Redistribution of Energy in Electromagnetic Wave Interactions: Interference of electromagnetic waves; a different approach

One of the well-known effects of electromagnetic waves is interference. Redistribution of energy in interference is well documented in literature but the mechanism has not been discussed in detail. A set of new experiments has been designed and conducted to observe the actual redistribution of the energy of the electromagnetic waves while being interfered and after leaving the region of interference. In this paper, it is shown that the redistribution of energy in interference of electromagnetic waves maintains the energy distribution prevailed at the moment they leave the disturbance (interference) area. Modified wave fronts which separated after intersection of two coherent waves in microwave frequency is demonstrated. Results are presented in pictorial and graphical models in order to understand the phenomena,. Further experiments are underway and possible mechanism will be discussed later.


INTRODUCTION
One of the unresolved problems in physics is wave-particle duality of electromagnetic (EM) waves. It is known that certain physical phenomena can be explained only using particle nature of EM waves [1,2] while the other phenomena can be explained only using their wave nature [3]. For example, photoelectric effect is described by the particle nature † E-mail: gaminickg@yahoo.com Institute of Physics -Sri Lanka C.K.G.Piyadasa /Sri Lankan Journal of Physics, Vol. 6 (2005) [51][52][53][54][55][56][57][58][59][60][61][62][63][64] 52 of EM waves and diffraction and interference are explained by the wave nature. The wave nature was first postulated by C. Huygens and he described that light propagates as a wavefront [4]. He further explained that at any given instant, each point on the wavefront is the origin of a secondary wave which propagates outwards as a spherical wave. The secondary waves then combine to form a new wavefront. In a monochromatic system, the time variation of optical disturbance, A (magnitude of electric vector |E|) can be written as (1) where A 0 is the maximum amplitude, ω is the angular frequency and φ is the phase angle.
This is true for all EM waves. One of the key features of EM wave nature is superposition.

Superposition of two waves
where A 10 where µ 0 is the permeability of free space and c is the speed of light. From eq. 3 and eq. 4, the resultant intensity (I) of two waves with intensities I 1 and I 2 is given by 53 Whenever the phase difference is 180 0 the intensity becomes zero.
Young's double slit experiment (1802) [3] was one of the landmark experiments to determine the wave nature of light ( Fig. 1(a)). It describes the superposition of two coherent light waves; intensities of the waves with same phase (in-phase) add up as in Eq.
6 and produce bright spots or in other words cause constructive interference. Waves that are 180 0 out of phase will create dark regions (Eq. 7) or cause destructive interference.
If λ is the wavelength, d is the distance between two slits and L is the distance to the screen from the slits, the general condition for a next bright area, y is given by following mathematical relation (see Fig. 1(a)) d L m y λ ≈ (8) where m = 0, 1, 2 …….. This is an important result applicable to all interference and diffraction effects where two primary coherent monochromatic sources are nearly parallel and predicts energy redistribution in space. Fig. 1(b) shows this energy (intensity) redistribution across an interference pattern on a screen. A single beam of light gives a uniform distribution of intensity, I 1 throughout the screen as shown in curve I of Fig. 1(b). Two non-coherent beams of equal intensities I 1 would yield a uniformly illuminated screen with an intensity 2I 1 . See curve II in Fig. 1(b). If the two waves are coherent, or in other words, the two beams have a phase relationship that satisfies the condition for interference in Eq. (9), they form alternative maxima and minima, hence energy redistribution. If initial amplitudes of the two coherent beams are equal, then the maxima are four times the intensity of the 54 individual contribution as shown in curve III of Fig. 1(b). However, the area under interference curve III is equal to that of the curve II. This leads to a following contradiction with the existing wave theory. According to the wave theory, energy of a EM wave is associated with the electrical vector E and is proportional to However if we consider zero nodes in a interference pattern, to construct destructive interference or zero intensity, electrical vectors of two waves should be equal and opposite at that particular point Fig. (1(c)). In other words that can be considered as Tug of War! If two forces are equal then there is no resultant movement in the rope.
At the same time, maxima carry an intensity which is four times the original intensity when both beams are coherent and identical in amplitudes. Although this is explained mathematically through an addition of eq. 4 and 5, it seems that the energy of minima has been shifted towards maxima. Since the two E vectors with equal amplitudes have to be present at minima to ensure zero intensities at those regions, the classical wave theory Furthermore, if the classical theory is true, redistribution of energy occurs only in the region where two coherent EM waves cross over, and each beam should regain their initial features that were in existence prior to the interference, as soon as the two beams leave the cross over zone. This is one of the primary conclusions that can be drawn from the wave theory.

EXPERIMENTAL APPROACH
The main objective of the present investigation is to measure energy distribution of interference quantitatively. The first step of the study was to re-investigate the energy redistribution due to the interference and confirm the validity of the eq. 6 above.
Interference of light can be observed easily with the naked eye in a simple experiment, and therefore a Michelson interferometer ( Fig. 2(a)), one of the most common instruments in students labs together with readily available He-Ne laser light, was used at the initial part of this investigation. A photo diode was used to scan and measure the energy distribution of the interference pattern. A high speed (FFD-040) photo diode (active area 2 0.9 0.9 mm × ) was used as an energy detector. The current flowing in the photo diode is linearly proportional to the intensity, and hence proportional to the incident power of the EM wave. The diode and the amplifier were mounted on a stepper motor driven platform (Aerotech, ATS100-50-20) and scanning was done using in-house developed software via the interface (Simple step, XY microxxA).
A He-Ne laser (632.8 nm Scientific Laser SLC.8mw CLR) was used as the monochromatic source of light and the interferometer was set-up as in Fig. 2 (5). This implies that the total energy of two light beams is equal to the energy of interference pattern and redistributed as shown in curve IV in Fig. 2(c). 57 (arbitrary units) and 20.92 (arbitrary units) respectively (Fig. 2(c)) and the difference is less than two percent. According to these results, it appears that the energy in the valleys has moved to the peaks of the curve IV.

This phenomenon can also be viewed from a different angle
The next study was planned to investigate whether the redistribution of energy that has been taken place within each beam, persists even after the two wavefronts have left the area where interference taken place. This experiment was carefully designed to overcome several drawbacks one would encounter when using a conventional experimental setup ( Fig. 3(a)) with a source of electromagnetic wave in the visible region. One of the important aspects addressed at the design stage was the isolation of the two outgoing beams, after being interfered, to avoid any subsequent overlapping due to diffraction etc,.
Conventional Young's double slit experiment setup ( Fig. 3(a)) is not suitable for this purpose as the two immerging beams are nearly parallel and therefore bound to produce ambiguous results. A desirable separation of the two beams, of course, can be achieved if they are allowed to crossover with a large angle ( Fig. 3(b)). Angle of crossover is independent of forming the minima because it is assumed that the E vector is always perpendicular to the direction of propagation Once beams crossed each other with certain angle as shown in Fig. 3(c), two adjacent maxima are expected to be formed at points x and z where wave fronts interfere constructively. λ is the wave length of the propagating wave. If the angle between the direction of propagation of the two waves is α, then the distance xz between the points x and z is given by α λ Sin xz = For beams whose wavelength is in the visible region, for example He-Ne laser light of λ=632 nm and crossing at right angle, the length xz between two adjacent maxima is about m . Currently a suitable detector is not available to measure such a small distance and detect maxima with a enough resolution, and therefore it is necessary to select two coherent beams of electromagnetic waves whose wave length is very much larger than that of visible light. However, in the experiment that was performed with the Michelson apparatus together with visible light, detection of the dark and bright fringes was possible as they were separated due to the fact that the two beams used were almost parallel ( 0 ≈ α ). see Fig. 2(b). For this reason, it was decided to carry out this experiment using microwave (band X -experimental band with centimeter wavelength region.) whose wave length is around 3 cm. For this wavelength region, the value of xz is around 3 cm when both beams cross each other at an angle of 90 0 , and currently available detectors should be capable of measuring intensity variation within such distance with good accuracy.

Interference with Microwaves
The experiment was carried out at the University of Manitoba, Canada and at the  Fig. 4(b) shows the results of the measurement carried out in Moratuwa. The curve II (green) of Fig. 4(b) shows the intensity measured by the sliding detector along the platform PQ when the antenna A was ON and the antenna B is properly terminated (OFF). As expected, the curve II gives the intensity pattern of a beam of microwave emanating from a single slit, within the main lobe of radiation pattern and which is more close to a bell shaped (close to Gaussian) distribution of a diffraction pattern. It is important to note that when the antenna B was ON and A was OFF, the intensity obtained from the sliding detector on platform PQ was close to the noise level. See Fig. 4(b), curve III (red). It clearly shows that the microwaves from antenna B do not travel through the region where the platform PQ is located. However, when both antennas radiate power, the bell shaped intensity distribution turns in to a prominent interference pattern along the platform PQ and that can be seen in curve I (blue in Fig. 4(b)). Here the overall intensity relationship between before (I 3A ) and after (I 3 ) interference is close to A I I 3 3 2 ≈ (see Fig. 6 Each platforms practically receives most of the energy from its opposite antennas but still exhibit prominent interference patterns even though the platforms are out side the crossover region of the beams (see Fig. 4(a)). Note that the interference pattern appears in each beam only when the other beam crossed over.  Figure 5 as the intensity of the microwave source available at Moratuwa was not strong enough to carry out measurements at distance. The maximum distance was limited by the sensitivity of the sensor diode. The measurements show the same behavior as in previous results. Only differences observed were reduction of intensity and divergence of the shape of the interference pattern with the distance (Fig. 5(a)). 62 -field" interference). However, the interference that we observed in this experiment is produced by two crossed beams. In other words, this interference pattern not exists in the region between the antenna and crossover area when both antennas are ON but generates at the crossover and persists after that (see Fig. 6).

RESULTS AND DISCUSSION
According to the classical theory the energy in the wavefront is redistributed only in the region of crossover. When the wavefront leaves the crossover zone, the energy redistribution should no longer be observed. However, in this experiment, interference patterns were observed even after the crossover. This clearly shows that the wavefronts which redistribute their energy at the crossover, retain the redistribution pattern even after leaving the crossover zone.  Prior to the interference, each wave has uniformly distributed energy in the wavefront.
When the two waves intersect, the wavefront is disturbed, resulting in new crests and troughs in each wavefront. The non-uniform energy distribution resulted due to the C.K.G.Piyadasa /Sri Lankan Journal of Physics, Vol. 6 (2005) [51][52][53][54][55][56][57][58][59][60][61][62][63][64] 63 interaction of waves is retained as the two waves travel away from each other. However, the redistributed energy of each beam after crossover is equal to the energy of the original beam before crossover. This is clearly demonstrated by the experiment. If the energy distribution evens out after each wave moves away from the influence of the other wave, the interference pattern would not have been observed. When two beams meet each other, interference occurs at crossover region with intensity I 2 = 4I 2A (4I 2B ).
However, when two beams propagate after intersection each beam keeps its altered energy distribution which occurred due to interaction with other similar coherent wave at the crossover region. The relation of this intensity pattern is I 3 = 2I 3A (2I 2A ), which corresponds to the energy redistribution of a single beam. Figure 6 pictorially summarize the observations made in this experiment. After each antenna, usual Gaussian or bell shaped distribution of a single slit diffraction exists with a certain intensities I 1A and I 1B respectively for antenna A and B. When two beams meet each other, interference occurs with intensity 4I 2A (assuming that both beams have equal intensities). Where I 2A is the intensity of the bell shaped energy distribution of a single beam at the crossover region (when no second beam is presented). When two beams propagate after intersection, each beam keeps its altered energy distribution, which occurred due to interaction with other similar coherent wave at the crossover region. After the crossover region, the overall value of this intensity pattern measured at PQ (which is similar to actual interference pattern) is 2I 3A , which corresponds to the energy