Indoor diffuse optical intensity channels are bandwidth constrained due to the multiple reflected paths between the transmitter and the receiver which cause considerable inter-symbol interference (ISI). The transmitted signal amplitude is inherently non-negative, being a light intensity signal. All optical intensity root Nyquist pulses are time-limited to a single symbol interval which eliminates the possibility of finding bandlimited root Nyquist pulses. However, potential exists to design bandwidth efficient pulses. This paper investigates the modified hermite polynomial functions and prolate spheroidal wave functions as candidate waveforms for designing spectrally efficient optical pulses. These functions yield orthogonal pulses which have constant pulse duration irrespective of the order of the function, making them ideal for designing an ISI free pulse. Simulation results comparing the two pulses and challenges pertaining to their design and implementation are discussed.