We investigate the angular distribution of the photon emission spectra in the nonlinear Compton scattering of electron driven by an ultrashort intense laser pulse. Within the framework of strong-field quantum electrodynamics theory, we numerically calculate the photon emission spectrum and analyze its angular dependence on the polar and azimuthal angles under three different conditions: the total photon energy, fixed photon energy, and fixed harmonic order. Our analysis reveals that the complex interference patterns originate from the electron’s motion, which can be decomposed into a constant-velocity motion along the initial incident direction and a laser-driven transverse harmonic oscillation. The constant-velocity motion determines an overall emission cone, focusing the radiation into the electron forward direction, and the transverse oscillation governs the interference fine structures in the spectra. Our key finding is that the number of nodes in the angular distribution of the
ℓth-order harmonic photon emission is
ℓ – 1. To elucidate this pattern, we introduce a redefined spherical coordinate system where the polar axis is aligned with the laser polarization (i.e., the electron oscillation direction). In this coordinate frame, the radiation spectra for different harmonic orders are presented in
Figure for
ℓ = 1, 2, 3, and 8. These plots clearly show that the
ℓ-th harmonic possesses exactly
ℓ – 1 nodes in its angular distribution, i.e., zero for
ℓ = 1, one for
ℓ = 2, two for
ℓ = 3, and seven for
ℓ = 8. We explain this structure using multipole radiation theory, based on the classical formula \mathrmdP/\mathrmd \varOmega \propto \sin2\theta'P'_\ell (\cos \theta')2, in which P'_\ell denotes the derivative of the
ℓ-th Legendre polynomial. This formula precisely predicts
ℓ – 1 nodes in the angular profile. Thus, the observed
ℓ – 1 node rule is in full agreement with multipole radiation theory. Our work exhibits how the combined effect of the electron’s initial constant-velocity motion and laser-driven oscillatory motions shapes the angular profile of nonlinear Compton radiation. Our results provide fundamental insights for understanding high-harmonic generation in strong-field physics and for designing new advanced light sources with tailored photon energy and angular properties.