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3.4 Diffraction gratings and their applications

3 min readLast Updated on July 22, 2024

Diffraction gratings are optical components with parallel slits or grooves that split light into its component wavelengths. They work by diffracting light waves, causing constructive interference at specific angles determined by the grating equation.

These gratings are crucial in spectroscopy, wavelength division multiplexing, and various optical systems. They enable precise wavelength analysis, increase data capacity in fiber optics, and find applications in laser technology, holography, and optical sensors.

Diffraction Gratings

Structure of diffraction gratings

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  • Consist of a large number of parallel, equally spaced slits or grooves on a substrate (glass, plastic, or metal)
    • Slits or grooves are typically very narrow compared to the wavelength of light (hundreds of nanometers)
    • Spacing between slits or grooves is denoted by the grating period, dd (typically on the order of micrometers)
  • Light incident on a diffraction grating is diffracted by each slit or groove
    • Diffracted waves from each slit or groove interfere with each other
    • Constructive interference occurs at specific angles, resulting in bright spots known as diffraction orders (principal maxima)
  • Angle at which constructive interference occurs depends on the wavelength of light and the grating period (determined by grating equation)

Derivation of grating equation

  • Grating equation relates the diffraction angle to the wavelength of light and the grating period:
    • dsinθm=mλd \sin \theta_m = m \lambda
      • dd: grating period (distance between adjacent slits or grooves)
      • θm\theta_m: diffraction angle for the mm-th order (angle between diffracted beam and grating normal)
      • mm: diffraction order (integer: 0, ±1, ±2, ...) (0th order is the direct transmission, higher orders are the diffracted beams)
      • λ\lambda: wavelength of light
  • Derived by considering the path difference between waves diffracted from adjacent slits or grooves
    • For constructive interference, the path difference must be an integer multiple of the wavelength (ensures waves are in phase)
  • Allows calculation of diffraction angles for a given wavelength and grating period (useful for spectroscopic applications)
    • Also enables determination of the wavelength of light if the diffraction angle and grating period are known (wavelength measurement)

Calculation of diffracted orders

  • To calculate angular positions of diffracted orders:
    1. Determine grating period, dd, and wavelength of light, λ\lambda (given or measured quantities)
    2. Choose diffraction order, mm, of interest (typically start with lower orders: ±1, ±2)
    3. Use grating equation, dsinθm=mλd \sin \theta_m = m \lambda, to solve for diffraction angle, θm\theta_m (trigonometric calculation)
  • Intensity of diffracted orders depends on the structure of the grating and the wavelength of light
    • Intensity distribution can be calculated using the interference pattern of the diffracted waves (requires advanced mathematical treatment)
    • Factors affecting intensity include the number of slits or grooves (more slits = narrower and more intense orders), width of slits or grooves (affects efficiency), and grating period (affects angular separation of orders)

Applications in optical systems

  • Spectroscopy:
    • Diffraction gratings used to disperse light into its constituent wavelengths (separates colors)
    • Allows analysis of the spectral composition of light sources (identifies elements or compounds)
    • Applications include atomic and molecular spectroscopy (emission and absorption spectra), astronomical spectroscopy (stellar composition), and Raman spectroscopy (molecular vibrations)
  • Wavelength Division Multiplexing (WDM):
    • In optical communication systems, diffraction gratings used to multiplex and demultiplex different wavelengths of light (combines or separates wavelengths)
    • Multiple wavelengths can be transmitted simultaneously over a single optical fiber, increasing data capacity (more channels per fiber)
    • Diffraction gratings used in WDM devices such as multiplexers (combines wavelengths), demultiplexers (separates wavelengths), and optical add-drop multiplexers (OADMs) (selectively adds or drops wavelengths)
  • Other optical systems:
    • Monochromators and spectrometers use diffraction gratings to select specific wavelengths of light (filters out unwanted wavelengths)
    • Laser systems employ gratings for wavelength tuning (adjusts laser output wavelength) and beam combining (combines multiple laser beams)
    • Holography (recording and reconstructing wavefronts), optical data storage (high-density data recording), and optical sensors (detect changes in wavelength or intensity) also utilize diffraction gratings


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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.