a Transmission electron micrographs of representative few-arm nanostars (50 nm scale bar) with insets displaying individual tips (5 nm scale bars). b Experimental configuration, in which photoelectrons with initial transverse (vx,vy) velocity are linearly mapped onto (x,y) position on a spatially-resolved microchannel plate detector. c Three example nanostars, each with a single dominant plasmon resonance mode excited via polarization aligned along the arm axes, as indicated by the arrows (50 nm scale bars). d Polarization-dependent photoemission rate at peak resonance wavelengths for each of the three stars, characterizing the peak polarization settings. Data is fit to cos2n(θ − θtip) for multiphoton process order n. e Summary of multiphoton process orders for plasmon resonance modes on different nanostars, determined via linear intensity-dependence fits on log–log plots (power-law behavior) as demonstrated for the three example stars. The resulting process order data is fit to a sigmoidal curve from n = 3.01(3) to n = 3.99(4), demonstrating the clear transition from the three-photon to the four-photon regime with decreasing photon energy. Intermediate values between 3 and 4 are effective process orders representing a weighted average of three- and four-photon contributions. All reported parenthetical values are standard errors of the variance-weighted nonlinear least-squares fits.