  We present the physical properties of AKARI sources without optical
counterparts in optical images from the Hyper Suprime-Cam (HSC) on the Subaru
telescope. Using the AKARI infrared (IR) source catalog and HSC optical
catalog, we select 583 objects that do not have HSC counterparts in the AKARI
North Ecliptic Pole (NEP) wide survey field ($\sim 5$ deg$^{2}$). Because the
HSC limiting magnitude is deep ($g_{\rm AB}$ $\sim 28.6$), these are good
candidates for extremely red star-forming galaxies (SFGs) and/or active
galactic nuclei (AGNs), possibly at high redshifts. We compile multi-wavelength
data out to 500 $\mu$m and use it for Spectral Energy Distribution (SED)
fitting with CIGALE to investigate the physical properties of AKARI galaxies
without optical counterparts. We also compare their physical quantities with
AKARI mid-IR selected galaxies with HSC counterparts. The estimated redshifts
of AKARI objects without HSC counterparts range up to $z\sim 4$, significantly
higher than that of AKARI objects with HSC counterparts. We find that: (i) 3.6
$-$ 4.5 $\mu$m color, (ii) AGN luminosity, (iii) stellar mass, (iv) star
formation rate, and (v) $V$-band dust attenuation in the interstellar medium of
AKARI objects without HSC counterparts are systematically larger than those of
AKARI objects with counterparts. These results suggest that our sample includes
luminous, heavily dust-obscured SFGs/AGNs at $z\sim 1-4$ that are missed by
previous optical surveys, providing very interesting targets for the coming
James Webb Space Telescope era.
