Square-integrable cylindrical waveguide modes

What is it about?

Diffraction has long been known as phenomena that limit the application of beams or pulses. Diffraction is always present, affecting any waves that propagate in any media and produces gradual spatial broadening. It is important, therefore, to develop any techniques able to reduce this phenomenon. Localized waves, also known as nondiffracting waves, are indeed able to resist diffraction for a long distance in free space. It was shown experimentally that the transverse intensity peak of a so called Bessel beam as well as the field surrounding it do not undergo any appreciable change in shape all along a large depth of field. The ideal Bessel beam is, however, not a square-integrable function and thus possesses infinite energy. We obtain a new type of square-integrable Bessel field distribution. We show that the cylindrical symmetric hollow waveguide as a resonator modulates its own field during propagation which leads a dramatic decay or attenuation of the Bessel mode.

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Photo by Camille Chambefort on Unsplash

Photo by Camille Chambefort on Unsplash

Why is it important?

We obtain analytically the physically realistic mode functions of a finite waveguide. This can be relevant from various points of view including the engineering of the field in the waveguide or its proper quantization. In case of a semi-infinte cylindrical waveguide we show that the field modulation preserves the position information of a fast-decaying waveguide mode, hence it offers the opportunity to measure the propagation length from the waveguide entrance.

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