Technical Note 14
FUNDAMENTALS OF DIFFRACTION GRATING TECHNOLOGY AND INDUSTRIAL LASER APPLICATIONS OF GRATINGS

Diffraction gratings are an important component in many optical systems, where their function is to separate light of various wavelengths, so that these separate wavelengths may be further utilized or manipulated. Although they may come in quite a few forms, most often a diffraction grating consists of a repeated series of relief structures or grooves, whose spacing is similar to the average wavelength of light projected onto the grating surface.

Figure 1 - An example of some planar diffraction gratings manufactured by Newport Corporation. Note the product's ability to separate white light into its various component wavelengths		DIFFRACTION GRATING THEORY When a beam of polychromatic (white) light is projected onto the surface of the diffraction grating, each of the grooves acts as a scattering element. The light, as it approaches a series of many grooves, is scattered and diffracted from each groove surface in all directions (Figure 2). Since light can be thought of as a wave with peaks and valleys (variations in the electromagnetic field intensity), the light that scatters from a particular groove surface can be added or subtracted to light which is scattered from all other groove surfaces. Usually, the addition of these waves scattered from many groove surfaces results in a scenario where the light intensity is lost very rapidly (destructive inter-
ference). However, for very particular angular geometries, the waves exhibit constructive interference, and the groove configuration supports a diffraction off the grating surface. The angle at which the diffraction occurs is intrinsically dependent on the wavelength of the light diffracted from the groove surfaces. Thus, via this scattering and constructive interference mechanism, the white light may be separated into its various component wavelengths (Figure 3).

A consequence of the geometry of the constructive interference, which occurs via light diffracted from the grooves, is that the diffracted beam angle of the blue light is different from the diffracted beam angle of the red light. The angles of diffraction of these various wavelengths are highly predictable. A close inspection of the geometry of the constructive interference allows us to derive the grating equation, from which a great deal of grating analysis is performed and performance specifications are projected.

Figure 2 - Side-view of a diffraction grating's periodic groove structure;
schematic of scattering of incident light from grooves

Figure 3 - Separation of white light into its various component wavelengths;
demonstration of dependence of angle of diffracted beam on wavelength

Figure 4 - The diffraction grating equation, and a diagram of the equation’s
various parameters of interest. m is the diffraction order and l is the wavelength of incident light

TYPES OF DIFFRACTION GRATINGS

There are quite a few various types of diffraction gratings – some which exhibit a surface relief pattern, and some that instead exhibit a refractive index¹ variation within a volume of a material. The two most historically common types of diffraction gratings are surface relief gratings, which are divided into two subgroups: ruled and holographic.

Ruled gratings have a cross section analogous to that which is depicted in Figure 4. The ruled gratings are fabricated by deposition of a metallic layer onto a substrate, which is usually glass. Then, under precise mechanical control a diamond tip is employed to burnish one groove at a time into the metal layer.

Although the movement of the initial ‘ruling engines’ was governed entirely via mechanical means, a significantly enhanced accuracy has been obtained through the incorporation of optical interferometry to more precisely account for the positioning of the burnishing instrumentation and the stage on which the grating is placed.

Since gratings have very closely spaced grooves, it is not uncommon for many kilometers of grooves to be ruled onto one average-size grating. Further, one ruling may take a few months to complete. For this reason, only ruled master gratings are fabricated via this burnishing mechanism. The gratings that are sold to customers are exact replicas of these masters, whose groove profile and optical dispersion characteristics identically match that of their predecessor masters.

In contrast to ruled gratings, holographic gratings are manufactured via a means that theoretically entirely eliminates mechanically derived errors. First, a photosensitive material is deposited onto a substrate, usually made of glass. Then, two coherent (laser) beams are made to coincide such that they form an interference pattern of light and dark fringes on the surface of the photosensitive material. The sinusoidal fringes of stronger intensity, from constructive interference of the two laser beams, result in the formation of valleys in the photosensitive material, after the material is treated with a developer solution. The resulting surface relief cross section is depicted in Figure 5.

Although ruled and holographic gratings exhibit similar diffraction characteristics, a direct consequence of their differing methods of manufacture is their slightly different efficiency (optical output versus input) and stray light characteristics. In general, since ruled gratings can be manufactured such that the groove profile is customized for a particular wavelength (called blazing), they exhibit a higher efficiency than their holographic counterparts.

However, in comparison to ruled gratings, due to their profile smoothness the holographic products typically exhibit minimal stray light, i.e. the light diffracted into regions which are not described by the grating equation is minimized. Typically stray light is attributable to a slight unavoidable imprecision in the burnishing mechanics, for example. With the help of modern interferometric feedback control, stray light from ruled gratings resulting from mechanical imperfections now rarely exceeds 0.05% of the parent line intensity.

No one grating type could be considered to be universally better than the other. Depending on the application requirements, it is usually apparent that one grating type is more appropriate over the other for the user’s particular situation.

Figure 5 - Typical groove cross-section of a holographic diffraction grating

GRATING LASER APPLICATIONS - SPECTRAL TUNING

All lasers have a few universal components. These include a gain medium whose energy levels specify the output wavelength(s), a resonator cavity, a highly reflecting element (a mirror or a Bragg reflector, for example), and an output coupler (a lossy mirror, for example). In addition, all lasers have a characteristic gain curve, which is a characterization of a laser’s output intensity as a function of wavelength. Although a perfect laser would output only one wavelength, fundamental considerations of physical optics require that all lasers have a nonzero spectral bandwidth to their output beam.

Since the laser’s total integrated energy output must remain constant, a narrowing of the spectral output profile results in significantly higher gain and output power for a particular wavelength. Diffraction gratings may be used to more accurately specify, or tune, a laser’s output wavelength by replacing the perfect mirror component in the laser system (Figure 6). The reflection grating will disperse all but a small range of center wavelengths in the system. The dispersed wavelengths will not be propagated back into the laser cavity, and hence will not propagate through the gain medium. Only wavelengths propagated back through the gain medium will be amplified. Depending on the dispersive power of the grating, a rotation of the grating through an angle of a few degrees will change the wavelength reflected back into the cavity. Thus, the center wavelength of amplification may be changed, or tuned, by rotating the grating. Not shown in Figure 6 is a collimating mirror, which is sometimes used to ensure the grating ruled surface is completely filled by the laser beam. This ensures a high resolution.

The laser tuning configuration shown in Figure 6 demonstrates a Littrow grating orientation. Littrow describes a particular scenario where the incident and diffracted beams coincide; the diffracted beam returns at the same angle as the incident angle. Thus, in terms of optical ray geometry, the grating acts like a mirror. An alternative approach to the Littrow tuning configuration is the Littman-Metcalf laser tuning configuration, shown in Figure 7. Littman tuning results in greater angular separation of the diffracted wavelengths, since the angle of incidence is high – approaching grazing incidence, usually 80 degrees or higher. Since greater spectral separation is imparted to the diffracted beam, a narrower range of wavelengths is diffracted back into the laser cavity. However, since the efficiency of a grating typically decreases at grazing incidence, Littman mounting is not appropriate for all tuning situations.

Figure 6 - Use of a reflecting diffraction grating for a laser tuning application;
the grating replaces the perfect mirror at one side of the resonator cavity

Figure 7 - The Littman-Metcalf laser tuning geometry

For both the Littrow and Littman-Metcalf geometries, replacing the laser’s reflecting mirror element with a diffraction grating allows specification of the spectral peak of the laser’s gain profile (i.e. laser tuning). However, the presence of a grating as a reflector in the system also promotes specifically a more monochromatic spectral gain curve, due to the dispersive properties of the grating. The width of the spectral gain curve depends on the capability of the grating to separate light into its various component wavelengths, along different angular geometries. In general, a grating with a greater ability to separate the various colors incident on it will result in a more monochromatic laser output. For this reason, the high dispersive capability of the echelle gratings makes them particularly useful for laser tuning applications.

GRATING LASER APPLICATIONS – PULSE COMPRESSION AND STRETCHING

When an optical pulse is transmitted through any dielectric medium (i.e. a medium whose refractive index is greater than unity), different spectral components of the pulse will typically travel at different speeds. The pulse, downstream in the system, will exhibit a quicker arrival time for the red wavelengths, and a slower arrival time for the blue wavelengths, thereby spectrally broadening the width of the pulse in time. In order to remedy this optical dispersion effect and ensure that all spectral components of the pulse arrive simultaneously, a pair of gratings can be used. The grating not only has the capability to compensate for the spectral broadening of the pulse as it propagates, but it is often the case that the pulse may be even shorter in time than the input pulse.

Figures 8a and 8b demonstrate the general operation of a grating pair used as an optical pulse compressor and stretcher, respectively. Note that the concept of pulse compression and stretching relies on the simple idea that light will travel a longer period of time before reaching its target, if it has a larger distance to traverse. The first grating in either figure separates the light into its component wavelengths, as indicated. After reflecting off the second grating, in Figure 8a the red light has a greater distance to travel (compared to the blue light) before reaching its destination. Thus, the blue light will arrive at the detector first. An opposite scenario where the red light arrives first is shown in Figure 8b. Note the additional optical components required in this scenario, used to ensure proper incident geometry.

Figure 8 - (a) Grating-based pulse compressor and (b) pulse stretcher

The above scenario of compression and stretching is often termed dispersion compensation. A special application of a dispersion compensating grating pair is the amplification of ultra fast optical pulses. Very short pulses can be produced by some lasers, but they typically exhibit low output intensity. Amplification of this ultra short pulse could cause substantial damage to the amplification optoelectronics. So, the pulse is broadened in time prior to amplification. Then, the amplified pulse is then recompressed in time.

Both the grating stretcher and compressor are most commonly used in a double-pass configuration, in order to maximize the amount of dispersion provided by the system. A double or even quadruple pass system not only provides incremental spectral dispersion capability, but also has the benefit of providing an output beam that is geometrically parallel to the input beam.

The pulse compression and stretching mechanism is a spectrotemporal manipulation of the laser beam, to reduce its total power (energy flux per unit time). As such, it is important to know the effect of laser damage on the grating and its specifications. High intensity pulses may cause a phase transformation of the grating’s coating, resulting in a deformation in the groove profile of the grating. Of course, this may adversely affect the groove shape, which often results in a variation in the grating efficiency. One must also keep in mind the substrate thermal expansion issues resulting from high power laser pulsing. Newport Corporation provides guidance for general damage thresholds. For pulsed lasers at 1.06 µm wavelength, standard gold replica gratings can withstand a 300 mJ/cm² pulse, of 100 ps duration. CW lasers at 10 µm can be operated with an incident energy flux of 100 W/cm² for a standard gold replica grating on copper, and 200 W/cm² for a water-cooled gold replica on copper.

Newport Corporation
705 St. Paul Street, Rochester, New York 14605 USA
Telephone: (585) 262-1331, Fax: (585) 454-1568
E-mail: gratings@newport.com,
Web Site: http://gratings.newport.com