List of photonics equations
This article summarizes equations in the theory of photonics, including geometric optics, physical optics, radiometry, diffraction, and interferometry.
Contents
Definitions
Geometric optics (luminal rays)
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General fundamental quantities
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Quantity (common name/s) (Common) symbol/s SI units Dimension Object distance x, s, d, u, x1, s1, d1, u1 m [L] Image distance x', s', d', v, x2, s2, d2, v2 m [L] Object height y, h, y1, h1 m [L] Image height y', h', H, y2, h2, H2 m [L] Angle subtended by object θ, θo, θ1 rad dimensionless Angle subtended by image θ', θi, θ2 rad dimensionless Curvature radius of lens/mirror r, R m [L] Focal length f m [L]
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Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Lens power P m−1 = D (dioptre) [L]−1 Lateral magnification m dimensionless dimensionless Angular magnification m dimensionless dimensionless
Physical optics (EM luminal waves)
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There are different forms of the Poynting vector, the most common are in terms of the E and B or E and H fields.
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Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Poynting vector S, N W m−2 [M][T]−3 Poynting flux, EM field power flow ΦS, ΦN W [M][L]2[T]−3 RMS Electric field of Light Erms N C−1 = V m−1 [M][L][T]−3[I]−1 Radiation momentum p, pEM, pr J s m−1 [M][L][T]−1 Radiation pressure Pr, pr, PEM W m−2 [M][T]−3
Radiometry
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For spectral quantities two definitions are in use to refer to the same quantity, in terms of frequency or wavelength.
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Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Radiant energy Q, E, Qe, Ee J [M][L]2[T]−2 Radiant exposure He J m−2 [M][T]−3 Radiant energy density ωe J m−3 [M][L]−3 Radiant flux, radiant power Φ, Φe W [M][L]2[T]−3 Radiant intensity I, Ie W sr−1 [M][L]2[T]−3 Radiance, intensity L, Le W sr−1 m−2 [M][T]−3 Irradiance E, I, Ee, Ie W m−2 [M][T]−3 Radiant exitance, radiant emittance M, Me W m−2 [M][T]−3 Radiosity J, Jν, Je, Jeν W m−2 [M][T]−3 Spectral radiant flux, spectral radiant power Φλ, Φν, Φeλ, Φeν W m−1 (Φλ)
W Hz−1 = J (Φν)[M][L]−3[T]−3 (Φλ)
[M][L]−2[T]−2 (Φν)Spectral radiant intensity Iλ, Iν, Ieλ, Ieν W sr−1 m−1 (Iλ)
W sr−1 Hz−1 (Iν)[M][L]−3[T]−3 (Iλ)
[M][L]2[T]−2 (Iν)Spectral radiance Lλ, Lν, Leλ, Leν W sr−1 m−3 (Lλ)
W sr−1 m−2 Hz−1 (Lν)[M][L]−1[T]−3 (Lλ)
[M][L]−2[T]−2 (Lν)Spectral irradiance Eλ, Eν, Eeλ, Eeν W m−3 (Eλ)
W m−2 Hz−1 (Eν)[M][L]−1[T]−3 (Eλ)
[M][L]−2[T]−2 (Eν)
Equations
Luminal electromagnetic waves
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Physical situation Nomenclature Equations Energy density in an EM wave - = mean energy density
For a dielectric:
Kinetic and potential momenta (non-standard terms in use) Potential momentum: Kinetic momentum:
Cononical momentum:
Irradiance, light intensity - = time averaged poynting vector
- I = irradiance
- I0 = intensity of source
- P0 = power of point source
- Ω = solid angle
- r = radial position from source
At a spherical surface:
Doppler effect for light (relativistic) Cherenkov radiation, cone angle - n = refractive index
- v = speed of particle
- θ = cone angle
Electric and magnetic amplitudes - E = electric field
- H = magnetic field strength
For a dielectric EM wave components Electric Magnetic
Geometric optics
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Physical situation Nomenclature Equations Critical angle (optics) - n1 = refractive index of initial medium
- n2 = refractive index of final medium
- θc = critical angle
Thin lens equation - f = lens focal length
- x1 = object length
- x2 = image length
- r1 = incident curvature radius
- r2 = refracted curvature radius
Lens focal length from refraction indices
Image distance in a plane mirror Spherical mirror - r = curvature radius of mirror
Spherical mirror equation Image distance in a spherical mirror
Subscripts 1 and 2 refer to initial and final optical media respectively.
These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation:
where:
- ε = permittivity of medium,
- μ = permeability of medium,
- λ = wavelength of light in medium,
- v = speed of light in media.
Polarization
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Physical situation Nomenclature Equations Angle of total polarisation - θB = Reflective polarization angle, Brewster's angle
intensity from polarized light, Malus' law - I0 = Initial intensity,
- I = Transmitted intensity,
- θ = Polarization angle between polarizer transmission axes and electric field vector
Diffraction and interference
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Property or effect Nomenclature Equation Thin film in air - n1 = refractive index of initial medium (before film interference)
- n2 = refractive index of final medium (after film interference)
- Minima:
- Maxima:
The grating equation - a = width of aperture, slit width
- α = incident angle to the normal of the grating plane
Rayleigh's criterion Bragg's law (solid state diffraction) - d = lattice spacing
- δ = phase difference between two waves
- For constructive interference:
- For destructive interference:
where
Single slit diffraction intensity - I0 = source intensity
- Wave phase through apertures
N-slit diffraction (N ≥ 2) - d = centre-to-centre separation of slits
- N = number of slits
- Phase between N waves emerging from each slit
N-slit diffraction (all N) Circular aperture intensity - a = radius of the circular aperture
- J1 is a Bessel function
Amplitude for a general planar aperture Cartesian and spherical polar coordinates are used, xy plane contains aperture - A, amplitude at position r
- r' = source point in the aperture
- Einc, magnitude of incident electric field at aperture
Near-field (Fresnel) Far-field (Fraunhofer)
Huygen-Fresnel-Kirchhoff principle - r0 = position from source to aperture, incident on it
- r = position from aperture diffracted from it to a point
- α0 = incident angle with respect to the normal, from source to aperture
- α = diffracted angle, from aperture to a point
- S = imaginary surface bounded by aperture
- = unit normal vector to the aperture
Kirchhoff's diffraction formula
Astrophysics definitions
In astrophysics, L is used for luminosity (energy per unit time, equivalent to power) and F is used for energy flux (energy per unit time per unit area, equivalent to intensity in terms of area, not solid angle). They are not new quantities, simply different names.
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Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Comoving transverse distance DM pc (parsecs) [L] Luminosity distance DL pc (parsecs) [L] Apparent magnitude in band j (UV, visible and IR parts of EM spectrum) (Bolometric) m dimensionless dimensionless Absolute magnitude (Bolometric)
M dimensionless dimensionless Distance modulus μ dimensionless dimensionless Colour indices (No standard symbols)
dimensionless dimensionless Bolometric correction Cbol (No standard symbol) dimensionless dimensionless
See also
- Defining equation (physics)
- Defining equation (physical chemistry)
- List of electromagnetism equations
- List of equations in classical mechanics
- List of equations in gravitation
- List of equations in nuclear and particle physics
- List of equations in quantum mechanics
- List of equations in wave theory
- List of relativistic equations
Footnotes
Sources
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Further reading
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