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Supplementary Information
Fully automated dual-frequency three-pulse-echo 2DIR spectrometer accessing spectral range
from 800 to 4000 wavenumbers
Joel D. Leger,1,a) Clara M. Nyby,1,a) Clyde Varner,1 Jianan Tang,1 Natalia I. Rubtsova,1 Yuankai Yue,1
Victor V. Kireev,1 Viacheslav D. Burtsev,1 Layla N. Qasim,1 Grigory I. Rubtsov,2 and Igor V.
Rubtsov1,*
1
2 Institute
Department of Chemistry, Tulane University, New Orleans, Louisiana 70118
for Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russian Federation
a)
These two authors contributed equally to this work
Corresponding author: E-mail: [email protected]
*
Phase-matching geometry using a parabolic reflector
In the case of using a parabolic reflector to focus the beams onto the sample, the angles at the focus, β1 and
β2 (see Fig.1), depend on the separation between beams before the parabolic reflector Δ1 (Δ1 is the half
distance between beams 1 and 2).
tan 𝛽1 =
∆1 (2𝑓 + ∆1 )
2𝑓(𝑓 + ∆1 )
tan 𝛽2 =
∆1 (2𝑓 − ∆1 )
2𝑓(𝑓 − ∆1 )
Fig. 1. An illustration of the phase-matched geometry with the use of a parabolic reflector. γ is the angle between the axis of the
parabola, a1, and the axis determined by bisection of angles β1 and β2, a2. β1 is the angle from beam 1 to the axis of the parabola and β2
is the same for beam 2.
To solve for optimal geometry at the sample, axis a2 is constructed as the bisecting line between β1 and β2
and the phase matching conditions are implemented.
𝛽1 + 𝛽2
𝑥 = 𝑘1 sin(𝛽2 − 𝛾) = 𝑘1 sin(𝛽2 + 𝛾) = 𝑘1 sin (
)
2
𝑥 = 𝑘3 sin(𝛽3 − 𝛾)
𝛽1 + 𝛽2
𝑘3 sin(𝛽3 − 𝛾) = 𝑘1 sin (
)
2
Thus, the phase matching conditions can be met exactly with:
𝑘
𝛽1 +𝛽2
𝑘3
2
𝛽3 = 𝛾 + asin ( 1 sin
)