  We show that the dominant absorption peak due to inter-subband transition in
a gated quantum wire, with two occupied subbands, will split into a main peak
and two satellite peaks if both Rashba and Dresselhaus spin-orbit interactions
are present. One satellite peak will be red-shifted, and the other
blue-shifted. From the relative intensity of either satellite peak, and the
magnitude of the red- or blue-shift, we can determine both Rashba and
Dresselhaus interaction strengths separately, if we also carry out a Hall
measurement to determine the carrier concentration and a quantized conductance
step measurement to determine the energy separation between subbands. This
method may be a convenient alternative to usual magneto-transport measurements
used to measure spin orbit interaction strengths. It is also more powerful
because it allows us to measure the strengths of the two types of interactions
separately.
