Table 1.

Some polarization conditions for 2D-IR spectroscopy

α*	β	γ	δ	Tensor element†
0	π/4	−π/4	0	1/2(〈xxyy〉 + 〈xyxy〉)
π/4	0	−π/4	0	1/2(〈xxyy〉 + 〈xyyx〉)
π/4	−π/4	0	0	1/2(〈xyyx〉 + 〈xyxy〉)
π/3	−π/3	0	0	1/4(〈xxxx〉 − 3〈xxyy〉)
0	π/3	−π/3	0	1/4(〈xxxx〉 − 3〈xyyx〉)
θ	−θ	π/2	0	1/2sin2θ(〈xyxy〉 − 〈xyyx〉)
π/2	θ	−θ	0	1/2sin2θ(〈xxyy〉 − 〈xyxy〉)
circ	circ	0	0	1/2(〈xxxx〉 + 〈xxyy〉)
circ	0	circ	0	1/2(〈xxxx〉 + 〈xyxy〉)

^*The angles measured with respect to one of the polarization axes; circ means circularly polarized light of a given sense, and results are obtained from laboratory fixed field unit vectors that are complex. For example, for a process generating a macroscopic polarization P_δ = χ_αβγδE_αE^*_βE^*_γ, the general tensor element would be 〈α_iβ^*_jγ^*_kδ_l〉. 

^† Subscripts have been removed, e.g. 〈xyxy〉 = 〈x_iy_jx_ky_l〉, because the relations are true for all paths i,j,k,l. In our experiment, x and y are orthogonal polarization axes perpendicular to the direction of pulse propagation, z.