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Origin and symmetry of optical nonlinearities
International Tables for Crystallography (2013). Vol. D, Section 1.7.2, pp. 181-186 [ doi:10.1107/97809553602060000906 ]
... in the case of organic crystals) per unit volume, a, b and c are the eigen states of the system, [Omega ... mu] component of the transition dipole connecting states a and b, and is the population of level a as given by ... tensorial nature of nonlinear molecular media. J. Opt. Soc. Am. B, 15, 257-288. Butcher, P. N. (1965). Nonlinear ...
Contracted notation for susceptibility tensors
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.2.1.3, p. 185 [ doi:10.1107/97809553602060000906 ]
Contracted notation for susceptibility tensors 1.7.2.2.1.3. Contracted notation for susceptibility tensors The tensors or are invariant with respect to ([alpha], [beta]) permutation as a consequence of the intrinsic permutation symmetry. Independently, it is not possible to distinguish the coefficients and by SHG experiments, even if the two fundamental waves have different ...
Manley-Rowe relations
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.2.1.2, p. 185 [ doi:10.1107/97809553602060000906 ]
Manley-Rowe relations 1.7.2.2.1.2. Manley-Rowe relations An important consequence of overall permutation symmetry is the Manley-Rowe power relations, which account for energy exchange between electromagnetic waves in a purely reactive (e.g. non-dissipative) medium. Calling Wi the power input at frequency [omega]i into a unit volume of a ...
ABDP and Kleinman symmetries
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.2.1.1, pp. 184-185 [ doi:10.1107/97809553602060000906 ]
... in the case of organic crystals) per unit volume, a, b and c are the eigen states of the system, [Omega ... mu] component of the transition dipole connecting states a and b, and is the population of level a as given by ...
Intrinsic permutation symmetry
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.2.1, pp. 184-185 [ doi:10.1107/97809553602060000906 ]
... in the case of organic crystals) per unit volume, a, b and c are the eigen states of the system, [Omega ... mu] component of the transition dipole connecting states a and b, and is the population of level a as given by ...
Symmetry properties
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.2, pp. 184-186 [ doi:10.1107/97809553602060000906 ]
... in the case of organic crystals) per unit volume, a, b and c are the eigen states of the system, [Omega ... mu] component of the transition dipole connecting states a and b, and is the population of level a as given by ...
Convention used in this chapter
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.1.4.2, p. 184 [ doi:10.1107/97809553602060000906 ]
Convention used in this chapter 1.7.2.1.4.2. Convention used in this chapter The K convention described above is often used, but may lead to errors in cases where two of the interacting waves have the same frequency but different polarization states. Indeed, as demonstrated in Chapter 1.6 and recalled in Section 1.7.3 ...
Classical convention
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.1.4.1, pp. 183-184 [ doi:10.1107/97809553602060000906 ]
Classical convention 1.7.2.1.4.1. Classical convention Insertion of (1.7.2.26) in (1.7.2.25) together with permutation symmetry provideswhere the summation over [omega] stands for all distinguishable permutation of , K being a numerical factor given bywhere p is the number of distinct permutations of , n is the order of the nonlinear process, m is the ...
Conventions for nonlinear susceptibilities
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.1.4, pp. 183-184 [ doi:10.1107/97809553602060000906 ]
Conventions for nonlinear susceptibilities 1.7.2.1.4. Conventions for nonlinear susceptibilities 1.7.2.1.4.1. Classical convention | | Insertion of (1.7.2.26) in (1.7.2.25) together with permutation symmetry provideswhere the summation over [omega] stands for all distinguishable permutation of , K being a numerical factor given bywhere p is the number of distinct permutations of , n is the order ...
Superposition of monochromatic waves
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.1.3, p. 183 [ doi:10.1107/97809553602060000906 ]
Superposition of monochromatic waves 1.7.2.1.3. Superposition of monochromatic waves Optical fields are often superpositions of monochromatic waves which, due to spectral discretization, will introduce considerable simplifications in previous expressions such as (1.7.2.20) relating the induced polarization to a continuous spectral distribution of polarizing field amplitudes. The Fourier transform of the induced ...
International Tables for Crystallography (2013). Vol. D, Section 1.7.2, pp. 181-186 [ doi:10.1107/97809553602060000906 ]
... in the case of organic crystals) per unit volume, a, b and c are the eigen states of the system, [Omega ... mu] component of the transition dipole connecting states a and b, and is the population of level a as given by ... tensorial nature of nonlinear molecular media. J. Opt. Soc. Am. B, 15, 257-288. Butcher, P. N. (1965). Nonlinear ...
Contracted notation for susceptibility tensors
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.2.1.3, p. 185 [ doi:10.1107/97809553602060000906 ]
Contracted notation for susceptibility tensors 1.7.2.2.1.3. Contracted notation for susceptibility tensors The tensors or are invariant with respect to ([alpha], [beta]) permutation as a consequence of the intrinsic permutation symmetry. Independently, it is not possible to distinguish the coefficients and by SHG experiments, even if the two fundamental waves have different ...
Manley-Rowe relations
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.2.1.2, p. 185 [ doi:10.1107/97809553602060000906 ]
Manley-Rowe relations 1.7.2.2.1.2. Manley-Rowe relations An important consequence of overall permutation symmetry is the Manley-Rowe power relations, which account for energy exchange between electromagnetic waves in a purely reactive (e.g. non-dissipative) medium. Calling Wi the power input at frequency [omega]i into a unit volume of a ...
ABDP and Kleinman symmetries
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.2.1.1, pp. 184-185 [ doi:10.1107/97809553602060000906 ]
... in the case of organic crystals) per unit volume, a, b and c are the eigen states of the system, [Omega ... mu] component of the transition dipole connecting states a and b, and is the population of level a as given by ...
Intrinsic permutation symmetry
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.2.1, pp. 184-185 [ doi:10.1107/97809553602060000906 ]
... in the case of organic crystals) per unit volume, a, b and c are the eigen states of the system, [Omega ... mu] component of the transition dipole connecting states a and b, and is the population of level a as given by ...
Symmetry properties
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.2, pp. 184-186 [ doi:10.1107/97809553602060000906 ]
... in the case of organic crystals) per unit volume, a, b and c are the eigen states of the system, [Omega ... mu] component of the transition dipole connecting states a and b, and is the population of level a as given by ...
Convention used in this chapter
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.1.4.2, p. 184 [ doi:10.1107/97809553602060000906 ]
Convention used in this chapter 1.7.2.1.4.2. Convention used in this chapter The K convention described above is often used, but may lead to errors in cases where two of the interacting waves have the same frequency but different polarization states. Indeed, as demonstrated in Chapter 1.6 and recalled in Section 1.7.3 ...
Classical convention
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.1.4.1, pp. 183-184 [ doi:10.1107/97809553602060000906 ]
Classical convention 1.7.2.1.4.1. Classical convention Insertion of (1.7.2.26) in (1.7.2.25) together with permutation symmetry provideswhere the summation over [omega] stands for all distinguishable permutation of , K being a numerical factor given bywhere p is the number of distinct permutations of , n is the order of the nonlinear process, m is the ...
Conventions for nonlinear susceptibilities
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.1.4, pp. 183-184 [ doi:10.1107/97809553602060000906 ]
Conventions for nonlinear susceptibilities 1.7.2.1.4. Conventions for nonlinear susceptibilities 1.7.2.1.4.1. Classical convention | | Insertion of (1.7.2.26) in (1.7.2.25) together with permutation symmetry provideswhere the summation over [omega] stands for all distinguishable permutation of , K being a numerical factor given bywhere p is the number of distinct permutations of , n is the order ...
Superposition of monochromatic waves
International Tables for Crystallography (2013). Vol. D, Section 1.7.2.1.3, p. 183 [ doi:10.1107/97809553602060000906 ]
Superposition of monochromatic waves 1.7.2.1.3. Superposition of monochromatic waves Optical fields are often superpositions of monochromatic waves which, due to spectral discretization, will introduce considerable simplifications in previous expressions such as (1.7.2.20) relating the induced polarization to a continuous spectral distribution of polarizing field amplitudes. The Fourier transform of the induced ...
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