We optimized the Si(substrate)/$SiO_2$(cladding)/$Si_3N_4$(antiresonant cladding)/$SiO_2$(core)/air multi-layers rib-optical waveguides of antiresonant reflecting optical waveguide (ARROW) for integrated optical biosensor structure utilizing beam propagation method (BPM). Thickness of anti-resonant cladding was derived to minimize the propagation loss and leaky field mode deeply related with evanescent mode was theoretically derived. Depth, width, refractive index and cladding thickness of anti-resonant cladding were numerically calculated into 2.3${mu}m$, 5${mu}m$, 1.488, and 0.11${mu}m$ respectively to minimize propagation loss using the BPM simulation tool. Finally one- and two-dimensional propagation characteristics of ARROW was confirmed.