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This paper deals with a new spectrograph on integrated optics. It is composed of an Y-junction where the two
junction arms are guided in a loop structure in order to obtain an interference pattern. The measurement of this
intensity distribution gives access to the optical spectrum source after a Inverse Fourier Transform. To measure
it, we use the property of the loop composed of a bent waveguide which is a leaky structure. Depending on
the radius of the bent waveguide, a part of the light leaks from the waveguide to outside. The radiated power,
proportional to the intensity in the waveguide, is coupled into a plan waveguide set near the bent waveguide.
Indeed the two structures are separated by a gap which changes along the periphery of the loop. This structure
enables both to control the leaking light part and to confine in the plan waveguide the propagation of the radiated
field. Thereby, the radiated intensity is measured at a peculiar distance of the loop on a perpendicular plan to the
input waveguide. So, the interference pattern measured is magnified by the ratio of the plan waveguide length
over the loop radius, allowing to use a commercial photodetectors array to sufficiently sample the interference
pattern. The spectrum is finally obtained operating a Discrete Fourier Transform. The device modelization is
divided in two parts. The first part describes the coupling between the bent and the plan waveguide modelised by
a modal method based on a Fourier series expansion (RCWA) combined with an exponential conformal mapping
in order to simulate the electromagnetic field near the loop. The second part describes the Helmholtz-Kirchhoff
theorem to simulate the far-electromagnetic field. From the interference pattern modelized, the spectrum of the
signal is then calculated. A demonstrator in integrated optics on glass is being developed.
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