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🔬Modern Optics

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1.3 Optical properties of materials: refractive index, dispersion, and absorption

3 min readLast Updated on July 22, 2024

Light behaves differently in various materials due to their optical properties. Refractive index, a key concept, describes how light slows down and bends when entering a medium. This affects everything from everyday phenomena like rainbows to advanced optical technologies.

Dispersion and absorption are crucial phenomena in optics. Dispersion causes different colors to travel at different speeds, while absorption removes specific wavelengths from light. Understanding these effects is vital for designing optical systems and explaining natural optical phenomena.

Optical Properties of Materials

Refractive index and light speed

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  • Refractive index (nn) dimensionless number describes how light propagates through a medium compared to its speed in vacuum (cc)
    • Defined as the ratio n=cvn = \frac{c}{v}, where vv is the speed of light in the medium
    • In a vacuum, n=1n = 1 because light travels at its maximum speed cc (299,792,458 m/s)
    • In a medium (water, glass), n>1n > 1 because light slows down to speed v<cv < c
  • Higher refractive index indicates slower light travel through the medium
    • Light travels about 1.33 times slower in water (n1.33n \approx 1.33) than in vacuum
    • Diamond has a high refractive index (n2.42n \approx 2.42), causing significant light slowing and strong refraction
  • Refractive index depends on wavelength, so its value can change for different colors of light
    • Dispersion occurs because refractive index varies with wavelength (red light has lower nn than blue light in most materials)

Dispersion and absorption phenomena

  • Dispersion phenomenon where refractive index of a material varies with the wavelength of light
    • Different wavelengths travel at different speeds through the material
    • Separates white light into its constituent colors (rainbow effect in a prism)
    • Pulse broadening can occur, limiting bandwidth in optical communication systems (chromatic dispersion in optical fibers)
  • Absorption phenomenon where material absorbs certain wavelengths of light as it passes through
    • Photon energy matches energy required to excite electrons in the material
    • Absorbed energy converted to other forms (heat, chemical energy)
    • Light intensity decreases as it propagates through the material (attenuation)
    • Colored glass filters work by absorbing specific wavelengths (red glass absorbs green and blue light)
  • Dispersion and absorption significantly impact light propagation through materials
    • Dispersion can distort signals and limit data rates in optical communications
    • Absorption reduces light intensity and limits transmission distance (fiber optic cable length limited by absorption losses)

Physical origin of dispersion

  • Dispersion arises from interaction between oscillating electric field of light and electrons in a material
  • Electronic structure determines how electrons respond to different light frequencies
    • Electrons bound to atoms by spring-like forces
    • Resonance occurs when light frequency matches natural frequency of electron oscillations
  • Near resonance, refractive index changes rapidly with frequency, causing strong dispersion
    • Higher refractive index for frequencies just below resonance
    • Lower refractive index for frequencies just above resonance
  • Lorentz oscillator model describes this behavior by treating electrons as damped harmonic oscillators driven by light's electric field
    • Predicts resonance behavior and dispersion shape
    • Quantum mechanical treatment needed for more accurate description (quantum electrodynamics)

Calculating refractive index

  • Kramers-Kronig relations mathematical equations connect real and imaginary parts of complex refractive index n~=n+iκ\tilde{n} = n + i\kappa

    • Real part nn describes dispersion
    • Imaginary part κ\kappa (extinction coefficient) describes absorption
  • Kramers-Kronig relations derived from causality principle and requirement that material response to electromagnetic field must be real

  • Relations given by: n(ω)1=2πP0ωκ(ω)ω2ω2dωn(\omega) - 1 = \frac{2}{\pi} P \int_0^\infty \frac{\omega' \kappa(\omega')}{\omega'^2 - \omega^2} d\omega'

    κ(ω)=2ωπP0n(ω)1ω2ω2dω\kappa(\omega) = -\frac{2\omega}{\pi} P \int_0^\infty \frac{n(\omega') - 1}{\omega'^2 - \omega^2} d\omega'

    where PP denotes Cauchy principal value of integral, ω\omega is angular frequency of light

  • If absorption spectrum κ(ω)\kappa(\omega) is known, refractive index n(ω)n(\omega) can be calculated using first relation

    • Measured absorption data can be used to compute refractive index dispersion
  • If refractive index is known, absorption spectrum can be calculated using second relation

    • Measured refractive index data can predict absorption resonances
  • Kramers-Kronig analysis powerful tool for characterizing optical properties of materials from experimental data



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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.