Example Of Diffraction Grating

Posted : admin On 1/26/2022

Problem: A diffraction grating with 12 thousand lines per cm separates a bright line at 24.5 degrees. What is the wavelength of the light? Solution: The separation between slits d on the grating is 1/12,000. 6.1 Diffraction Diffraction grating Single slit diffraction Circular diffraction Diffraction and Interference. Diffraction and interference are similar phenomena. Interference is the effect of superposition of 2 coherent waves. Diffraction is the superposition of many. The diffraction grating considered in this example produces a rainbow of colors on a screen a distance from the grating. The distances along the screen are measured perpendicular to the x-direction. In other words, the rainbow pattern extends out of the page.

Di↵raction Grating Equation with Example Problems1 1 Grating Equation In Figure 1, parallel rays of monochromatic radiation, from a single beam in the form of rays 1 and 2, are incident on a (blazed) di↵raction grating at an angle i relative to the grating normal. These rays are then di↵racted at an angle r.

Image credit: https://www.opcolab.com/

Diffraction gratings are optical devices that are used in instruments such as spectrometers to separate polychromatic light into the underlying constituent wavelengths of which it is comprised. This process disperses the light in such a way that each wavelength is directed to a different angle as a result of the interference pattern that results from the incident light’s reflection off of or transmission through the grating structure.

In this article, we will review the different types of diffraction gratings that exist and discuss their applications. In order to understand diffraction gratings as a product, it will be useful to first review what diffraction is and how a diffraction grating functions to split the different wavelengths of light into spatially separate components that can then be examined and analyzed.

Understanding Diffraction and the Grating Equation

We know that ordinary white light is polychromatic, meaning that it consists of light energy that has different wavelengths which our eyes detect as colors. A prism is an optical instrument that can be used to split the white light into different colors. The process by which this occurs is known as refraction.

Polychromatic light can also be separated into its underlying constituent colors through the use of diffraction. Diffraction refers to the fact that when light from a source encounters an obstacle, be it transparent or opaque, a region of the wavefront of the light is altered in amplitude or phase. The segments of the wavefront that propagate past the obstacle will then interfere with each other and produce an energy density distribution at a point beyond the obstacle that is known as a diffraction pattern. If an opaque screen is fitted with a regular series of elongated openings or slits that are uniformly spaced, then light that is incident on that screen will be altered and the individual wavefronts that emerge through each of the slits will constructively interfere and generate a diffraction pattern with peak intensities that occur at certain angles relative to the plane of the screen and the angle of the incident light wave. So, a diffraction grating is simply a surface that has been fitted with a series of slits or rulings that are spaced geometrically with a uniform identical distance between each successive slit or groove.

It turns out to be the case that diffraction can occur from either using a transmissive or a reflective approach – meaning that it doesn’t matter if the incident light reflects off of the grating or if it is transmitted through the grating. When the grating is completely transparent, there is negligible amplitude modulation and instead, a modulation in phase occurs, resulting in what is called a transmission phase grating. If the grating design instead resembles a series of opaque and transparent regions or slits, then the grating is said to be a transmission amplitude grating. If a reflective surface is used on the diffraction grating, then the grating is referred to as a reflection phase grating.

A diffraction grating, therefore, serves as an angular dispersion device, meaning that it functions to separate wavelengths of light based on the angle with which they emerge from the grating. The dispersion that results from a diffraction grating is expressed in terms of the grating equation shown below, which relates the wavelength of the diffracted light to the diffraction and incident angles of the light that is directed from and to the grating and to the groove spacing:

In the above expression:

  • λ represents the wavelength of the diffracted light
  • d represents the groove spacing of the lines or grooves that are in the diffraction grating
  • θi is the incident angle of the wave that is directed towards the diffraction grating
  • θd is the diffraction angle of the light of wavelength λ that reflects off or is transmitted through the grating
  • n is an integer value that designates the order of the diffraction

Figure 1 below illustrates the light wave angles and their measurement reference line, which as can be seen from the figure below is a normal drawn relative to the plane representing the surface of the diffraction grating. The case illustrated below is for a reflection style of diffraction grating.

Figure 1 - Illustration of a reflection style diffraction grating

Image credit: https://andor.oxinst.com/

In the grating equation above, the term n deserves some further explanation. The term n represents an integer value which means that diffraction angle θd is related to an integer multiple of the diffracted light energy’s wavelength. These diffraction angles correspond to what is known as the order of the diffraction, and since n can be positive or negative values, the order of diffraction can be designed as being a positive or negative value. The situation where n = 0 (the zeroth-order) is the case where there is no diffraction occurring – instead, the incident beam is reflected from the diffraction grating and so the incident angle θi is equal to the angle of reflection of θd. By convention, the sign of the order of diffraction is positive when the diffracted ray is to the left of (or counter-clockwise from) the position of the zeroth order and is negative when it falls to the right (clockwise from) the zeroth-order. If the incident beam of light that is incident in the diffraction grating is monochromatic, then the diffraction pattern will produce an energy density distribution occurring at angles that correspond to the integer values such as …-3, -2, -1, 0, 1, 2, 3, etc. For polychromatic light, each individual wavelength will generate a diffraction pattern by satisfying the grating equation shown above for the specific value of the wavelength λ. Figure 2 below provides an illustration of the order of diffraction for a reflecting diffraction grating and polychromatic light incident on the grating. Note that there are a few nomenclature differences in this illustration compared to the representation as found in this article – what we have termed n is labeled m in Figure 2; our θi is labeled as α, and our θd is labeled as β. The meaning of these values in terms of the grating equation is the same, however.

Figure 2 - Diagram showing the orders of diffracted light from a reflection style grating

Image credit: https://www.newport.com/

Types of Diffraction Gratings

Example of interference

Diffraction gratings are available in several different types which are summarized below. Manufacturers and suppliers offer a variety of stock gratings and custom gratings reproduced from masters. From the perspective of how they are constructed, the most common types of diffraction gratings are ruled gratings and holographic gratings.

Ruled Diffraction Gratings

Ruled gratings, also called blazed gratings, are created by the use of a ruling engine, which is a precision machine that uses a diamond-tipped tool to press or cut fine parallel lines onto a polished surface. A so-called master grating is typically created by first adding a coating of gold or aluminum using an evaporative process to a highly polished surface or substrate. The diamond tool then burnishes grooves into the surface with high precision to maintain absolute parallelism between subsequent grooves, using a heterodyne laser control system. Besides the parallelism, the groove profile must be maintained across the entire surface of the diffraction grating. An instrument such as an Atomic Force Microscope, or AFM, is used to compensate for any wear in the tooling that might occur as the groove pattern is being cut into the surface of the substrate. The profile shape, also called the blaze angle, is related to the range in wavelength for which the grating is optimized.

Example of diffraction grating analysis

Of importance in diffraction grating design is the groove density (also called the groove frequency), which is the reciprocal of the groove spacing (the parameter d in the grating equation above). It is a measure of the number of grooves contained in the grating per unit length. In addition to the blaze angle, the groove density effectively determines the angles at which a single wavelength of light will constructively interfere to produce the distribution of light intensity across the orders of diffraction. For increased efficiency, it is desirable to have the light concentrate into a single order, such as the first-order diffraction, as opposed to being distributed across higher-order diffractions or concentrated in the zeroth-order. Adjusting the blaze angle and the groove density can result in a more efficient diffraction pattern for applications. This may involve adjusting the profile of the groove, its depth, and the facet angles. The wavelength for which the grating has been optimized is known as the blaze wavelength.

Example

Example Of Refraction

A type of ruled grating called an Echelle grating is one that is relatively course, meaning that the groove density is low. These types of gratings feature high blaze angles and utilize the higher diffraction orders, the advantage being high dispersion and resolution within a compact design,

Holographic Diffraction Gratings

By the nature of the manufacturing process, ruled gratings can suffer from periodic errors, spacing errors, and other irregularities, the presence of which may result in stray light and ghosting. Holographic gratings are designed to address some of these issues by using a different production method. A holographic diffraction grating is created by the use of an interference lithography process. A master grating is created by exposing photosensitive material to two interfering laser beams. The beams create an interference pattern on the substrate that can then be treated to produce a sinusoidal surface groove pattern. The photoresist layer is overcoated with a metal layer that is applied using vacuum deposition. From this master, molds can be created to generate replicated gratings. Besides the traditional sinusoidal groove pattern, holographic blazed gratings can be fabricated by taking a finished holographic grating and bombarding it with an angled beam of ions in order to generate a symmetric triangular groove or sawtooth profile.

Example of refraction

Holographic gratings use an optical technique to create the grating pattern and as such address some of the issues that can occur with ruled gratings, such as ghosting and high amounts of scattered light. At one time, they achieved these objectives albeit with reduced efficiency in some instances. But the introduction of blazed holographic diffraction gratings means that the high efficiency normally associated with ruled grating can be achieved holographically as well.

Transmission and Reflection Gratings

As mentioned earlier, diffraction gratings may be characterized as either transmission or reflection gratings. Transmission gratings generate a diffraction pattern after passing incident light through the grating, where reflection gratings have the diffracted light pattern on the same side as the incident beam. Reflection gratings feature a reflective coating of typically aluminum or gold while transmission gratings are equipped with an anti-reflection coating. Transmission gratings tend to provide high efficiency and offer greater ease of alignment in optical systems as compared with reflection gratings.

Diffraction Grating Formula

Grating profiles are usually planar or concave, however, there are other potential profile shapes available such as convex and toroidal, the selection of which is determined by the specific application conditions.

Diffraction Grating Applications

Diffraction gratings have a number of applications, the most common of which is in monochromators and spectrometers. Monochromators are used to select a narrow band of light from a much wider range of available wavelengths at the source. A common variety of these devices, known as a Czerny–Turner monochromator, uses a diffraction grating in combination with a set of flat and concave mirrors to perform the selection of wavelength. Figure 3 below illustrates the basic concept behind the monochromator.

Figure 3 - Basic structure of a Czerny–Turner monochromator (note the diffraction grating D)

Image credit: https://link.springer.com/

A spectrometer, specifically an optical spectrometer, allows scientists and researchers to analyze the light that is emitted by atoms from a sample of material and in so doing, gain knowledge about the constituent elements that are present in that sample. Spectrometers are used in a variety of applications from measuring the dissolved oxygen content in marine ecosystems to studying the light emitted from distant galaxies.

Besides monochromators and spectrometers, diffraction gratings can be used in optical-based communication systems to split or combine optical signals or to perform pulse compression or stretching. They are also employed in lasers to perform wavelength tuning, meaning creating a laser light output that emits a desired frequency of electromagnetic energy.

Diffraction gratings are also characterized by the specific frequency or wavelength of light for which they are intended to be used. This includes Near Infrared (NIR), Mid-Infrared, Visible, or Ultraviolet (UV) light applications.

Summary

This article provided a summary of the types of diffraction gratings, their applications, and an explanation of the underlying principle of diffraction in optics. For information on other topics, consult our additional guides or visit the Thomas Supplier Discovery Platform where you can locate potential sources of supply for over 70,000 different product and service categories, including suppliers of optical diffraction gratings.

Sources:

Related Articles

More from Other

Related Resources

  • Email Marketing Do's And Don'ts For Manufacturers

  • Penny For Your Thoughts?

  • The Death of the Mechanical Fastener Is Upon Us

  • Manufacturing Institute, Charles Koch Institute Partner on 'Second Chance Hiring' Initiative

  • New Electric Boat Flies Over Waves on Hydrofoils

Browse by Category