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Complex refractive index of a medium (relative to vacuum), a function of the wavelength of light in vacuum, λ, is defined as follows:
| m(λ) = m'(λ) - m"(λ) i | (1) |
where m' is the real part of the refractive index, also referred to as the refractive index itself, a ratio of the velocity of light in the medium to that in vacuum, m" is the imaginary part of the index and i = √(-1). The use of the term "ratio" implies that the refractive index is always relative to a medium. Generally, if referred to as the relative refractive index, it is relative to a medium other then vacuum. It is relative to vacuum otherwise. In the optics of particles, the refractive index of the particle material is generally taken to be relative to that of the medium surrounding the particle.
The imaginary part of the refractive index is sometimes referred to as the extinction coefficient (for example, in a Wikipedia article on the refractive index) or as the absorption index. The extinction coefficient referred to in this context is not the same as that referred to in Attenuation coefficient. Hence, the use of the term "extinction coefficient" in reference to the imaginary part of the refractive index may be confusing and is discouraged.
There is a variety of notations for the refractive index, for example: m = n - ki, n = nr - nii. Bohren and Huffman (1983) point out that the sign convention for the imaginary part of the refractive index is related to a choice of the sign of the exponent in the time-dependent part, exp(iωt), of the expression for an amplitude of a monochromatic electromagnetic wave. Thus, with exp(-iωt), one would have m = m' + m" i.
The imaginary part, m"i, of the complex refractive index, mi, is related to the absorption of light by the medium. Indeed, the electric field, E, of a plane monochromatic electromagnetic wave propagating in the medium depends on position, expressed by z, as follows:
| E | = E0 exp(-imkz) | |
| = E0 exp(-im' kz) exp(-m"kz) | (2) |
where k = 2π /λ is the wave number in vacuum. The first exponential term in the second line of this equation describes a non-decaying oscillation of the wave amplitude in space. The second exponential term describes a decay of those oscillations with distance, z, in the medium, an effect of absorption of light by that medium.
If the imaginary part of the refractive index in Eq. 1 becomes positive, the amplitude of an electromagnetic wave increases as it propagates through the medium. Such a medium, as in a laser cavity, provides gain.
The power of the wave is the time average of the product E E*, where E* is the complex conjugate of E. Hence, the power of the wave decays in a medium with a non-zero imaginary part of the refractive index as exp(-2m"kz). On the other hand, the Lambert law expresses this decay as exp(-az), where a is the absorption coefficient of the medium. By comparing the exponents, we obtain the following relationship between the imaginary part of the refractive index, m", and the absorption coefficient, a:
| m"(λ) = a(λ) λ / (4π) | (3) |
See also Refractive indices of various materials
| CITATION: Jonasz M. 2006. Refractive index (www.tpdsci.com/Tpc/RI.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 22-Feb-2006 Modified: 11-Jul-2009 Peer-reviewed: PENDING |
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