  We have investigated optical properties of 4248 infrared galaxies (IRGs) by
positionally matching data from the IRAS and the SDSS DR3. Our sample includes
3 hyper luminous infrared galaxies (L >10^13Lsun) and 178 ultra luminous
infrared galaxies (10^12Lsun < L < 10^13Lsun). Our findings are as follows: (i)
more IR luminous galaxies tend to have smaller local galaxy density, being
consistent with the picture where luminous IRGs are created by the
merger-interaction of galaxies that happens more often in lower density
regions; (ii) the fractions of AGNs increase as a function of Lir; (iii) there
is a good correlation between Lir and L[OIII] for AGNs, suggesting both of the
parameters can be a good estimator of the total power of AGNs; (iv) a good
correlation is found between Lir and optically estimated star formation rate
(SFR) for star-forming galaxies, suggesting Lir is a good indicator of galaxy
SFR. However, caution is needed when SFR is estimated using Lir, i.e., high SFR
galaxies selected by Lir is frequently merger/interaction, whereas high SFR
galaxies selected by optical emission is often normal spiral or
Magellanic-cloud like irregular galaxies. (v) more IR luminous galaxies have
slightly larger Halpha/Hbeta ratio; (vi) more IR luminous galaxies have more
centrally-concentrated morphology, being consistent with the morphological
appearance of galaxy-galaxy merger remnants. Optical image of ultra/very
luminous infrared galaxies also show frequent signs of merger/interaction.
(vii) comparison with the SED synthesis models indicate that majority of
luminous infrared galaxies (L > 10^11Lsun) may be in a post-starburst phase,
sharing a similar (but not the same) merger/interaction origin with E+A
galaxies. (abridged)
