  We have done theoretical calculations and simulations for infrared
spectroscopy at the MMT 6.5 m with laser guide star AO, which provides almost
full sky coverage. The results show we can expect 40-60% of the photons from a
unresolved source within 0.2 arcsec diameter circle for J, H, K, L and M bands
under typical atmospheric seeing condition at 2.2 micron. Therefore, the
spectrograph entrance slit size should match the 0.2 arcsec image to obtain
high throughput. Higher resolution can be achieved by narrowing down the slit
size to match the diffraction-limited image core size of about 0.1 arcsec in
the infrared. However, the throughput will be correspondingly reduced by a
factor of two. Due to the limited atmospheric isoplanatic angle in the J, H and
K bands, the encircled photon percentage within 0.2 arcsec diameter drops from
40-60% when the object is at the laser pointing direction to 20-40% when the
object is about 30 arcsec away from the laser direction. Therefore, the useful
field of view for AO multiple object spectroscopy is about 60 arcsec. Further
studies of IR background (sky and thermal) and IR detector performance show
that spectral resolution of R = 2,000 can take full advantage of AO images
without much penalty due to the dark current of the IR detector and IR OH sky
emission lines.
  We have also studied natural guide star AO spectroscopy. More details are in
the paper.
