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We have developed a Fresnel diffraction analysis that provides an analytic expression for the passband response of virtually imaged phased-array (VIPA) demultiplexers. Our analysis shows that although the passband can be inherently symmetric, a strong asymmetry can develop when the output plane is detuned longitudinally. The symmetric passband has the minimum -3 dB transmission bandwidth. We also identify a spatial chirp effect that arises when the passband becomes asymmetric. Our theoretical predictions are confirmed via experiment. The experimental results include a demonstration of a hyperfine wavelength demultiplexing response with 10 pm (1.25 GHz) -3 dB transmission bandwidth.