Subsidiary Maxima in Multiple Slit Interference: Algebraic Equations

Mitra Shojania Feizabadi

E. L. Cleveland

Heung‐Ryoul Noh

We present a theoretical study on the amplitudes and the linewidths of the subsidiary and principal maxima in multiple-slit interference patterns in the Fraunhofer regime. In the limit of a large slit number, we observe that the calculated amplitudes of the subsidiary maxima relative to the principal maximum are slightly different from the values presented in textbooks. We also present the calculation of the widths for the diffracted intensity patterns of the principal and the first several subsidiary maxima.

Morio Yamada

Ralf Otte

The bicomplex extension of quantum mechanics introduces an ideal sector J1 whose phases are algebraically coupled to the complex sector C1 via the algebraic identity e^(iα)*k*e^(jβ) = k*e^j(α+β). In an earlier work, a double-slit test proposal for a possible physical realization of this phase coupling was formulated, which contained a calculation error. The present work refines this proposal and presents the corrected theoretical interpretation. The starting point is a bicomplex state Y = S + R, where S represents the complex component and R the ideal component, which is phenomenologically associated with a monochromatic laser source. In a nonlinear, frequency-doubling crystal, the state is phenomenologically mapped to Y^2 = S^2 + 2SR + R^2. The component S^2 lies in the complex sector, while the mixing term SR according to the above equation lies in the ideal sector and carries phase information transferred by the algebraic phase coupling. For a measurement at a detector or screen, this ideal mixing term must be transferred into a complex measurable channel with an effective coupling strength ηeff . This detector coupling is a phenomenological assumption and does not follow from the algebra alone. The mathematical evaluation of the double-slit interference, taking into account the given field structure (superposition of two slit contributions, cosine profile), shows that within the used Fraunhofer effective model the principal maxima follow the classical geometric shift to first approximation. An effectively coupled SR term at the detector primarily generates contrast and brightness modulations of the interference pattern. The double slit is interesting as a spatial structure test because a brightness modulation of the interference fringes depending on the position of the source is at least surprising.

Li Wang, B.-J. Zhang, Z. Hua +3 more

We study electronic multiple-slit diffraction with a quantum mechanical approach. Our theoretical results are in good agreement with classical theoretical calculations and we obtain the following resluts: (1) There are N − 2 secondary maxima and N − 1 minima between the two principle maxima in diffraction pattern. (2) As the slit number N increasing, the diffraction intensity increases and the pattern width becomes narrow. (3) The slit thickness c dose not have any influence on diffraction pattern when slit width a is far greater than the electronic wavelength λ, for example, the ratio of a λ = 10, and at the ratio, the missingorder phenomenon can be observed when d+a a = n (n = 1, 2, 3 . . .), where d is the distance of slit-to-slit. (4) When a is not far greater than λ (the ratio of a λ = 500), the slit thickness c has an effect on diffraction pattern. The missing-order phenomenon can be shown only if the slit thickness c is small enough, and it disappears when the slit thickness c becomes large. In addition, the slit thickness c affects the relative diffraction intensity of the diffraction pattern.