The most common use for the diffraction grating is to serve as the wavelength separation device in an analytical laboratory instrument in which matter is analyzed by studying its interaction with light (this analysis is called spectroscopy). The spectral separation of the wavelengths is not strictly required for this interaction; instead its purpose is to provide data that can be interpreted unambiguously.

The techniques of analytical chemistry (i.e., that branch of chemistry that determines the chemical composition of a substance by measuring its physical properties) may be considered qualitative or quantitative. A qualitative technique seeks to identify what is present; a quantitative technique seeks to determine how much is present. Grating-based optical systems can be used to identify or to quantify, by using the properties of light that is absorbed or emitted by a substance (called absorption spectroscopy and emission spectroscopy, respectively).

Most instruments designed for absorption spectroscopy are composed of four primary elements (see Figure 13-1): a light source, a monochromator, a sample illumination system, and a detector. Sometimes the monochromator and sample illumination system are interchanged (that is, some instruments disperse the light before it interacts with the sample, and some do this afterwards). Some instruments use a spectrograph instead of a monochromator so that the entire spectrum may be recorded at once.

The field of atomic spectroscopy started with the observation by Balmer that the discrete spectral lines emitted by a hydrogen source in the ultraviolet had wavelengths that could be predicted by a simple formula; with the development of quantum physics, the existence of a unique and predictable set of discrete emission (and absorption) wavelengths for each chemical element was hypothesized and subsequently observed. We now defined atomic absorption spectroscopy as the measurement of the light absorbed by ionized atoms, and atomic emission spectroscopy as the measurement of light emitted by energized atoms or ions. Both the wavelength and the intensity of the light can be measured using monochromators and spectrographs to provide information about the atomic species.

Figure 13-1.   Absorption Spectrometer. Light from a broad-spectrum source, such as deuterium (D2) or tungsten (W), is transmitted through the absorbing sample to be analyzed and focused through the entrance slit of a monochromator (or spectrograph), and the intensity of the light at each wavelength is recorded, producing an absorption spectrum. In (a) the sample is illuminated by light after it has been spectrally tuned by the monochromator; in (b) the sample is illuminated by the broad spectrum.

Many atomic emission instrument use an inductively coupled plasma (ICP) composed of the atoms to be studied as the light source.

Molecular spectroscopy instrumentation is generally designed to transmit light through a molecular species (often in a liquid suspension) and measure the absorption at each wavelength.

Atomic and molecular spectroscopy is usually undertaken in the UV, visible and IR portions of the spectrum, since atomic and molecular transition energies lie in this range. Generally one instrument will cover only a portion of this wide spectral range, leading to the classifications of UV spectrometers, UV-visible spectrometers, visible spectrometers and IR spectrometers.

Both the wavelength and the intensity of the light can be measured using monochromators and spectrographs to provide information about the atomic species.

Many atomic and molecular species fluoresce; that is, they absorb energy in the UV-visible spectral region and rapidly emit most of that energy (the remainder being converted to heat or vibrational energy in the medium). Generally, this emission takes place on the order of nanoseconds after absorption, and (because of the energy loss) the emission spectrum will appear at higher wavelengths than the excitation spectrum (or, usually, a single excitation spectral line). Fluorescent compounds may be identified by their unique fluorescence spectra; in some applications, a non-fluorescent material may be tagged with a fluorescent dye or fluorophore so that the non-fluorescent material may be detected using fluorescence instrumentation.

Fluorescence instrumentation generally contains an excitation monochromator, serving as a tunable filter for the excitation light, and an emission spectrometer to disperse the emission spectrum (see Figure 13-2).

Colorimetry is the measurement and specification of color, used in analytical chemistry, color matching, color reproduction and appearance studies. Because color as perceived cannot be associated with a single wavelength – it is a more complicated function of how the three different light receptors in the human eye respond to the entire visible spectrum when looking at an object – it is common to use a multiwavelength instrument such as a grating spectrometer.

Figure 13-2.   Fluorescence Spectrometer. Light from a broad-spectrum source is spectrally tuned by an excitation monochromator; a spectrally narrow beam emerging from this monochromator is absorbed by the sample. The fluorescence spectrum of the sample is viewed (generally at an angle perpendicular to the excitation beam) and resolved by an emission monochromator.

The interaction of light with matter falls into two broad categories: absorption (on which absorption spectroscopy and fluorescence spectroscopy are based), and scattering. Light can scatter elastically (i.e., energy is conserved) or inelastically - the latter is called Raman scattering, and the study of the spectrum of inelastically scattered light from matter is called Raman spectroscopy. Since the ratio of intensities of inelastically scattered light to elastically scattered light is generally under 10^-6, the reduction of instrumental stray light in Raman spectrometers is of paramount importance.

Diffraction gratings are also used in laser systems to perform a number of functions: to tune the lasing wavelength, to narrow the distribution of wavelengths in the laser, and to control the pulse shape (vs. time).

Lasing media have characteristic gain curves that describe the lasing intensity vs. wavelength. In order to "tune" the laser to a wavelength with higher gain with the gain curve, a grating can be used at one end of the resonant cavity (in place of a mirror); using a grating instead of a mirror will disperse the wavelengths in the laser, and the grating can be oriented so that the desired wavelength propagates back into the lasing medium.¹⁵⁶

External-cavity semiconductor diode lasers are often used for their single-mode operation and spectral tunability. Plane reflection gratings can be used in the Littrow configuration to tune the lasing wavelength, as shown in Figure 13-3, or in the grazing-incidence mount.

Figure 13-3.   Tuning a dye laser – the grating as a total reflector in the Littrow configuration. Light from the dye laser cell is diffracted by the grating G, which is oriented so that light of the desired wavelength is redirected back toward the cell; the output beam is transmitted by an output coupler OC (which reflects most of the light back into the laser). The wavelength is tuned by rotating the grating.

In some systems a beam expander is used to illuminate a larger area on the grating surface, in order to achieve high resolution. Since the grating will allow the zero-order to propagate as well as the (Littrow) diffraction order, the output beam may be taken from the grating as in Figure 13-4.

Grazing-incidence tuning with one grating associated with a mirror (or a second grating) can also be used to tune dye lasers without the need for a beam expander, leading to a more compact laser cavity; this is called the Littman-Metcalf design¹⁵⁷ and is shown in Figure 13-5.

Figure 13-4.   Tuning a dye laser – the grating as output reflector. In this case, the zero-order from the grating G is the output beam, and the output coupler in Figure 13-3 is replaced by a mirror. The wavelength is tuned by rotating the grating.

Figure 13-5.   The Littman-Metcalf arrangement The light diffracted by grating G is retroreflected by mirror M, which diffracts the light again back into the dye laser cell.

Molecular lasers, operating in either a pulsed or continuous-wave (cw) mode, have their output wavelength tuned by Littrow-mounted gratings. High efficiency is obtained by using the first diffraction order at diffraction angles |b | > 20°. The output is polarized in the S-plane, since the efficiency in the P plane is quite low.

Some molecular lasers operate at powers high enough to destroy gratings. For pulsed laser tuning, extra-thick replica films may help, but at maximum power only master gratings survive. Due to their far greater thermal conductivity, replica gratings on metal substrates are superior to glass for cw laser applications; in some cases, the grating substrates must be water-cooled to prevent failure.

Excimer lasers – used in surgery, micromachining and photolithography – generally select a narrow spectral range from the emission profile by using an echelle grating in the Littrow configuration.¹⁵⁸ A coarse echelle (d > 10 µm) is used in very high diffraction orders (m >> 10) at very high incidence angles (a = 65° to 79°) in order to obtain high dispersion (see Eq. (2-15)). At such an oblique angle, a beam with circular cross section will illuminate an ellipse on the grating that is three to five times wider in the dispersion direction than it is in the cross-dispersion direction.

For optical systems employing lasers with very high peak powers, such as those that use temporally short (< 1 ps) yet energetic (» 1 J) pulses, the required damage thresholds of the optical components in the system can exceed the performance of state-of-the-art components. Strickland and Mourou¹⁶⁰ demonstrated that such pulses can be stretched (in time) so that their pulse energy is spread out over a large time period (thereby reducing the peak power) and then compressed using a grating compressor to return the pulse to its original temporal profile. Between the two operation (stretching and compression), optical components are exposed to much lower peak powers than that of the original (or final) pulse. By amplifying the pulse between the stretcher and compressor, higher peak power pulses may be obtained.

A dual-grating pulse stretcher is shown in Figure 13-6.

Figure 13-6.   A grating-based pulse stretcher. Intermediate lenses are not shown.

Much of what we know of the universe is due to our analysis of light reaching the earth from planets, stars and galaxies. Grating-based spectrometers play a key role in astronomical measurements. For example, the spectroscopic analysis of starlight allows us to determine the composition of stars as well as their relative velocities. The analysis of absorption lines in starlight that passes through nebulae allows us to determine the composition of the nebulae. From the analyses of these emission and absorption spectra, we can infer ages of stars, distances to galaxies, etc.

Ground-based astronomical telescopes generally have quite large apertures, to maximize the light energy collected from distant astronomical objects; this leads to the need for very large gratings to spectrally disperse the light received. Often these gratings are so large that their resolving power exceeds the value for which the spectrometer's resolution would be grating-limited; that is, in most cases the grating is 'better' than the instrument's resolution requires.

Newport's 'B' engine can rule large echelles and echellettes up to 320 mm x 420 mm in size (which provides a ruled area of 308 mm x 408 mm), suitable for all but the largest ground-based astronomical instruments.¹⁶² The requirement for even larger gratings for ground-based astronomical telescopes has led to three alternative solutions: a static fixture to hold smaller gratings in a larger configuration, an adjustable fixture with optical feedback to move the gratings with respect to each other (to maintain focus)¹⁶³, and a mosaic grating produced by high-accuracy multiple replication onto a single substrate.¹⁶⁴ Such monolithic mosaic gratings have the advantage of long-term alignment stability over the other two alternatives.

In the 1990s, Newport developed the capability to replicate two large submaster gratings onto one monolithic substrate. Except for a "dead space" between the two replicated areas, the entire face of the larger product substrate contains the groove pattern. This mosaic grating must have its two grating areas aligned to very high accuracy if the mosaic is to perform as one high-quality grating. Typical specifications for two 308 mm x 408 mm ruled areas on a 320 mm x 840 mm substrate are one arc second alignment of the groove directions, one arc second tilt between the two faces, and one micron displacement between the two grating planes.

A large mosaic echelle grating produced by Newport for the European Southern Observatory is shown in Figure 13-7. Two submasters from Newport master MR160 (a 31.6 g/mm echelle blazed at 75.1°) were independently replicated onto a large monolithic substrate to form this mosaic grating; the two halves of its surface are clearly seen in the photograph.

Figure 13-8 shows a six-inch aperture Fizeau interferogram of an echelle mosaic (31.6 g/mm) in the m = 98^th order, tested at l = 632.8 nm. The grooves are vertical in the photos and the blaze arrow is facing left. One fringe over this aperture is 0.43 arc seconds. These measurements indicate that the two sides of the mosaic are aligned to 0.3 arc seconds.

Figure 13-9 shows a focal plane scan on a ten-meter optical test bench using a mode-stabilized HeNe laser (l = 632.8 nm) as the light source. The entrance slit width is 25 microns, and the exit slit is opened just enough to get signal through. The grating is operating in the m = 97^th order with full aperture illumination. The image seems to be dominated by the wavefront characteristics of the individual segments, but still indicates a system resolving power better than R = 900,000.

Figure 13-7.   A large mosaic grating. A monolithic 214 x 840 mm replica mosaic grating was produced from two 214 x 415 mm submasters.

Figure 13-8.   Six-inch-aperture Fizeau interferograms of a 31.6 g/mm echelle mosaic produced from two 214 x 415 mm submasters. The photograph on the left shows alignment perpendicular to the grooves; that on the right shows alignment in the direction of the grooves. These interferograms were taken in the 98^th diffraction order.

Figure 13-9.   Signal trace of a 31.6 g/mm echelle mosaic at 632.8 nm in the 97^th order.

Neither master nor replica gratings suffer in any measurable way over extended periods of time in a space environment. The advantage of replica gratings lies not only in their greater availability and lower cost, but in making possible the provision of exact duplicates whenever needed.

Since most space work involves the study of ultraviolet (UV) and extreme ultraviolet (EUV) wavelengths, special problems exist in setting and aligning the optics. For this purpose Newport can rule gratings matching the EUV grating but with a groove spacing modified so that the mercury 546.1-nm line lies in the spectrum just where the main wavelength under study will lie. Another possibility is to rule a small section on the main grating with similar coarse spacings and then mask off this area when the alignment is complete. Sometimes special tolerances on substrate radii are required for complete interchangeability.

Synchrotron radiation is generated by electrons traveling in circular orbits at relativistic speeds; this radiation covers the x-ray through infrared portions of the electromagnetic spectrum and may be used to investigate the electronic properties of matter. Synchrotron beamlines are optical systems oriented tangentially to synchrotron rings, and often gratings are used to disperse the portion of the radiation in the extreme ultraviolet (UV) and vacuum ultraviolet (VUV) spectra.¹⁶⁶

In addition to the "traditional" uses of gratings – in analytical instruments, lasers and astronomical telescopes – there are a number of other uses for which diffraction gratings are well-suited.

Diffraction gratings may be employed as reflectance filters when working in the far infrared, in order to remove the unwanted second- and higher- diffraction orders from the light.¹⁶⁷ For this purpose, small plane gratings are used that are blazed for the wavelength of the unwanted shorter-wavelength radiation. The grating acts as a mirror for the longer-wavelength light, reflecting the desired light into the instrument, while diffracting shorter wavelengths out of the optical path. The groove spacing d must be chosen so that

where l_C is a wavelength between the short wavelengths to be diffracted and the long wavelengths to be reflected (see Eq. (2-1)).

A grating can also be used as a color filter if it is illuminated such that its zero-order efficiency is highly wavelength-dependent.¹⁶⁸

It should be recognized that a diffraction grating by itself cannot serve as a spectral bandpass filter. The grating provides spectral dispersion but not spectral resolution, so the analogue of a thin-film filter designed to pass a narrow spectral band would be the combination of a grating and a slit (see Figure 13-10). A grating monochromator (as described in Chapter 3) may be thought of as a tunable filter – rotating the grating tunes the central wavelength in the transmitted spectral band, and the exit slit serves to narrow this band.

In the late 1990s, surface-relief diffraction gratings became widely used in two types of equipment for fiber-optic telecommunications networks operating in the 1.3–1.7 µm wavelength range. While other wavelength selective tech-nologies exist (e.g., interference filters, fiber Bragg gratings and array waveguide gratings), the cost advantage of surface-relief gratings becomes significant as the channel count increases, since a system with N channels requires N–1 filters but only a single grating; that is, the filters must act in series (in a cascade arrangement) but the grating acts on all channels in parallel. Moreover, as N increases, the spectral bandpass of the filters must decreases, further increasing their cost.

Figure 13-10.   Spectral resolution using a grating and a slit. Polychromatic light incident on and diffracted by the grating G is not spectrally resolved; the grating merely diffracts each wavelength in the incident beam in a different direction. A spectral narrow band Dl is obtained by using exit slit XS to prevent all wavelengths outside this band from passing to the detector.

Multiplexers & Demultiplexers.¹⁶⁹ A multiplexer (see Figure 13-11(a)) is a component in a fiber-optic network that combines many input channels into one output channel; as the input channels have different wavelengths, the multiplexer can be considered a spectrograph used in reverse. A demultiplexer (Figure 13 11(b)) separates many wavelengths in a single input channel so that each is transmitted into a unique output channel (this is functionally equivalent to a spectrograph). Multiplexers and demultiplexers may be employed together to produce add-drop routers.

Figure 13-11.   Fiber-optic network components. (a) Multiplexer: many input beams (each of a unique wavelength) are combined to propagate down the same output path. (b) Demultiplexer: the several signals in the (combined) input beam are separated by wavelength. For simplicity, only four wavelengths are shown.

Optical Spectrum Analyzers. In addition to serving in network components, gratings are used in optical spectrum analyzers which use a small fraction of the light in the network to monitor the intensity and stability of each channel. These systems are essentially spectrographs, and may use plane or concave gratings.

Gratings can be used as beam splitters in conjunction with Moiré fringe applications or interferometers. Under normal illumination (a = 0), a grating with a symmetric groove profile will diffract both first-order beams with equal intensity. A diffraction grating used as a beam divider provides higher efficiencies when its groove profile is rectangular, whereas a grating used for spectroscopic purposes should have a sinusoidal or triangular groove profile.

Transmission gratings can be used as two-beam splitters (where the zero-order beam has negligible efficiency or is otherwise trapped), three-beam splitters (where the groove profile is chosen so that the zero-order beam has the same intensity as the two first-order beams), or for multiple beam sampling, depending on the choice of groove profile.¹⁷⁰

Gratings can be used to couple light into and out of waveguide structures.¹⁷¹ Generally the groove spacing d is specifically chosen to ensure that only one diffraction order (other than the zero order) propagates.

Diffraction gratings can be employed in a variety of metrological applications. The precise microscopic surface-relief pattern can be used to calibrate atomic force microscopes (AFMs). Gratings can also be used in systems designed to measure displacement¹⁷² and strain.¹⁷³