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CASTEP Studies of Non-linear Optical Properties of Materials

CASTEP Studies of Non-linear Optical Properties of Materials. Ming-Hsien Lee. Tamkang University, Taiwan. SHG (Second Harmonic Generation). P = P 0 + c (1) E + c (2) E E + c (3) E E E + … p = m 0 + a E + b E E + g E E E + …. w. 2w. Optical Storage

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CASTEP Studies of Non-linear Optical Properties of Materials

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  1. CASTEP Studies of Non-linear Optical Properties of Materials Ming-Hsien Lee Tamkang University, Taiwan

  2. SHG (Second Harmonic Generation) • P = P0 + c(1) E + c(2)E E + c(3) E E E + … • p = m0 + aE + bE E + gE E E + … w 2w Optical Storage Fiber Optics Communication Lithography Fundamental Research

  3. Methods Planewave Optimized/Ultrasolt Pseudopotential DFT (CASTEP : CAmbridge Serial Total Energy Package) Sum-over-states χ(2) formalism*** Band-resolved Analysis χ(2) or β re-evaluation Wavefunction Partitioning Analysis** * R.N.Rashkeev, W.R.L. Lamberrecht, B. Segall, PRB 57 3905 (1998) ** J. Lin, M-H.Lee, Z.P. Liu, C.T. Chen, C.J. Pickard, PRB 60 13380 (1999)

  4. I-III-VI2 IR NLO crystals Case study :

  5. IR NLO crystals AgGaS2 AgGaSe2 Small band gap Large band gap Low IR threshold High IR threshold Mix AgGa (SxSe1-x)2 Mechanical Properties IR absorption edge Band gap (in preparation) This work : How does c(2)change ?

  6. Calculated χ(2)123 of Ag16Ga16 (Sx Sey)32 AgGaSe2 AgGaS2

  7. What’s the difference between S and Se ? S=32,Se=0 S =24,Se=8 S=16 ,Se=16 S=8,Se=24 S=0,Se=32 No difference in terms of their chemical behavior => more “physical” reason ?

  8. Cell Volume vs Substitution Ratio Black marks : Experiment Red marks : Calculation

  9. Band-gap vs Substitution Ratio Black marks : Calculation Red marks : Experiment

  10. Black marks : Calculation Red marks : Experiment

  11. Cell volume effect ? Cell Volume χ (2) Black line:Expt Red line:Cal Band-gap Correlation between volume, band-gap and χ (2)clearly exist But is it a real effect ?

  12. Band-Gap and χ(2) variation : Purely Volume Effect ? Expanding AgGaS2 compressing AgGaSe2 100% Volume ratio Volume ratio 115% 100% 85% Sufficient to reproduce gap and c(2) variation. The observed correlation is not an accident. Can it be only due to gap?

  13. Band-Gap Effect ? Sum-over-states χ(2) formalism

  14. Is it totally controlled by gap ? gap replacement AgGaSe2 AgGaS2 χ(2) variation is largely controlled by the band-gap Is that all ?

  15. Detailed Analysis : Based on sum-over-states formalism J. Lin, M-H.Lee, Z.P. Liu, C.T. Chen, C.J. Pickard, PRB 60 13380 (1999) R.N.Rashkeev, W.R.L. Lamberrecht, B. Segall, PRB 57 3905 (1998)

  16. Pattern & Spacing Sign reversed

  17. Pattern & Spacing Sign reversed

  18. χ(2) using energy level spectra substitution Anion size effect volume energy level χ(2) Particle in the box picture !(we believe)

  19. Both the trend and the value of c(2) can be predicted for the anion substitution in AgGa(SxSe1-x)2 crystals.Contribution from zone center is stronger.VE and VH contribute in opposite direction. Computationally proved :Anion size effect => volume => band-gap => c(2) Conclusion : AgGa(SxSe1-x)2

  20. What about Molecules ?

  21. Case study : Push-pull benzenes : H2N-C6H4-NO2 Benzene is one of the most important building blocks in organic molecules. Exist three structural isomers. (p-, o-, m- nitroaniline)

  22. Isomers of push-pull benzene (nitroaniline) p-NA o-NA m-NA Is the number of empty bands enough ?

  23. Convergence test on # of unoccupied orbital β/ βmax Unoccupied Not very many unoccupied orbitals are needed Now we can analyze further detail.

  24. Band-resolved β of p-NA, o-NA and m-NA 26 27 26 30 27 29 27 26 30 26 27 30 26 27 29 26 27 30 26 27 26 27 26 27 27 27 26 21 21 27 26 10 21 10 8 26 10 21 8 21 10 21

  25. Observed • VH Process remine more or less constant, VE process vary a lot. • Only a few orbitals are important (∵energy denominator). • They are all in p –symmetry (∵ p –bonding is pool). • Two groups of orbitals : push-derived and pull-derived. What does that (4) mean ? Have a closer look.

  26. pNA oNA mNA

  27. Energy level spacing No important trend Energy level effect ?

  28. Energy level deformation We want to exam energy level spacing effect, but direct replacement of spectrum will be impossible (total # of orbitals not same) and meaningless (level crossing). What we really want is to adjust the energy level difference between those important orbitals.

  29. Re-evaluate β with same set of energy level spectrum 1.97 0.65 0.25 0.26 0.26 2.05 0.66 0.46 0.41 0.48 1.80 0.76 Matrix element effect

  30. Wavefunction Partitioning Analysis More contribution from benzene ring

  31. VH contribution does not change much among the three structural isomers. Not the case for VE (pNA > oNA > mNA).We have proposed a level-spacing deformation scheme to allow the re-evaluation and comparison of beta for the isomers. The SHG is determined by the matrix element part, which is supposed to be sensitive to the change of orientation and bonding of push and pull functional groups on the plane of benzene ring.More contribution come from benzene ring than end groups. Conclusion : nitroaniline

  32. Case study : Push-pull polyenes : H2N-(-CH=CH-)n-NO2 Largest b reported is found in this type of molecules. One-dimensional system : pure and simple model

  33. Push-pull polyenes : H2N-(-CH=CH-)n-NO2 βcalc = 7.74 βcalc = 42.14 βcalc = 168.64 βcalc = 421.44 βcalc = 917.27 Case study : It is known that β of H2N-(-CH=CH-)n-NO2 increase dramatically with respect to the length of conjugate chain Our calculation reflects this trend Again, is there enough empty orbital ?

  34. Unoccupied state convergence test fairly small # of unoccupied orbitals are needed Very tempting to think it as gap effect. Is it ?

  35. H2N-(-CH=CH-)n-NO2 : HOMO/LUMO gap effect Gap effect ? x10-30 Gap effect is not very important What else ? Lets resolve bands and see.

  36. Push-pull polyenes : Band-Resolved β (x1) Huge increase indeed.

  37. Push-pull polyenes : Band-Resolved β (x10) What are these ?

  38. Push-pull polyenes : Band-Resolved β (x1)

  39. Push-pull polyenes : Band-Resolved β (x10) Same character and order. (All p again) Similar orbitals ! Energy level effect ?

  40. Key orbitals are all p-symmetry type n = 1 band index 17 18 20 7

  41. n = 2 9 22 23 25

  42. n = 3 10 27 28 29

  43. n = 4 32 33 34 12

  44. n = 5 39 14 37 38 Similar orbitals ! Energy level effect ?

  45. β of H2N-(-CH=CH-)n-NO2 3.38 3.07 2.28 2.03 1.57 1.61 1.63 1.64 1.67 3.46 3.11 2.29 2.04 1.28 1.29 1.29 1.29 1.29 3.48 3.11 2.29 2.04 1.06 1.07 1.08 1.09 1.09 3.54 3.14 2.30 2.04 1.04 1.04 1.05 1.06 1.06 3.56 3.17 2.32 2.05 Important effect comes from energy level spacing ! Again no entanglement. Given fewer levels now, we can actually exam the energy level.

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