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Nonlinear Optics and Photonics$

Guang S. He

Print publication date: 2014

Print ISBN-13: 9780198702764

Published to Oxford Scholarship Online: December 2014

DOI: 10.1093/acprof:oso/9780198702764.001.0001

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(p.620) Appendix 7 Tensor Elements of the Nuclear Third-Order Susceptibility in the Born–Oppenheimer Approximation

(p.620) Appendix 7 Tensor Elements of the Nuclear Third-Order Susceptibility in the Born–Oppenheimer Approximation

Source:
Nonlinear Optics and Photonics
Publisher:
Oxford University Press

Since the tensor element χijkl(3)nuc of the nuclear third-order susceptibility is invariant under the permutations (ij), (kl), and (ijkl), it can be denoted by a new compact symbol Dll. The relations of the cartesian indices between these two symbols are:{ij,kl=xxyyzzyzxzxyl,l=123456. The distributions of nonzero elements of Dll are the same as those of the elastic compliance constant tensors of crystals. The number of the independent nonzero elements is given in parentheses.

Crystal System

Crystal Class

Triclinic

{11¯

D11D12D13D14D15D16D12D22D23D24D25D26D13D23D33D34D35D36D14D24D34D44D45D46D15D25D35D45D55D56D16D26D36D46D56D66

(21)

Monoclinic

{2m2/m

D11D12D130D150D12D22D230D250D13D23D330D350000D440D46D15D25D350D550000D460D66

(13)

Orthorhombic

{222mm2mmm

D11D12D13000D12D22D23000D13D23D33000000D44000000D55000000D66

(9)

Trigonal

{33¯

D11D12D13D14D250D12D11D13D14D250D13D13D33000D14D140D4402D25D25D2500D442D140002D252D142(D11D12)

(7)

{3m3¯m32

D11D12D13D1400D12D11D13D1400D13D13D33000D14D140D44000000D442D1400002D142(D11D12)

(6)

Tetragonal

{44¯4/m

D11D12D1300D16D12D11D1300D16D13D13D33000000D44000000D440D16D16000D66

(7)

{4mm4224¯2m4/mmm

D11D12D13000D12D11D13000D13D13D33000000D44000000D44000000D66

(6)

Hexagonal

{66¯6/m6226mm6/mmm6¯m2

D11D12D13000D12D11D13000D13D13D33000000D44000000D440000002(D11D12)

(5)

Cubic

{23m34324¯3mm3m

D11D12D12000D12D11D12000D12D12D11000000D44000000D44000000D44

(3)

Isotropic

[D11D12D12000D12D11D12000D12D12D110000002(D1100D12)00002(D110D12)000002(D11D12)]

(2)

See R. W. Hellwarth, Prog. Quantum Electron. 5, 1(1977); J. F. Nye, Physical Properties of Crystals (Oxford University Press, London, 1957).

(p.621)