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1 Supporting normation Quantiication o the Depolarization and Anisotropy o Fluorophore Stokes-Shited Fluorescence, On- Resonance-Fluorescence, and Rayleigh-Scattering Kumudu Siriwardana, Buddhini C.N. Vithanage, Shengli Zou, and Dongmao Zhang,* Department o Chemistry, Mississippi State University, Mississippi State, Mississippi, 39762, United States Department o Chemistry, University o Central Florida, Orlando, Florida 32816, United States * Corresponding author: Dongmao@chemistry.msstate.edu Fax: S1

2 Contents Page S1. Determination o eective excitation and emission path lengths d x and d m... S3 S2. Justiication o eqs. 39 and 40 in the main text.... S4 S3. Excitation wavelength and emission wavelengths or luorophore SSF spectrum... S6 S4. Cuvette Resonance Synchronous Background Spectra... S7 S5. Experimental Validation o the nstrument G-actor Spectrum... S8 S6. Experimental spectra or quantiication o the luorophore SSF depolarization and Anisotropy... S9 S7. Experimental quantiication o luorophore ttering and depolarization and anisotropy and cross-sections or AOH... S10 S8. Experimental quantiication o luorophore ttering and depolarization and anisotropy and cross-sections or FTC S11 S9. Experimental quantiication o luorophore ttering and depolarization and anisotropy and cross-sections or Eosin Y... S12 S10. Experimental quantiication o luorophore ttering and depolarization and anisotropy and cross-sections or QD S13 S11. Experimental quantiication o luorophore ttering and depolarization and anisotropy and cross-sections or R6G...S14 S12. RS2 spectra obtained or R6G with dierent excitation and emission polarization combinations...s15 S13. Reerence.....S16 S2

3 S1. Determination o eective excitation and emission path lengths d x and d m Figure S1. Determination o eective excitation and emission path lengths. (A) UV-vis spectra o series o Ni(NO 3 ) 2 and K 2 Cr 2 O 7 mixture solutions. The Ni(NO 3 ) 2 concentration was held constant and K 2 Cr 2 O 7 concentration was varied orm 0, 0.05, 0.1, 0.2, 0.3, and 0.4 mm. Red dashed and red solid lines indicate the excitation and water Raman photon wavelengths or the Raman spectra acquired with an excitation wavelength o 300 nm. (B) As-acquired Raman spectra with 300 nm excitation. (C) Curve-itting determination o eective excitation and emission path lengths using previously reported method. 1 (D) FE-corrected Raman spectra o the solutions. S3

4 S2 Justiication o Eqs. 39 and 40 in the main text. To acilitate the discussion, we use the X-, Y-, Z- axes shown in Figure 1 in the main text to discuss the photon propagation and polarization direction. We assume that the light propagates along X-axis in all spectral acquisitions. Taking light ttering as an example, the ttering cross-section derived rom UV-vis measurement is based on plane polarized light excitation that excitation photons can be viewed as the sum o equal amount o photons polarized perectly along the Y- and Z-axis. The total ttered photon intensity can be viewed as the sum o ttered photons with polarization along X,Y, and Z-directions. Mathematically the intensity o photons ttered by can be expressed with Eq. S1. ( ) (J, K=X, Y, or, JK Z) reers to intensity o the ttered photons with polarization along K axis that is excited with light with polarization along the J axis. = ( ) (S1) (, ZZ, ZX, ZY, YY, YX, YZ Assuming that has a depolarization o P (, the above equation can be simpliied into Eq. S2 and urther to Eq. S3. n this simpliication, we considered the act that, =, and = = = ( ). This is because YY, ZZ, ZX (, ZY, YX, YZ s in solution are uniormly distributed and the depolarization rom Z to X, Z to Y, and Y to X, and Y to Z must be identical. = 2 + 4P ( ) (S2) (, ZZ, ZZ = (2+ 4P ), (S3) ZZ Same arguments are applicable or calculating total luorophore photon ttering (Eq. S4) and photons (Eq. S5) excited with plane polarized photons. = (2+ 4P ), (S4) ZZ = (2+ 4P ), (S5) The experimentally measured ( ), ( ), and ( ) spectra are related to, VV, VV ZZ, VV ( ), ( ), and ( ) as expressed with Eq. S6, S7, and S8, respectively. δ ( is an, ZZ, ZZ, ZZ instrument parameter that is related to the detector acceptance angle and sampling volume. = δ ( ) (S6), VV (, ZZ = δ ( ) (S7), VV (, ZZ S4

5 = δ ( ) (S8), VV (, ZZ Dividing Eq. S7 and S8 by Eq. S6 leads to Eq. S9 and Eq. S10, respectively., VV, VV, VV, VV, ZZ( = (S9), ZZ, ZZ( = (S10), ZZ Using the expression o, ZZ and, ZZ( derived rom Eq. S4 and Eq. S5, respectively, one can derive the Eq. S11 and Eq. S12, respectively Since, VV, VV, VV, VV C σ = and C σ PNSP PNSP C with σ C σ and C σ C (2+ 4P ) = (S11) (2+ 4P ) (2+ 4P ) = (S12) (2+ 4P ) σ PNSP PNSP C σ =, replacing C σ in Eq. S11 and S12 and with simple and rearrangement leads to Eq. S13 and S14, respectively. Eq. S13 and S14 are Eqs 39 and 40, respectively in the main text. σ (1+ 2P = (1+ 2P ) C ) C, VV, VV σ σ (S13) (1+ 2P ) C, VV = σ ( (S14) (1+ 2P ) C, VV S5

6 S3. Excitation wavelength and emission wavelengths or luorophore SSF spectrum Table S1. Excitation and emission wavelengths o luorophores. Fluorophore Excitation wavelength (nm) QD QD AOH R6G FTC Eosin Y Emission wavelength range (nm) S6

7 S4. Cuvette Resonance Synchronous Background Spectra Figure S2. Resonance synchronous background spectra or empty cuvette. Background PRS 2 PRS 2 PRS 2 spectra were acquired as (red) ( ), (black) ( ), (blue) ( ), bg, NN bg, VV bg, VH PRS 2 PRS 2 (magenta) ( ), and (green) ( ). The spectrum with NN is acquired with bg, HV bg, HH neither excitation nor detection polarizer. S7

8 S5. Experimental Validation o the nstrument G-actor Spectrum Figure S3. Experimental data or G( validation. (top row) The as-acquired (black) SSF and (red) SSF spectra or the speciied validation luorophore. HV HH (Bottom row) comparison o the (black) SSF and (red) G( SSF spectra or the HV validation spectra. The act that the SSF and (red) G( SSF spectra overlapped HV near perectly or all the luorophore indicates the G( is valid or correcting the detection polarization bias o the instrument. t is noted that the luorophores used in this validation are all dierent rom those used or the G-actor spectrum determination. HH HH S8

9 S6. Experimental spectra or quantiication o the luorophore SSF depolarization and Anisotropy Figure S4. (Top) Solution polarized SSF emission spectra, (Bottom) SSF (black) depolarization and (red) anisotropy spectra obtained or the speciied model luorophores. S9

10 S7. Experimental quantiication o luorophore ttering and depolarization and anisotropy and cross-sections or AOH Figure S5. Experimental data obtained with luorophore AOH in water. (A) as-acquired (black) solution, VH( and (red) solution, VV(. (B) as-acquired solvent spectrum (black) PRS 2 Solv, VH and (red) PRS 2 Solv, VV. (C) the ttering spectra (black), VH and (red), VV. (D) The sample-fe-corrected solution spectra (black) solution, VH and (red) solution, VV. (E) luorophore-speciic polarized spectra (black) PRS 2, VH and (red) PRS 2, VV. (F) Comparison o the luorophore (blue) multiplication spectrum, VH G / P( with (red) PRS 2, VV. (G) The, VV spectrum obtained by subtracting PRS 2 2, VV with PRS, VH G / P(. (H) (red) luorophore polarized and (black) photon ttering cross-section spectra calculated using the polarized as the external reerence. S10

11 S8. Experimental quantiication o luorophore ttering and depolarization and anisotropy and cross-sections or FTC Figure S6. Experimental data obtained with luorophore FTC in water. (A) as-acquired (black) solution, VH( and (red) solution, VV(. (B) as-acquired solvent spectrum (black) PRS 2 Solv, VH and (red) PRS 2 Solv, VV. (C) the ttering spectra (black), VH and (red), VV. (D) The sample-fe-corrected solution spectra (black) solution, VH and (red) solution, VV. (E) luorophore-speciic polarized spectra (black) PRS 2, VH and (red) 2, VV. (F) Comparison o the luorophore (blue) multiplication spectrum PRS 2, VH G / P( with (red) PRS 2, VV. (G) The, VV spectrum obtained by subtracting PRS PRS 2 2, VV with PRS, VH G / P(. (H) (red) luorophore polarized and (black) photon ttering cross-section spectra calculated using the polarized as the external reerence. S11

12 S9. Experimental quantiication o luorophore ttering and depolarization and anisotropy and cross-sections or eosin Y Figure S7. Experimental data obtained with luorophore eosin Y in water. (A) as-acquired (black) solution, VH( and (red) solution, VV(. (B) as-acquired solvent spectrum (black) PRS 2 Solv, VH and (red) PRS 2 Solv, VV. (C) the ttering spectra (black), VH and (red), VV. (D) The sample-fe-corrected solution spectra (black) solution, VH and (red) solution, VV. (E) luorophore-speciic polarized spectra (black) PRS 2, VH and (red) PRS 2, VV. (F) Comparison o the luorophore (blue) multiplication spectrum, VH G / P( with (red) PRS 2, VV. (G) The, VV spectrum obtained by subtracting PRS 2 2, VV with PRS, VH G / P(. (H) (red) luorophore polarized and (black) photon ttering cross-section spectra calculated using the polarized as the external reerence. S12

13 S10. Experimental quantiication o luorophore ttering and depolarization and anisotropy and cross-sections or QD570 Figure S8. Experimental data obtained with luorophore QD570 in water. (A) as-acquired (black) solution, VH( and (red) solution, VV(. (B) as-acquired solvent spectrum (black) PRS 2 Solv, VH and (red) PRS 2 Solv, VV. (C) the ttering spectra (black), VH and (red), VV. (D) The sample-fe-corrected solution spectra (black) solution, VH and (red) solution, VV. (E) luorophore-speciic polarized spectra (black) PRS 2, VH and (red) PRS 2, VV. (F) Comparison o the luorophore (blue) multiplication spectrum, VH G / P( with (red) PRS 2, VV. (G) The, VV spectrum obtained by subtracting PRS 2 2, VV with PRS, VH G / P(. (H) (red) luorophore polarized and (black) photon ttering cross-section spectra calculated using the polarized as the external reerence. S13

14 S11. Experimental quantiication o luorophore ttering and depolarization and anisotropy and cross-sections or R6G Figure S9. Experimental data obtained with luorophore R6G in water. (A) as-acquired (black), and (red),. (B) as-acquired solvent spectra solution VH solution VV (black) PRS 2 Solv, VH and (red) PRS 2 Solv, VV. (C) the ttering spectra (black), VH and (red), VV. (D) The sample-fe-corrected solution spectra (black) solution, VH and (red) solution, VV. (E) luorophore-speciic polarized spectra (black) PRS 2, VH and (red) PRS 2, VV. (F) Comparison o the luorophore (blue) multiplication spectrum, VH G / P( with (red) PRS 2, VV. (G) The, VV spectrum obtained by subtracting PRS 2 2, VV with PRS, VH G / P(. (H) (red) luorophore polarized and (black) photon ttering cross-section spectra calculated using the polarized as the external reerence. S14

15 S12. RS2 spectra obtained or R6G with dierent excitation and emission polarization combinations Figure S10. RS 2 spectra obtained or R6G by changing excitation and emission polarizer. E (Black) NN and (red) VV. S15

16 S13. Reerences 1. Nettles, C. B.; Hu, J.; Zhang, D. Anal. Chem. 2015, 87, S16