Traversable wormholes in f ( R , L m ) gravity with gravitational lensing and photon dynamics

We study static and spherically symmetric traversable wormhole solutions within the framework of Formula: see text gravity, considering anisotropic matter sources. We focus on the specific functional form Formula: see text, in which Formula: see text is identified with the energy density of the matter distribution. By adopting a Morris-Thorne spacetime with a constant redshift function and a power-law shape function Formula: see text (Formula: see text), we analyze the geometrical properties, matter content, and energy conditions. Two distinct cases, namely Formula: see text and Formula: see text, are examined in detail. We show that the flare-out condition and asymptotic flatness are satisfied in both models. The null energy condition is violated only in the radial direction near the throat, while remaining satisfied transversely. The amount of exotic matter, quantified through the volume integral, is finite and controlled by the parameter Formula: see text. Further, the embedding diagrams confirm the traversable wormhole geometry. Moreover, we analyze the gravitational lensing signatures of the wormhole geometry through the effective potential and the light deflection angle, thereby characterizing the photon dynamics in the vicinity of the throat. Finally, we conclude that Formula: see text gravity admits viable traversable wormhole solutions supported by anisotropic matter, with the parameters Formula: see text and Formula: see text offering control over the distribution of matter and the degree of energy-condition violation.