In the rapidly advancing landscape of 6G, characterized by ultra-high-speed wideband transmission in millimeter-wave and terahertz bands, our paper addresses the pivotal task of enhancing physical layer security (PLS) within near-field wideband communications. We introduce true-time delayer (TTD)-incorporated analog beamfocusing techniques designed to address the interplay between near-field propagation and wideband beamsplit, an uncharted domain in existing literature. Our approach to maximizing secrecy rates involves formulating an optimization problem for joint power allocation and analog beamformer design, employing a two-stage process encompassing a semi-digital solution and analog approximation. This problem is efficiently solved through a combination of alternating optimization, fractional programming, and block successive upper-bound minimization techniques. Additionally, we present a low-complexity beamsplit-aware beamfocusing strategy, capitalizing on geometric insights from near-field wideband propagation, which can also serve as a robust initial value for the optimization-based approach. Numerical results substantiate the efficacy of the proposed methods, clearly demonstrating their superiority over TTD-free approaches in fortifying wideband PLS, as well as the advantageous secrecy energy efficiency achieved by leveraging low-cost analog devices.