Deep iris recognition models are often trained on Cartesian grids, whereas iris texture follows a concentric structure with angular periodicity. This representational mismatch can weaken rotation robustness and limit pupil-to-limbus context modeling, while many pipelines still rely on accurate segmentation masks. We propose RadialFormer, an efficient mask-free iris recognition framework that performs representation learning directly in the polar domain. The pipeline first estimates pupil/iris parameters (cx , cy, rin, rout) using a percentile radial-gradient operator with anatomical constraints, and then applies a crop-based polar transform to obtain a compact 64 × 512 unwrapped iris map. To better match polar geometry, we introduce Learnable Polar Position Encoding (LPPE) with separable radial–angular embeddings, where Fourier terms in the angular branch enforce continuity at θ = 0/2π. We further propose Radial Stripe Window Attention (RSWA), which computes self-attention within full-height radial stripes and uses modular angular shifting to preserve circular consistency. Trained end-to-end with batch-hard triplet loss under P × K sampling, RadialFormer achieves 99.04% TPR@1%FPR with 0.48% EER on CASIA-V4-Lamp, and 93.63% TPR@1%FPR with 2.92% EER on CASIA-V4-Interval. Ablation and cross-dataset evaluations further validate the contributions of polar processing, LPPE, and RSWA and demonstrate robust generalization across acquisition conditions. Under the same input resolution, RadialFormer reduces computation by about 3.5× compared with a standard transformer baseline while maintaining competitive recognition accuracy.