  We determine lower and upper bounds on the capacity of bandlimited optical
intensity channels (BLOIC) with white Gaussian noise. Three types of input
power constraints are considered: 1) only an average power constraint, 2) only
a peak power constraint, and 3) an average and a peak power constraint.
Capacity lower bounds are derived by a two-step process including 1) for each
type of constraint, designing admissible pulse amplitude modulated input
waveform ensembles, and 2) lower bounding the maximum achievable information
rates of the designed input ensembles. Capacity upper bounds are derived by
exercising constraint relaxations and utilizing known results on discrete-time
optical intensity channels. We obtain degrees-of-freedom-optimal (DOF-optimal)
lower bounds which have the same pre-log factor as the upper bounds, thereby
characterizing the high SNR capacity of BLOIC to within a finite gap. We
further derive intersymbol-interference-free (ISI-free) signaling based lower
bounds, which perform well for all practical SNR values. In particular, the
ISI-free signaling based lower bounds outperform the DOF-optimal lower bound
when the SNR is below 10 dB.
