Chapte 4 continued Chial o not chial esponse functions otational aveages linea and nonlinea signals
Undestanding this
And maybe this
Non-linea signal signal ( ( ( ( f E( tn sf... E( t2 q E( t 0q aveage ove oientations * f ˆ fs s e dψ f ( ψ ( s f q n ( t n ( t ( s 0 2 ( t 2 Incoming fields Sample Polaize defining emitted field (compae NM Detecto
E( t M α L E( t E α e e α E( t α β... { X Y Z} l m... { x y z} Fame Tansfomation Genealization E Polaization of field in lab fame ( χ φ M α ( α χ φ ϑ ϑ α L L L L ( (... ( ( pol n α β γ.. l... γ n n... β 2 Field oientations 2 α 2 m pol l n Tansition dipole in molecula fame m Column index (latin molecule... 2 Tansition dipole components γ l... Aveage ove otation matix elements β α - sinφ sinχ + cosθ cosφ cosχ sinφ cos χ cosφ sin χ cosθ cosφ sinθ sinχ cosφ + sinφ cosθ cosχ -sinφ cosθ sinχ - cosφ cosχ sinφ sinθ cos χ sinθ sin χ sinθ cosθ ow index α (gee fields
D. L. Andews and T. Thiunamachandan J. Chem. Phys. 67 (977 5026-5033 Oientational aveages ae invaiant unde otation of coodinate system Any otationally invaiant tenso can be witten in tems of Konece Deltas and Levi Civita symbols and can be deived fom geneal goup-theoetical aguments Oientational Aveage γ β α α γ β α β γ α β γ 4 4 4 30 l m l m m l l m l l αβγ α β γ 6 αβ α β 3 else if 0 β α αβ γ α γ β β α αβγ αβγ αβγ o if anticyclic if cyclic if 0 Absoption CD OD SHG sum-fequency mixing Photon echo 2D aman
Linea Spectoscopy X Y X b Y ; m E-field Electic dipoleallowed B-field Magnetic and electic dipoleallowed
X Y X b Y ; L L ( X ( X 0 Linea Spectoscopy Y 0 0 Y m m m L L ( ( 0 0 0 YY 0 0 0 0 0 0 X XX X 0 0 0 2 Electic dipoleallowed Magnetic and electic dipoleallowed
Geneal polaization ules Allowed Field polaizations: (ection polaize in X-diection l l l 2 m l lm m l m T 2 3 αβγ γ β α α γ β α β γ α β γ ββγ 4 4 4 30 l m l m m l l m lm T 5.. +.. +.. Coesponding molecula quantities: Absoption SHG sum-fequency mixing Photon echo 2D aman Fluoescence
Allowed Field polaizations: (ection polaize in X-diection Geneal polaization ules Consequences st ode If the sample is isotopic CD and OD ae the only linea signals that could be measued with cossed polaizes. Magnetic dipole inteaction equied. Coesponding molecula quantities: m m CD ( t Y X Sample Polaize defining Detecto OD Optical activity: otation of polaization independent of oientation!
Allowed Field polaizations: (ection polaize in X-diection In isotopic samples thee is no second hamonic geneation (fequency doubling because all fields ae in the same XY plane when they popagate along the same Z axis. 2 ( t 2 ( t Sample Geneal polaization ules Consequences 2nd ode Polaize defining Detecto Coesponding molecula quantities: l l l 2 esonant l 2 χ ( l l Non- esonant Suface-sensitive spectoscopy (not full ot. Symmety!
Allowed Field polaizations: (ection polaize in X-diection In non-collinea sum fequency mixing (fequency doubling 3 fields can be pependicula to each othe Geneal polaization ules Consequences 2nd ode Coesponding molecula quantities: l l 2 esonant l 2 ( t 2 ( t Sample Polaize defining Detecto l χ ( l 2 l Non- esonant
Allowed Field polaizations: (ection polaize in X-diection Geneal polaization ules Consequences 2nd ode Coesponding molecula quantities: In non-collinea sum fequency mixing 3 fields can be pependicula to each othe. No magnetic dipole inteaction needed! l χ l (2 l χ + χ + χ xyz yzx zxy χ χ χ xzy yxz zyx 2 ( t 2 The sample esponse vanishes unless the molecule is chial! ( t Sample Polaize defining Detecto Half - esonant
Chial SFG SPP PSP 2 ( t 2 ection Y vis ω << I ω vis sum X 2 ( t Z I Sample Polaize defining Belin M. A.; Kulaov T. A.; Enst K. H.; Yan L.; Shen Y.. Phys. ev. Lett. 2000 85 4474.
chial bacgound: achial SFG 2 ( t 2 vis ( t I Sample Polaize defining Belin M. A.; Kulaov T. A.; Enst K. H.; Yan L.; Shen Y.. Phys. ev. Lett. 2000 85 4474.
bacgound: achial SFG achial m 2 ( t 2 vis PPP ( t Sample Polaize defining I Belin M. A.; Kulaov T. A.; Enst K. H.; Yan L.; Shen Y.. Phys. ev. Lett. 2000 85 4474.
bacgound: achial SFG achial m 2 ( t 2 vis PPP ( t I Sample Polaize defining Belin M. A.; Kulaov T. A.; Enst K. H.; Yan L.; Shen Y.. Phys. ev. Lett. 2000 85 4474.
What maes the signal chial? Chial signal Achial bacgound ( E ( B m ( E ( E wea stong Fast polaization modulation equied ( E ( E ( E ( E ( E ( B ( ( E E ( t E q wea Bacgound fee ( E ( E ( E ( B m vey wea ( E ( E ( E ( E vey wea stong Fast polaization modulation o filteing equied 4 D
Why cicula polaized light? X ( t Sample Y Polaize defining Tansmitted signal would be vey wee No distinction between enantiomes! m cos( ωt x cos( ωt x + CD sin( ωt On esonance emitted field is phase shifted by +/-90 depending on enantiome y
Why cicula polaized light? Linea polaization cos( ωt x ight-handed cicula cos( ωt x sin( ωt y Destuctive intefeence CDsin( ωt sin( ωt y y X CDsin( ωt y cos( ωt x + sin( ωt y CDsin( ωt + sin( ωt y y Y z Left-handed cicula Constuctive intefeence
Why cicula polaized light? ight-handed cicula cos( ωt x sin( ωt y Destuctive intefeence CD sin( ωt y E sin( ωt y y CD y ± E y y 2 CD 2 + E y 2 ± 2 e( CD E y Without polaize: intefeence E x x cos( ωt geneates CD y sin( ωt E y y cos( ωt CD x cos( ωt intefeence
Field view of optical activity Signal geneation Intefeence
Signal Sign in Chial SFG
Signal Sign in Chial SFG SPP Chial 2nd ode ection SPPS ω0 ω ω 2 ω +ω 2 Achial 3d ode (solvent ( t Static electic field Y Opposite sign fo enantiomes 2 ( t 2 Z Y X Sample X Polaize defining Opposite sign fo opposite static electic fields
Signal Sign in Chial SFG S (2 chial x ± S (3 achial x 2 S (2 chial 2 + S (3 achial 2 ± 2 e( S (2 chial S (3 achial ( t Static electic field Y Opposite sign fo enantiomes 2 ( t 2 Z Y X Sample X Polaize defining Opposite sign fo opposite static electic fields
3d ode chial spectoscopy
3d ode chial spectoscopy signal ( ( ( ( 0 E( tn 0 E( t2 0 B( t m0 aveage ove oientations SSSP 3 ( t 3 ( t 0 2 ( t 2 Incoming fields Sample Polaize defining emitted field (compae NM Detecto
3d ode (chial spectoscopy sign-sensitivity signal ( ( ( ( 0 E( tn 0 E( t2 0 B( t m0 aveage ove oientations SSSP ( t 0 Signal is ovelapped with additional field 3 ( t 3 2 ( t 2 Sample Polaize defining Detecto Incoming fields emitted field (compae NM
B850 B800
Chial pump-pobe spectoscopy signal ( ( ( ( 0 E( tn 0 E( t2 0 B( t m0 aveage ove oientations SSSP pump pobe 3 ( t 3 2 ( t 2 ( t Incoming fields Sample Polaize defining emitted field (compae NM 0 Signal is ovelapped with pobe pulse Detecto
Chial pump-pobe spectoscopy Niezboala C.; Hache F. J. Am. Chem. Soc. 2008 30 2783.
Chial pump-pobe spectoscopy Niezboala C.; Hache F. J. Am. Chem. Soc. 2008 30 2783.
Chial pump-pobe spectoscopy
I pobe λ-selection polaize x etadation (PEM Time-esolved VCD sample visible pump Detecto Cicula pobe L L Delay τ VCD with pump VCD without pump Tansient VCD Bonmain Helbing Opt. Lett. 33 (2008 2086 Xie and Simon 992 (electonic CD
I pobe λ-selection polaize x etadation (PEM Time-esolved VCD sample visible pump Detecto Pobe A Cicula pobe N Cl N Co Cl 0.4 0.2 B A 6 C 32 C -0.3-0.6-0.9 VCD and Absoption change Pobe B 25 OD 0.3 mod 2900 2850 2900 2850 Bonmain Helbing Opt. Lett. 33 (2008 2086 Xie and Simon 992 (electonic CD -00 0 00 Time (ps