The spider structure in the photoelectron momentum distributions (PMDs) of ionized electrons from the hydrogen atom is simulated by solving the time-dependent Schrödinger equation (TDSE). We find that the spider structure exhibits sensitive dependence on carrier envelope phase (CEP) of the few-cycle pulses. To elucidate the striking CEP dependence of the spider structure, we select three physical parameters I L, I R, and I R/I L to quantitatively characterize the variations of the spider structure induced by altering the CEPs. I L is the sum of the left half panel of the transverse cut curves (i.e., the sum of all the negative momenta along the laser polarization direction), I R is the sum of the right half panel of the transverse cut curves (i.e., the sum of all the positive momenta along the laser polarization direction), and I R/I L is the ratio between the two sums. These parameters are shown to have monotonic relation with the CEP value, which is exploited to extract the CEPs. We anticipate that our method will be useful for obtaining CEPs encoded in the spider structure of PMDs.

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We present results of numerical simulations on the photoelectron momentum distributions of the p-orbital electrons of neon atoms ionized by a pair of time-delayed and oppositely circularly polarized intense laser pulses. Deploying the strong-field theory, we can readily produce vortex-shaped momentum distributions. Similarity and disparity in the vortex patterns between the neon and hydrogen atoms are observed. The optical Stark effect is found to induce distortions in the vortex momentum distributions, which are quantitatively described by introducing several physical quantities. Among these quantities, the autocorrelation parameter turns out to be the most sensitive probe for extremely weak Stark effect. The nonlinear phase induced by the optical Stark effect deciphers the distortions of the vortex momentum distributions.