An optical phased array (OPA) in silicon nitride (SiN) is conspicuously highlighted as a vital alternative to its counterpart in silicon. However, a limited number of studies have been conducted on this array in terms of wavelength-tuned beam steering. A SiN OPA has been proposed and implemented with a grating antenna that incorporated an array of shallow-etched waveguides, rendering wavelength-tuned beam steering along the longitudinal direction. To accomplish a superior directionality on a wavelength-tuned beam steering, the spectral beam emission characteristics of the antenna have been explored from the viewpoint of a planar structure that entails a buried oxide (BOX), a SiN waveguide core, and an upper cladding. Two OPA devices having substantially different thicknesses of the resonant cavities, established by combining the BOX and SiN core, were considered theoretically and experimentally to scrutinize the spectral emission characteristics of the antenna on beam steering. Both of the fabricated OPA devices steered light by an angle of 7.4° along the longitudinal direction for a wavelength ranging from 1530 to 1630 nm, while they maintained a divergence angle of 0.2°×0.6° in the longitudinal and lateral directions. Meanwhile, the OPA fabricated on a substantially thick BOX layer featured a limited steering performance to attain a stabilized response over a broad spectral region. We examined the influence of the cavity thickness on the spectral response of the antenna in terms of optical thickness. Based on the two antenna characteristics, it was confirmed that the grating antenna emitted the beam with a higher efficiency when the optical thickness of the cavity corresponded to odd integer multiples of the quarter wavelength. This work is a considerable strategy for designing a stabilized SiN OPA over a desired spectral region.