A Mach-Zehnder interferometer (MZI) that includes in an arm either a reflective image inverter or a Gouy phase shifter (RGPS) can (de)multiplex many types of modes of a few mode fiber without fundamental loss. The use of RGPSs in combination with binary phase plates for multiplexing purposes is studied for the first time, showing that the particular RGPS that shifts π the odd modes only multiplexes accurately low order modes. To overcome such a restriction, we present a new exact refractive image inverter, more compact and flexible than its reflective counterpart. Moreover, we show that these interferometers remove or reduce the crosstalk that the binary phase plates could introduce between the multiplexed modes. Finally, an experimental analysis of a MZI with both an approximated and an exact refractive image inverter is presented for the case of a bimodal multiplexing. Likewise, it is proven experimentally that a RGPS that shifts π/2 demultiplexes two odd modes which can not be achieved by any image inverter.
We present a derivation of the paraxial geometrical laws starting from a wave-optics approach, in particular by using simple continuity conditions of paraxial spherical waves at boundaries (discontinuities) between optical media. Paraxial geometrical imaging and magnification laws, under refraction and reflection at boundaries, are derived for several instructive cases and without using Fresnel diffraction theory. The primary aim is to provide a complementary insight into the standard axiomatic approach of paraxial geometrical optics and likewise to allow the introduction of some wave imaging concepts, such as the transmittance function, with a notable didactic interest for advanced subjects such as Fourier optics. This approach provides a more homogeneous vision of classical optics in which the use of the optical field continuity conditions at a boundary is a usual requirement as is clearly seen, for example, in the case of the derivation of Fresnel formulas. The work is particularly intended for university physics teachers and pregraduate and first year postgraduate students.
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