Novel Double Slit and Cross-Double Slit Experiments--- Interference Patterns Depending on Orientation of Diaphragm


 Young’s double slit experiments represent the mystery of quantum mechanics. To explore the mystery, in this article, we report experimental results that show novel phenomena that the interference patterns of the double slit and cross-double slit experiments depend on the orientation of the diaphragms. Those experiments provide comprehensive data for developing/testing a theoretical model.


Apparatuses
The experiments utilize a laser source, the diaphragm of the standard double slit (Figure 1a

Novel Phenomena: Interference Patterns Depending on Orientations of Double Slit
The standard optical equation describing the interference pattern of the double slit experiments relates the positions of fringes, wave length, the spacing between two slits and distance from the double slit to detector/screen as = . This equation is derived for a special situation that the source is on the normal vector of the plane of the double slit.
We are interested in how the interference patterns vary with angle of the diaphragm of double slit/cross-double slit.
Let us start with a schematic drawing ( Figure 2). The double-slit-AB is in the y-z plane, slit A and slit B are along the z-axis, its normal vector is along the x-axis and points to source, the coordinates of slit-A and slit-B are = /2 and = − /2, the spacing between slits A and B is "d", and photons travel along the negative x direction.

Figure 2 Standard diaphragm of double slit and its pattern
We study the orientation-dependence of the interference pattern of a standard double-slit rotating around the x-axis, y-axis, and z-axis, respectively.

Rotating Double Slit Around X-axis: Normal Vector.
We consider two situations: discrete and continuous rotations.
First situation: discrete rotation.
Experiment-1: (Figure 3). Rotating the double-slit clockwise a discrete angle, 15 degree. The interference pattern is perpendicular to the double slit. The combination of the interference patterns of the cross-double slit experiments with different   number of double slits crossing to each other suggests that the double slit and cross-double slit have rotation-invariance around their normal vectors. If we increase the number of double slits that intersect at the same spot, the shape of the intersection will approach a circular disc, each slit is tangent to the intersection and forms disc-3, which is surrounded by ring-2 ( Figure 4a). The zero-order fringe rotates at the same spot, and forms a bright fringe 0, while the rotation of its first-, second-and third-order fringes form bright rings 1, the dark fringes form dark rings 2, and so on (Figure 4b).

Second situation: continuous rotation
.(a) (b) Figure 4 Predicted pattern of continuously rotating double slit/cross-double slit around x-axis The above prediction has been tested by the experiment.

Experiment-2:
The apparatus consisting of obstacle 1 with a hole, disc 3 placed at the center of hole-2 and leaving ring-shape gap 2 between disc 3 and obstacle 1 ( Figure 5).

Rotate Double Slit Around Y-axis
The interference pattern before rotating is shown below (Figure 6), for the purpose of comparison, Figure 6 Experiment-3: The double slit rotates 75 degree around Y-axis ( Figure 7, not to scale).

Figure 7. Double slit at an angle and its interference pattern
Observation: the interference pattern has no noticeable change, except dimmer.

Rotating Double Slit Around Z-axis
The experiments show the orientation-dependence of the interference patterns visually.

Experiment-4:
The diaphragm at the original orientation and its interference pattern ( Figure 8).     The formular describing the interference pattern of double slit at an angle relative to the z-axis has been derived: Figure A17 1 The detail derivation is shown in Appendixes A-2.

Rotating Cross-Double Slits Around Z-axis: Two Double Slits Crossing
We study the orientation-dependence of the pattern of a cross-double slit rotating around the X, Y and Z-axis. A cross-double-slit apparatus consists of source, cross-double-slit and screen. Let us consider a simple cross-double slit that consists of double-slit-AB and double-slit-CD, and double-slit-AB is perpendicular to double-slit-CD ( Figure 13).

Rotating Cross-Double Slits Around Z-axis: Six Double Slits Crossing
Now consider a cross-double slit that consists of six double slits crossing to each other ( Figure   21). The Z-axis is between two vertical double slits and parallel to them. The laser source is on the normal vector of the cross-double slit at the original orientation. Here we consider the rotation of the cross-double slit around the Z-axis.    Conclusion: The interference patterns created by two tilt double slits tend to closer to the Z-axis.

Summation
We show that the interference patterns of the double slit and cross-double slit depend on the orientation of the diaphragms. It is a challenge to interpret the experiments in Section 4 consistently.
The significances of those experiments are to provide comprehensive phenomena/data for developing theoretical model to explore the mystery of the double slit experiments.

Appendixes (A-1) Novel Multi-Slits for Exploring Mystery of Cross-Double Slit
To explore the mystery of the double slit/cross-double slit, we designed novel multi-slits in which a cross-double slit is divided into different parts/sections to test the function of each part/section of the cross-double slit. The widths of every slit are the same, and spacing between all of vertical double slits and between all of horizontal double slits are the same.
The normal Cross-double-slit-ABCD, the double slit-AB perpendicular to the double slit-CD, is shown in Figure A1 for the purpose of comparation.
The novel multi-slits are shown below.
Novel Multi-Slits-1: Figure A2 shows the intersection of the cross-double slit-ABCD. The purpose: testing whether the intersection of the cross double slit creates the whole interference pattern. Novel Multi-Slits-4 ( Figure A5).

(A-2) Derivation of Orientation-dependence Formular of Interference Pattern of Double Slit
The schematic drawing is the following. We obtain the equation of the orientation-dependence of the interference pattern of the double slit,