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High Resolution Coherent 3D Spectroscopy of Bromine Benjamin R. Strangfeld Georgia Institute of Technology, Atlanta, GA Peter C. Chen, Thresa A. Wells, and Zuri R. House Spelman College, Atlanta, GA

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Simulated spectra of 79 Br 2, 79,81 Br 2, and 81 Br 2 513 nm 514 nm 4 (nm) 1 (nm) Expansion into two dimensions provides separation and ordering of peaks Bromine chosen to explore 3D Coherent Spectroscopy

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Show 2D data and 3D data (put oval around the 2D area being shown in the 3D plot) For Bromine, several peaks per square nanometer in 3D, as opposed to hundreds per square nanometer in 2D Expanding the 2D plot into 3D space 1 2 3 4

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1 2 3 4 5 67 8 910 hgfahgfa hgdahgda gdbagdba gfeagfea hfcahfca hdcahdca 1 3 2 4 3 1 2 4 3 2 1 4 1 2 3 4 1 3 2 4 2 1 3 4 1 2 3 4 3 1 2 4 2 3 1 4 3 2 1 4 1 = dye laser 2 = tunable OPO 3 = broadband OPO 4 = output

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Experimental Setup Nd:YAG Laser Nd:YAG Laser Raman Shifter Broadband OPO Monochromator with CCD sample Tunable dye laser Tunable OPO

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“Process 4” gfeagfea X state, low v” X state, high v” B state, low v’ B state, high v’ 1 2 3 4 X state B state E r V” = 1 V” = 31-34 V’ = 6 V’ = 24-33

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Acquired dataSimulated data ω 1 = 16326.42 cm -1 corresponds to v”=1, J”=62 to v’=6, J’=61 in the 79-81 isotopomer, columns correspond to v’ = 25-27, diagonals correspond to v” = 31-33 ω 1 = 16326.53 cm -1 corresponds to v”=2, J”=49 to v’=8, J’=48 in the 79-79 isotopomer, columns correspond to v’ = 29-32, diagonals correspond to v” = 32-34 ω 1 = 16326.39 cm -1 corresponds to v”=2, J”=48 to v’=8, J’=47 in the 81-81 isotopomer, columns correspond to v’ = 29-32, diagonals correspond to v” = 32-34 Gerstenkorn and Luc, J Phys France, 50 (1989) Dye Laser set to ω 1 = 16326.42 cm -1 (P-type resonance) with a linewidth of about 0.15 cm -1

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Selectivity Change ω1 to the corresponding R-type resonance ω 1 = 16340.21 cm -1 corresponds to v”=1, J”=62 to v’=6, J’=63 in the 79-81 isotopomer, columns correspond to v’ = 25-27, diagonals correspond to v” = 31-33 ω 1 = 16340.18 cm -1 corresponds to v”=0, J”=71 to v’=4, J’=72 in the 79-81 isotopomer, columns correspond to v’ = 21-23, diagonals correspond to v” = 29-32 ω 1 = 16340.36 cm -1 corresponds to v”=2, J”=43 to v’=8, J’=42 in the 79-81 isotopomer, columns correspond to v’ = 28-32, diagonals correspond to v” = 32-35

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Have seen that the horizontal spacing between clusters depends on the spacing of the higher vibrational levels in the B state, v’, and that the vertical spacing depends on the higher vibrational levels in the X State, v” Inter- and Intra-cluster Relationship What determines the shape of the cluster itself, and what is the spacing between peaks within a cluster? 33

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1 2 3 4 For a parametric process:Process 4: 33 (where x=J”) x, B” x+1, x-1, B’ x, x+2, x-2, B” x+1, x-1, B’ Zeroth order rotational energy term E = B v J(J+1) Two possible x-axis ( 4) values: x-1 x : B’(x 2 -x) – B”(x 2 +x) x+1 x : B’(x 2 +3x+2) – B”(x 2 +x) Four possible y-axis ( 3) values: x+2 x+1 : B’(x 2 +3x+2) – B”(x 2 +5x+6) x x-1 : B’(x 2 -x) – B”(x 2 +x) x-2 x-1 : B’(x 2 -x) – B”(x 2 -3x+2) x x+1 : B’(x 2 +3x+2) – B”(x 2 +x) (Keep in mind, this is an easy, rigid-rotor analysis, not as in depth as doing a full Dunham coefficient analysis)

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Diagram of Process 4 cluster spacing

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It’s now possible to calculate J” or B from the data: J” = 62 J” = 49 Cluster size depends on J” and the rotational contants, B, of two of the electronic states involved Calculated from our Bromine data: B” = B v” = 0.0695 B’ = B v’ = 0.0372 In general: B v = B e – α e (v + ½) + γ e (v + ½) 2 + … Using the constants B e, α e, γ e from Coxon, Barrow, and Clark: B” = B v” = 0.0706 B’ = B v’ = 0.0445 B” agrees fairly well, however the error in B” is carried into the calculation for B’, causing there to be a higher amount of error in the B’ calculation

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1 2 3 4 Take a look at Process 1: 33 (where x=J”) x, B” x+1, x-1, B’ x, x+2, x-2, B’’’ x+1, x-1, B’ Zeroth order rotational energy term E = B v J(J+1) Two possible x-axis ( 4) values: x-1 x : B’(x 2 -x) – B”(x 2 +x) x+1 x : B’(x 2 +3x+2) – B”(x 2 +x) Four possible y-axis ( 3) values: x+1 x+2 : B’’’(x 2 +5x+6) – B’(x 2 +3x+2) x-1 x : B’’’(x 2 +x) – B’(x 2 -x) x-1 x-2 : B’’’(x 2 -3x+2) – B’(x 2 -x) x+1 x : B’’’(x 2 +x) – B’(x 2 +3x+2)

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Diagram of Process 1 cluster spacing

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What about Processes 2 & 3? From Density Matrix Theory, we know we only get triply resonant signal for Process 2 when da = ha and for Process 3 only when ba = ga (or is at least close enough that it is within the linewidth of the laser) which happens infrequently and without pattern

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“Process 1” fafa X state, low v” X state, high v” B state, low v’ B state, high v’ 1 2 3 4 X state B state E r V” = 1 V” = 31-34 V’ = 6 V’ = 24-33

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Inter-cluster pattern OPO 44 44 dye laser ea da ha ba fa ha ba ga da ga Process 1Process 2Process 3Process 4 OPO scan: rectangular gridrarerare parallelogram Dye laser scan: rare rectangular grid parallelogramrare fa ha ga da ha ga da ba ga fa ea ga Denominator:

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