polarization independent optical isolator / circulator devices based on mach - zehnder interferometers . the devices utilize either polarization splitting and nonreciprocal polarization conversion or nonreciprocal phase shift within the interferometric arm . for devices with nonreciprocal phase shift , the relative phase difference is 0 ° in the forward propagation direction and 180 ° in the backward propagation direction , or vice versa , so that light goes into a bar or cross port depending on the propagation direction . the devices have advantages over previous designs in the use of inexpensive device components , simple alignment , minimal space requirement , and negligible polarization mode dispersion or polarization dependent loss . in addition , the devices can be made in a waveguide form with minimal loss and with high fabrication ease . an additional phase compensator and / or a variable attenuator can be integrated in order to relax the fabrication tolerances .