Theory
Consider a system are of localized, non-interacting absorbing centers. Based on the semi-classical radiation absorption theory within the electric dipole approximation, the electric vector of the circularly polarized waves propagates in the +z direction, where + and -denote to RCP light and LCP light respectively. In this system, ω = 2nν is the circular frequency, and Ii = n – ik is the complex refractive index. As the light travels, the attenuation of the beam is expressed as
- I(z) = I0exp(−2ωkz/c)
where k is the absorption coefficient of the medium in the z direction. Circular dichroism (CD) is then defined as Δk = k– – k+, and it follows the sign convention of natural optical activity. In the presence of the static, uniform external magnetic field, the Hamiltonian for the absorbing center takes the form Ĥ = Ĥ0 + Ĥ1 which is parallel to the direction of the propagation of the electric field k. Because the transition occur between the two eigenstates of Ĥ0, a and j, the absorption and the CD intensity are determined as follows:
Read more about this topic: Magnetic Circular Dichroism
Famous quotes containing the word theory:
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)
“We commonly say that the rich man can speak the truth, can afford honesty, can afford independence of opinion and action;—and that is the theory of nobility. But it is the rich man in a true sense, that is to say, not the man of large income and large expenditure, but solely the man whose outlay is less than his income and is steadily kept so.”
—Ralph Waldo Emerson (1803–1882)
“The things that will destroy America are prosperity-at-any- price, peace-at-any-price, safety-first instead of duty-first, the love of soft living, and the get-rich-quick theory of life.”
—Theodore Roosevelt (1858–1919)