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In this note we consider the Iwatsuka model with a postive increasingmagnetic field having finite limits. The associated magnetic Laplacian isfibred through partial Fourier transform, and, for large frequencies, the bandfunctions tend to the Landau levels, which are thresholds in the spectrum. Theasymptotics of the band functions is already known when the magnetic fieldconverge polynomially to its limits. We complete this analysis by giving theasymptotics for a regular magnetic field which is constant at infinity, showingthat the band functions converge now exponentially fast toward the thresholds.As an application, we give a control on the current of quantum states localizedin energy near a threshold.

Band functions of Iwatsuka models : power-like and flat magnetic fields