Intensity-induced phase in linear optics

We identify situations where optical phase modulation can be induced by intensity variations in the linear domain. In particular, for scalar two-beam in and two-beam out spatial unitary systems (beam splitters), we find that the phase difference between the output beams can be altered by changing the intensity ratio of the input beams. Utilizing this principle, we show that in linear optics (even in a very low-intensity regime), it is possible to introduce a two-dimensional spatial phase profile by spatial intensity modulation, thus affecting the propagation and far-field distribution of the ensuing beam.