A novel single-mode large-mode-area (LMA) optical fiber is proposed. The primary part of the cladding is a thin layer with high refractive index. The layer possesses a periodic array of holes (or intrusions) which are either drawn in the propagation direction or drilled in the radial direction. When the holes (or intrusions) are drawn in the propagation direction, the periodicity of their array is in the azimuthal direction. The core may be hollow. The light confinement is achieved via a transmission anti-resonance. Namely, the array of holes allows coupling between an optical mode inside the primary cladding layer and the light both in the core and in the outer space. The light then sees two channels to penetrate the cladding: direct transmission and holes-assisted transmission. A distractive interference between these channels is achieved at an appropriate combination of fiber parameters. The fiber can be designed to hold nearly anyone of TE/TMnm modes. Computer simulations of the fiber were performed using COMSOL. The open boundary was simulated using a perfectly matched layer and the attenuation constants of different modes were determined via the imaginary parts of their propagation constants. As an example, a fiber holding a single TE01 mode inside a core of 100 μm diameter for the vacuum wavelength 1.55 μm was designed. The attenuation constant of the TE01 mode was found to be 5.8 ⋅ 10−6 [dB/cm] while the other modes had attenuation of at least 4 orders of magnitude larger. Required fabrication tolerances were calculated and the fabrication of fibers of lengths 10 – 1000 m was found to be feasible. The bandwidth of the fiber was found to be in the range of 5 – 35 nm, depending on its length. Possible applications include high-power CW and pulsed lasers and amplifiers, sensors and others.