microscopy but also in nanospectroscopy. Extremes conditions High-pressure synchrotron IR spectromicroscopy represents an ideal coupling of diamond anvil cells (DAC) and IR radiation in the entire spectral region (THz to mid-IR) for spectroscopic studies under extreme conditions such as static and dynamic compression and at variable temperatures. The method was initiated at NSLS by the Hemley group (Hemley, 1999) and is now an important technique at several synchrotron radiation facilities. Several examples can be found in (Martin and Dumas 2012).
47 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Earth and planetary science Synchrotron Fourier transform infrared microspectroscopy has provided paramount information regarding the molecular structure of organic and inorganic components for chemical characterization of geological samples, being, in addition non-destructive for the characterization of minute microfossils, small fluid and melt inclusions within crystals, and volatiles in glasses and minerals. SR FTIR examination of the interplanetary durst particles, and has demonstrated its ability to detect organic matter in small particles within picokeystones from the Stardust interstellar dust collector (Keller 2006). (Bechtel et al. 2014; Martin et al. 2010) Archaeology The study of cultural heritage and archaeological materials has benefited a lot from the synchrotron infrared microscopy. The range of materials that have been studied is very broad, ranging from painting materials, stone, glass, ceramics, metals, cellulosic and wooden materials in relation with the diversity of samples found at archaeological sites, museums, historical buildings, etc. The main objectives were the study of the alteration and corrosion processes, the understanding of the technologies and identification of the raw materials used to produce archaeological artifacts and art objects and, the investigation conservation and restoration practices. (Bertrand et al. 2012; Cotte et al. 2009; Salvadó et al. 2005) Biology Biology and biomedical studies represent a most important user community at many infrared beamlines facilities (Miller and Dumas 2010) and include studies of biological samples in situ (Vaccari et al. 2012; Mitri et al. 2014; Loutherback et al. 2016). The high spatial resolution and higher spectral quality have brought a lot of interest for single cells, tissues, and subcellular imaging in biology. In addition, the synchrotron infrared beam induces a negligible sample heating, and opens the way of in-vivo studies, without the beam damage issue faced with X-ray beams (Martin et al. 2001) . Beyond the determination of atomic resolution structures, there is the daunting task of understanding how macromolecules assemble and function inside a living cell, where thousands are simultaneously interacting in a complex biochemical environment. Infrared spectroscopy has been identified as one of the key approaches for this field of ‘functional biology’. Based of the relevant biomarkers, there are a lot of information contained in FTIR spectra : protein secondary structure (Amide I (1600–1700 cm-1) and Amide II (1500– 1560 cm-1), features arise primarily from the C and C–N stretching vibrations of the peptide backbone, respectively. The infrared signature of the protein has been shown to be particularly sensitive to protein secondary structure based on the vibrational frequency of the Amide I (C = O) band, which is affected by different hydrogen-bonding environments for 훼-helix, 훽-sheet, turn, and unordered structures. (for a review, see (Miller & Dumas 2010) ). In addition to protein structure, FTIR simultaneously provides information about sample biochemistry, with predominant absorption features of the lipid spectrum (region 2800–3000 cm-1), ester C=O groups in the lipid (strong band at 1736 cm-1), nucleic acid spectra have C-O stretching vibrations from the purine (1717 cm-1) and pyrimidine (1666 cm-1) bases. In addition, the region between 1000 and 1500 -1 cm contains contributions from PO2 stretching (symmetric and antisymmetric) vibrations. Because FTIR microspectroscopy monitors the global biochemical composition in the probed volume (i.e. tens of cubic microns), the vibrational signatures recorded are a superposition of the spectra of thousands of
48 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020) constituents. Yet despite the complexity, it has been demonstrated that the technique is highly sensitive to slight changes in the composition. The interpretation of these composite spectra requires sophisticated data analysis, which is still evolving through the continue development of multivariate methods. These approaches are based on the principle that there exist small, but reproducible changes in the spectra that can be associated with the variations in sample properties that are investigated. There are several known statistical approaches for infrared data analysis but perhaps the most frequently used is principal components analysis (PCA). Spectroscopy using coherent radiation Coherent Synchrotron Radiation (CSR) has opened up the ability to perform measurements within the so- called THz-gap using this novel high- power THz and sub-THz source (Carr et al. 2002; Abo-Bakr et al. 2002; Abo-Bakr et al. 2003). Several facilities now offer a few days a year where the accelerator is run in a mode to specifically produce the short electron bunches required for CSR. One scientific area where this has been specifically exploited is the low-frequency study of novel superconductors, even though the initial use spread over solid state and biology (Basov et al. 2004) A high-flux synchrotron source allows a high accuracy in the detection of small effects in the reflectivity spectra and overcomes the problem of the very low intensity transmitted by these systems. The reflectivity of such samples were measured in the traditionally difficult sub-THz region and fit to a BCS model like on cuprate high temperature superconductor (Singley et al. 2004), V3Si (Calvani et al. 2008) (Perucchi et al. 2010). THz has potential to become a supplemental method to imaging methods for granular media (Born & Holldack 2017) and Fourier transform THZ-EPR (Nehrkorn et al. 2017). The potential of frequency combs using coherent synchrotron radiation has been recently demonstrated and applied for the study of pure rotation transitions in acetonitrile (Tammaro et al. 2015). Nanospectroscopy and Nanoimaging SINS is broadly applicable to a wide range of sample types, spanning scientific disciplines in the same manner as far-field FTIR with a synchrotron IR beamline. The only additional constraint is that the sample must be suitable for an AFM, meaning relatively flat, and that the measurements are confined to near-surface probing. Even though SINS is a relatively new technique, the number of users working with it is rapidly growing, so at the time of this review’s publication there will already be a number of new publications and results beyond what is covered here. Some examples of science being done with SINS including plasmonics, nanoparticles, biopolymers, semiconductors, electrochemistry, biominerals, and space sciences. Bechtel et al. (Bechtel 2014) measured the phonon modes of calcium carbonate polymorphs in natural biomineral specimens, as shown on Figure 36. And in Figure 36 the symmetric and antisymmetric phonon modes of LiFePO4 (LPF) and FePO4 (FP) single microcrystals are studied to show the changes due to lithiation and delithiation of this Li-ion battery cathode material. The broad spectral coverage of SINS in both of these examples shows how the phonon modes can be followed and studied with nanoscale spatial resolution.
49 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Figure 36: Phonon mode shifts between different polymorphs of calcium carbonate are clearly visible in a line scan obtained across the transition point in this natural biomineral shell sample. From Bechtel 2014.
Figure 37: LFP and FP microcrystal showing distinct spectral changes of the phonons associated with Li intercalation into and out of this Li-ion battery cathode material.
50 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Liu et al. (Liu 2015) have used SINS and laser-based s-SNOM to study a number of VO2 samples in crystalline and thin film form. By measuring the spectroscopic signatures of VO2 phonon modes at 20 nm resolution they were able to map out lattice and electronic changes that occur during the metal-to-insulator phase transition that is triggered via heat or mechanical strain. In a VO2/TiO2 film they observed a red shift of the M1 phonon at 540cm-1 which correlates with compressive strain along the c-axis. Plasma polaritons and phonon polaritons are quasiparticles that can be excited by the IR light scattered off the AFM tip. Dai et al. (Dai 2014) has demonstrated with laser-based s-SNOM that the momentum provided by the confined light field at the apex of the tip will optically excite phonon polaritons in hexagonal boron nitride (hBN), which has also been seen in graphene (Fei 2012, Chen 2012, Gerber 2014). Shi et al. (Shi 2015) have used SINS to investigate both in-plane and out-of-plane phonon modes in hBN flakes, Figure 38. Although both modes show signs of the phonon polariton as a function of wavelength, the sign is reversed. This is consistent with the lower-frequency hyperbolic mode being of Type I whereas the higher frequency mode is Type II.
Figure 38 : Phonon polaritons observed in flakes of hexagonal boron nitride (hBN). As the AFM tip approaches the edge of the hBN flake, spatio-spectral SINS show that the out of plane 780cm-1 and in plane 1370 cm-1 phonon modes have a dispersing spectral feature which have opposite signs. From Shi 2005.
Single nanoparticles can now be individually measured thanks to the high spatial resolution of SINS. Johns et al. (Johns 2016, Runnerstrom 2016) have used SINS at the ALS to measure the very broadband plasmonic response of single doped metal oxide nanocrystals. They were able to carefully show that much narrower linewidths are observed in individual nanoparticles than the ensemble average as seen in far-field measurements of many nano-particles together. These results indicate that sample heterogeneity is causing the anomalously large bandwidth and that the intrinsic damping of metal oxide localized surface plasmon resonances may be less than that of metal nanoparticles, allowing for the development of intriguing real- world applications.
51 From Synchrotron Light Sources and Free-Electron Lasers (Springer, 2020)
Measurements on single nanoparticles catalyst (Chung-Yeh 2017) revealed chemical reactions on individual gold or platinum catalysts, showing enhancement of reactivity that is site-specific. Reactants and product distribution across the particles after exposure to oxidative or reductive conditions were studied with SINS at the ALS. They showed that the edges of the nano-particles are indeed more chemically active than the middle flat regions, for the first time directly confirming the role of surfaces and reactive edges in nano-particle catalysis (Figure 39).
Figure 39: Catalysis measured on individual catalytic particles. From Chung-Yeh 2017.
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