1.5 Scattering and absorption

Scattering and absorption are key phenomena in electromagnetic wave interactions with matter. These processes influence how light behaves in metamaterials and photonic crystals, affecting properties like refraction, localization, and energy transfer.

Understanding scattering and absorption is crucial for designing materials with specific optical characteristics. By manipulating these processes, scientists can create metamaterials and photonic crystals with unique properties for applications in sensing, energy harvesting, and optical communication.

Scattering of electromagnetic waves

• Scattering occurs when electromagnetic waves interact with matter, causing the wave to deviate from its original path
• The type of scattering depends on the size, shape, and composition of the scattering object relative to the wavelength of the incident wave
• Scattering plays a crucial role in the optical properties of metamaterials and photonic crystals, influencing phenomena such as light localization, slow light, and negative refraction

Elastic vs inelastic scattering

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• Elastic scattering conserves the energy of the incident wave, with no energy transfer between the wave and the scattering object (Rayleigh scattering)
• Inelastic scattering involves an energy exchange between the wave and the scattering object, resulting in a change in the wavelength of the scattered wave (Raman scattering, Brillouin scattering)
• The type of scattering affects the optical response of metamaterials and photonic crystals, influencing properties such as dispersion, absorption, and emission

Scattering cross section

• The scattering cross section quantifies the probability of an electromagnetic wave being scattered by an object
• It depends on factors such as the size, shape, and material properties of the scattering object, as well as the wavelength and polarization of the incident wave
• The scattering cross section can be engineered in metamaterials and photonic crystals by controlling the geometry and arrangement of the constituent elements

Rayleigh scattering

• Rayleigh scattering occurs when the size of the scattering object is much smaller than the wavelength of the incident wave
• The intensity of Rayleigh scattering is proportional to $1/\lambda^4$, where $\lambda$ is the wavelength of the incident wave
• Rayleigh scattering is responsible for the blue color of the sky, as shorter wavelengths (blue light) are scattered more strongly by atmospheric molecules than longer wavelengths (red light)

Mie scattering

• Mie scattering occurs when the size of the scattering object is comparable to or larger than the wavelength of the incident wave
• It is a more complex phenomenon than Rayleigh scattering, involving the solution of Maxwell's equations for spherical objects
• Mie scattering is important in the design of metamaterials and photonic crystals, as it can be used to control the optical properties of the constituent elements (metallic nanoparticles, dielectric spheres)

Scattering in metamaterials

• Metamaterials can be designed to exhibit unusual scattering properties, such as enhanced or suppressed scattering at specific wavelengths
• By engineering the size, shape, and arrangement of the constituent elements, metamaterials can achieve highly directional scattering, enabling applications such as beam steering and light focusing
• The collective scattering response of metamaterials can give rise to exotic phenomena, such as negative refraction and cloaking

Absorption of electromagnetic waves

• Absorption occurs when electromagnetic waves transfer their energy to matter, resulting in the attenuation of the wave
• The absorption of light depends on the material properties, such as the electronic band structure and the presence of absorbing centers (atoms, molecules, defects)
• Absorption plays a crucial role in the optical properties of metamaterials and photonic crystals, influencing phenomena such as light confinement, energy harvesting, and thermal emission

Absorption cross section

• The absorption cross section quantifies the probability of an electromagnetic wave being absorbed by an object
• It depends on factors such as the material properties, size, and shape of the absorbing object, as well as the wavelength and polarization of the incident wave
• The absorption cross section can be engineered in metamaterials and photonic crystals by controlling the composition and geometry of the constituent elements

Absorption in dielectrics

• In dielectrics, absorption occurs due to the excitation of electrons from the valence band to the conduction band
• The absorption spectrum of dielectrics is characterized by a bandgap, which determines the minimum energy required for electron excitation
• Dielectric materials with a wide bandgap (insulators) exhibit low absorption in the visible range, while those with a narrow bandgap (semiconductors) can absorb visible light

Absorption in metals

• In metals, absorption occurs due to the excitation of free electrons in the conduction band
• The absorption spectrum of metals is characterized by a plasma frequency, which determines the frequency above which the metal becomes transparent
• At frequencies below the plasma frequency, metals exhibit strong absorption and reflection, while at higher frequencies, they become transparent

Resonant vs non-resonant absorption

• Resonant absorption occurs when the frequency of the incident wave matches a natural frequency of the absorbing system (electronic transitions, vibrational modes)
• Non-resonant absorption occurs when the frequency of the incident wave does not match any natural frequencies of the absorbing system
• Resonant absorption is characterized by sharp peaks in the absorption spectrum, while non-resonant absorption exhibits a broader and less intense response

Absorption in metamaterials

• Metamaterials can be designed to exhibit enhanced or suppressed absorption at specific wavelengths by incorporating absorbing elements (metallic nanoparticles, dyes, quantum dots)
• The absorption properties of metamaterials can be tuned by controlling the size, shape, and arrangement of the absorbing elements
• Metamaterials with strong absorption can be used for applications such as energy harvesting, thermal emission control, and sensing

Scattering and absorption interplay

• Scattering and absorption are closely related phenomena that often occur simultaneously when electromagnetic waves interact with matter
• The relative strength of scattering and absorption depends on factors such as the size, shape, and material properties of the object, as well as the wavelength of the incident wave
• Understanding the interplay between scattering and absorption is crucial for designing metamaterials and photonic crystals with desired optical properties

Scattering vs absorption dominance

• When scattering dominates over absorption, the object appears transparent or translucent, with little attenuation of the incident wave (glass, water)
• When absorption dominates over scattering, the object appears opaque or dark, with significant attenuation of the incident wave (metals, pigments)
• The balance between scattering and absorption can be tuned in metamaterials and photonic crystals by controlling the composition and geometry of the constituent elements

Kramers-Kronig relations

• The Kramers-Kronig relations are mathematical expressions that connect the real and imaginary parts of the complex refractive index, which describe the scattering and absorption properties of a material
• The relations state that the real part (scattering) can be determined from the imaginary part (absorption) and vice versa, through a Hilbert transform
• The Kramers-Kronig relations provide a powerful tool for analyzing and predicting the optical properties of metamaterials and photonic crystals

Sum rules for scattering and absorption

• Sum rules are integral expressions that relate the scattering and absorption cross sections to fundamental physical quantities, such as the number of electrons or the polarizability of the object
• The optical theorem is a sum rule that connects the extinction cross section (sum of scattering and absorption) to the forward scattering amplitude
• Sum rules provide constraints on the design of metamaterials and photonic crystals, ensuring that the desired optical properties are consistent with fundamental physical principles

Applications of scattering and absorption

• The control of scattering and absorption in metamaterials and photonic crystals enables a wide range of applications in various fields, such as sensing, energy harvesting, and optical communication
• By engineering the scattering and absorption properties at specific wavelengths, metamaterials and photonic crystals can be tailored for specific applications, offering unprecedented control over light-matter interactions

Sensing and detection

• Metamaterials and photonic crystals can be designed to exhibit strong scattering or absorption at specific wavelengths, enabling highly sensitive and selective sensing of chemical or biological analytes
• By incorporating functional materials (plasmonic nanoparticles, molecular receptors), metamaterials and photonic crystals can be used for surface-enhanced Raman scattering (SERS), fluorescence enhancement, and refractive index sensing

Cloaking and invisibility

• Metamaterials can be designed to manipulate the scattering of electromagnetic waves, enabling the realization of cloaking devices that render objects invisible to specific wavelengths
• By carefully engineering the scattering properties of the metamaterial, it is possible to guide the incident waves around the object, making it appear as if the object were not there
• Cloaking has potential applications in stealth technology, imaging, and optical illusions

Solar energy harvesting

• Metamaterials and photonic crystals can be designed to exhibit strong absorption in the solar spectrum, enabling efficient solar energy harvesting
• By incorporating absorbing elements (metallic nanoparticles, semiconductors) and optimizing their size, shape, and arrangement, metamaterials can achieve broadband and omnidirectional absorption
• Metamaterial-based solar absorbers can be used in solar thermal collectors, photovoltaic cells, and solar fuel production

Thermal emission control

• Metamaterials and photonic crystals can be designed to control the thermal emission properties of surfaces, enabling the realization of selective emitters and absorbers
• By engineering the absorption and emission spectra of the metamaterial, it is possible to create surfaces that emit radiation at specific wavelengths and directions, while suppressing emission at other wavelengths
• Thermal emission control has applications in thermophotovoltaics, radiative cooling, and infrared signature management