Curved Diffraction Patterns of 2D-Cross-Grating Experiments---Double Slit Still Has Much to Offer

Young’s double slit experiments represent the mystery of quantum mechanics. To explore the mystery, varieties of the single slit, double slit, cross-double slit and 1D-grating experiments were performed, which show the universal phenomena that the interference/diffraction patterns are curved, expanded and inclined. In this article, we show novel phenomena that the diffraction patterns of the 2D-cross-grating experiments can be curved, expanded and inclined simultaneously and continuously. Those experiments provide comprehensive data for developing/testing a theoretical model.


Introduction
Young's double slit experiment was performed in 1801 [1] [2], which, 100 years later, led to wave-particle duality. Feynman called it "a phenomenon […] has in it the heart of quantum mechanics.
In reality, it contains the only mystery [of quantum mechanics]" [3]. Moreover, the nature of photons truly puzzled Einstein. He wrote to M. Besso: "All these 50 years of conscious brooding have brought me no nearer to the answer to the question: What are light quanta?" [4]. A. Jogalekar explained: "Yet P1 P2 P1 P2 we have no clue how any of the fundamental facts of quantum mechanics including wave-particle duality, …, or the double-slit experiment, that disarmingly simple setup which …-actually work." [5].
To further explore the mystery, the 1D-double slit-AB ( Figure 1) has been extended to 2D-cross-double slit-ABCD ( Figure 2) [6].  The universal phenomena of the curved, expanded and inclined patterns of the dynamic double slit, cross double slit and 1D-grating experiments have been shown [7] [8]. The double slit experiment still has more to offer (Pinner).

Curved Patterns of 1D-Grating and 2D-Cross-Grating
It has been shown that the photons' behaviors depend on the orientations of the diaphragms of the 1D-grating [7]. In this article, we study further the orientation dependance of the diffraction patterns of the 2D-cross-grating experiments. Let us compare the 1D-Grating ( Figure 3) and the 2D-cross grating ( Figure 4). The 1D-Grating is referred to the grating with multiple parallel slits (Figure 3), where the vertical slits S2 may be more than four. With a laser source, the diffraction pattern of the 1D-grating experiment is shown in Figure 3.  The cross-grating consists of the multiple vertical slits S2 and the multiple horizontal slits S1, and is referred as 2D-cross-grating. For simplicity, in Figure 4, we draw only four vertical slits, referred as S2, and 4 horizontal slits, referred as S1. The patterns P1 and P2 are created by the horizontal slits S1 and vertical slits S2 respectively.

Curved and Expanded Diffraction Pattern
To compare the 1D-grating and pattern with 2D-cross-grating and pattern, we arrange both gratings and patterns side by side. Hereafter, simply referrer the "diffraction patterns" as "patterns". The experiments utilize a laser source, a 1D-grating ( Figure 5a) and a protractor. Figure 5a shows the 1D-grating and its pattern created when the grating is at the original orientation, i.e., the laser light is perpendicular to the plan of the 1D-grating. counterclockwise. The direction the pattern curved toward obeys the left-hand rule [9]. While Figure 5c shows the curved pattern created when the 1D-grating rotating around Y-axis clockwise. The direction the pattern curved toward obeys the right-hand rule [9]. The spacings between fringes keep the same.

Rotating 1D-Grating: Expanded Pattern
Experiment-2 ( Figure 6): The expanded patterns of 1D-Grating experiments. Figure 6a shows the 1D-grating and its pattern when it is at the original orientation. Figure 6. 1D-Grating and its pattern Then rotating the 1D-grating around Z-axis, either clockwise or counterclockwise, the pattern expands as shown in Figure 6b.

Rotating 2D-Cross-Grating: Curved and Expanded Patterns
Experiment-3 ( Figure 7): The experiments utilize a laser source, a 2D-cross-grating and a protractor. Rotating the 2D-cross-grating around Z-axis clockwise and counterclockwise respectively with a discrete angle, for example, 75 0 .
Observation (Figure 7a): the 2D-cross-grating rotates around Z-axis counterclockwise (1) the vertical patterns, P1, are curved towards the right continuously, which obey the left-hand rule.
The larger the rotation angle, the larger the curvature of the patterns.
(2) The spacings between the fringes of the horizontal patters, P2, expanded continuously. The larger the rotation angle, the larger the spacings.
(3) The patterns are curved and expanded simultaneously.
Observation (Figure 7b): the 2D-cross-grating rotates around Z-axis clockwise (1) the vertical patterns, P1, are curved towards the left continuously, which obey the right-hand rule.
The larger the rotation angle, the larger the curvature of the patterns.
(2) The spacings between the fringes of the horizontal patters, P2, expanded continuously. The larger the rotation angle, the larger the spacings.
(3) The patterns are curved and expanded simultaneously.
The 1D-grating rotates twice around two different axes to observe the curved and expanded patterns as shown in Experiment-1 and Experiment-2. The 2D-cross-grating rotates once around one axis and observe the both phenomena.

Curved, Expanded and Inclined Pattern
In this section, first, rotating the tilt-1D-grating.

Rotating 1D-Grating: First Orientation
Rotating the 1D-grating around its normal vector counterclockwise a discrete angle, say 60 0 , such that the A-axis is perpendicular. Namely the 2D-Cross-Grating is tilted. Observation: Figure 8b shows that the pattern is curved upward, expanded and inclined towards the horizontal axis simultaneously. Figure 8c shows that the pattern is curved downward, expanded and inclined towards the horizontal axis simultaneously.

Rotating Tilt-1D-Grating: Second Orientation
Rotating the 1D-grating around its normal vector clockwise a discrete angle, say 60 0 , such that the A-axis is perpendicular (Figure 9a). Namely the 2D-Cross-Grating is tilted.
Experiment-5 ( Figure 9): Then rotating the grating around the A-axis counterclockwise ( Figure 9b) and clockwise (Figure 9c). respectively. Observation: Figure 9b shows that the pattern is curved downward, expanded and inclined towards the horizontal axis simultaneously. Figure 9c shows that the pattern is curved upward, expanded and inclined towards the horizontal axis simultaneously.

Rotating Tilt-2D-Cross Grating
Rotating the 2D-Cross-Grating around its normal vector clockwise a discrete angle, say 45 0 , such that the A-axis is perpendicular (Figure 10a). Namely the 2D-Cross-Grating is tilted. Figure 10. 2D-cross-grating experiment and its pattern at original position Figure 10 shows the pattern, the pattern P1 is created by S1, while P2 by S2. (1) the spacings between fringes of the pattern P1 created by S1 is expanded, while the spacings between the fringes of the patten P2 created by S2 is expanded;

Experiment
(2) the pattern P1 is curved upward, which obeys the right-hand rule, while the pattern P2 is curved downwards, which obeys the right-hand rule; the green line and the orange line show that the P2 and P1 are curved; (3) the pattern P1 and P2 are inclined towards the horizontal direction, respectively.
(4) the pattern is curved, expanded and inclined simultaneously.  (1) the spacings between fringes of the pattern P1 created by S1 is expanded, while the spacings between the fringes of the patten P2 created by S2 is expanded; (2) the pattern P1 is curved downwards, which obeys the left-hand rule, while the pattern P2 is curved upwards, which obeys the left-hand rule; the green line and the orange line show that the P2 and P1 are curved; (3) the pattern P1 and P2 are inclined towards the horizontal direction, respectively.
(4) the pattern is curved, expanded and inclined simultaneously.
The 1D-grating rotates twice around two different axes to observe the curved, expanded and inclined patterns as shown in Experiment-4 and Experiment-5. The 2D-cross-grating rotates once around one axis and observe all three phenomena as shown in Experiment-6 and Experiment-7.

5.Summation
We show that the diffraction patterns of the 2D-cross grating depend on the orientation of the grating. More specifically, the patterns are bended by rotating the grating around Z(Y)-axis.
The experiments of the 2D-cross grating in this article show the phenomena of the curved, expanded and incline pattens attributing to the rotations of the 2D-cross-grating, which confirm that the phenomena of the curved, expanded and incline pattens attributing to the rotations of the single slit, 1D-double slit, 2D-cross-double slit, 1D-grating and 2D-cross-grating are universal (Table) [8] [10]. It is a challenge to interpret the phenomena/experiments consistently.