We propose an alternative approach to the description and analysis of
photoelectron angular distributions (PADs) resulting from isotropic samples in
the case of few-photon absorption via electric fields of arbitrary
polarization. As we demonstrate for the one- and two-photon cases, this
approach reveals the molecular frame information encoded in the bl,mβ
expansion coefficients of the PAD in a particularly clear way. Our approach
does not rely on explicit partial wave expansions of the scattering wave
function and the expressions we obtain are therefore interpreted in terms of
the vector field structure of the photoionization dipole D(k) as
a function of the photoelectron momentum k. This provides very compact
expressions that reveal how molecular rotational invariants couple to the setup
(electric field polarization and detectors) rotational invariants. We rely
heavily on this approach in a companion paper on tensorial chiral setups. Here
we apply this approach to one-photon ionization and find that while b0,0β
depends only on the magnitude of D(k), b1,0β (non-zero for
chiral molecules) is sensitive only to the components of D(k)
perpendicular to k encoded in the propensity field
B(k)β‘iDβ(k)ΓD(k), and
b2,0β is sensitive only to the the component of D(k) along
k. We also analyze the resonantly enhanced two-photon case where we
show that b0,0β and b1,0β can be written in terms of an effectively
stretched D(k), and that b1,0β and b3,0β reveal
structural information of the field B(k) encoded in three of its
vector spherical harmonic expansion coefficients.Comment: 26 pages, 5 figure