How EM waves cancel each other?

Hi,
We generally consider to out of phase EM waves will cancel each other in EM theory, but the EM wave is an energy wave and how an energy can be destroyed... according to energy conservation rule it is not possible. More over where that energy is going or simply disappearing..how it is possible?
Please clarify

Thank you
Srikanth

The energy isn't destroyed. When you have a position where you have full destructive interference, you have other positions where you have full constructive interference. That means both H and E will double, hence the power density will be 4 times higher.

If you have two coherent sources with large separation and same strength, you get grating lobes with deep nulls, but the lobes itself have twice the E and H field of a single source. The power density in the lobe maximum is 4 times the power density of a single source. When you integrate everything, you will find that no energy/power is lost but only the spatial distribution has changed.

WimRFP said:

The energy isn't destroyed. When you have a position where you have full destructive interference, you have other positions where you have full constructive interference. That means both H and E will double, hence the power density will be 4 times higher.

If you have two coherent sources with large separation and same strength, you get grating lobes with deep nulls, but the lobes itself have twice the E and H field of a single source. The power density in the lobe maximum is 4 times the power density of a single source. When you integrate everything, you will find that no energy/power is lost but only the spatial distribution has changed.

Click to expand...

Thank you for your reply, but i couldn't understand it clearly.

You mean to say that in a particular direction energy may not present but it appears in some other directions with energy doubled. Is it right?

But for instance consider a sinusoidal E field hits a conductor with normal incidence and reflected back with exactly 180 degrees phase (consider there is no energy reflected in any other direction except in opposite direction to incidence). In this case both incident and reflected waves cancel each other and no energy available in that direction. Then how the doubled energy appears in some other direction, if it is then which direction it appears?

In this case energy travels in opposite directions (as in a transmission line).

Where goes the reflected energy?
You have two extreme options: 1. It travels further after being reflectend, so it isn't lost, but only changed direction. 2. It reaches the source again and is dissipated there (as in a transmission line problem where you have full reflection (open or shorted termination) ). In the last case, the source delivers zero net power/energy (Forward power - reflected power = 0). In both examples the energy conservation law is valid.

Note the in the full reflection case (compare a transmissin line) where the propagation directions are opposite (as in the example above), you get a standing wave pattern where at each position along the path, the average poynting vector is zero (hence no energy passes, as the source delivers 0 energy). Some easy to understand locations along the path: at the E-field knot/node E = 0, H = maximum,
though at the E-field maximum on the standing wave pattern, E = maximum, H = 0.

Energy transfer requires both E and H field (at correct time phase and spatial orientation as governed by poynting vector theory).

1.So there is no net change in energy, so net power is zero.
you are saying that source doesn't deliver any energy( or delivers zero energy) because it delivered energy to move electrons up to termination end( short/open), and the energy reflects back and reached the source, so finally there is no gain or loss in energy by source. But my doubt is source lost energy when it moved electrons but how it gains energy back from the reflected energy (means a battery lost energy and recharged back from reflected energy how?)..it is difficult for me to understand.

2.In the second point you mentioned about standing wave (both E and H individually forms standing waves) which doesn't propagate but oscillates , can we consider that the energy is not propagating but oscillating, if it is then the standing wave at a time instant is zero means the energy at that time instant is also zero..is my understanding correct? I am little confused in correlating energy and waves

Over multiples of a period (T), the net energy, hence the power is zero in case of full reflection of waves. However there can be back and forth energy exchange, as is the case with a capacitor that is charged and discharged.

So when an open or shorted transmission line doesn't show a short or open circuit to the source (that means the transmission line behaves as a reactive load), there is exchange of energy from the source to the transmission line and back, but the net energy is zero. You are correct, electrons can move (oscillate), like a ball connected to a lossless spring in vacuo. You only have to supply the energy to start the oscillation of the mass spring sysem.

In a wave it is the same, you need to supply energy to fill the space with EM fields, but once the wavefront returns to the source, there will be no net energy exchange anymore. When the source becomes zero (but keeps its impedance), the energy that is in the standing wave pattern returns to the source and is absorbed there. So in the end, there is no net energy exchange.

Regarding oscillation of energy, you are correct in that. The energy oscillates between the magnetic field and the electric field. When the E-field standing wave pattern is maximum, there is no H-field and all the energy is stored into the electric field. T/4 seconds later, the H-field standing wave pattern reaches its maximum (and there is no E-field anymore) and all energy is in the magnetic field.

It is the same sitaution as a standing wave pattern in a rope where travelling waves move back and forth (as long as the rope is connected to a stiff non-absorbing tie point). When the amplitude is maximum, the velocity of all the mass in the rope is zero, and all energy is stored as elastic energy (like energy storage in a spring). When the rope is fully straigth, the lateral velocity is maximum, hence all energy is stored as kinetic enery.

You may start with the DC case in a parallel pair of strips (as this approaches the plane wave situation). The E-field lines go from strip to strip (like in a parallel plate capacitor), and the H-field lines go between the strips, perpendicular to the E-field. You will only have instantaneous power (dE/dt) when you have E- and H- components that are perpendicular to each other (therefore there is cross product in the Poynting Theorem). If in the time domain H and E are 90 degrees apart, the net energy over T is zero.

You can make it very complicated when you have wave fronts that travel in non-opposite direction. Then the direction of the E and H fields change versus time.

So I should't call it as cancellation of EM waves. It should be energy reflection in opposite direction and absence in forward direction. Correct right?
Thank you very much for your help.

I prefer to treat waves with interference, So I first calculate the wave (E- and H-field), and then the power or energy involved. The reason for doing that is as long as the direct path and relfected path length do not change, the two waves are coherent and you need vector (phasor) calculus to calculate the fields.

The energy approach may fail. If you have (for example) a horizontally polarized transmitting antenna that uses the earth as a reflector. You may get a direct wave and a reflected wave that travel almost in the same direction and have almost same strength. The phase difference between the waves determines the energy.

When waves travel in almost same direction, have same strength and are in phase, both H- and E-field will double, hence the power flux density (W/m2) is 4 times higher that that of a single wave. Based on energy you would expect double energy. When they are fully out of phase, both H en E are zero. Of course energy doesn't come for free, therfore you have areas with full constructive interference (giving 4 times the energy density) and areas with full destructive interference giving zero energy density.

If you are going to work with antennas, it is nice to measure the elevation radiation pattern of a horizontal polarized antenna at a height of (for example) 2 lambda above good conductive ground. You will find places where the field strengh is higher then that of the antenna alone, and places with lower field strength. You can't explain this with the energy approach.

Using energy approach works well with uncorrelated sources (for example from a incandescent light bulb or other noise like sources).