Double slit displaying anti-fringes?

[Marco Masi]

The conventional Young double slit experiment displays the interference fringes with the first intensity maxima at the center of the detection screen ('center' means aligned with the center between two slits of equal aperture). These are simply called 'fringes'. However, I'm wondering if and how one can construct a similar double slit experiment with anti-fringes appearing? Anti-fringes have the maxima where the fringes have minima, and vice-versa. That should be the case when the phase difference between the two slit-beams is of 90°. However, putting in front of one of the slits a 90° retarding plate won't result in an anti-fringe pattern alone but is mixed and blurred up with the diffraction envelope (the usual normal distribution Gaussian Bell-shaped function). If one places two retarding plates of 45° on each slit one won't get the anti-fringe pattern either, one gets again only the diffraction pattern (as the sum of the fring+anti-fringe). So, I'm wondering if there is a simple experimental arrangement that displays only the anti-fringes?

 

[Andy Resnick]

. So, I'm wondering if there is a simple experimental arrangement that displays only the anti-fringes?

Hmmm.. my initial guess was to try as you suggest- putting one slit in phase quadrature with the other. Why do you say that results in a 'mixed and blurred' diffraction pattern?

 

[sophiecentaur]

one slit in phase quadrature

Two pieces of glass, with one piece λ/4 thicker. As you say, "why blurred?" The cancellation and enhancement will still occur at the same rate (near the axis). Blurring would only occur if there were other sources of light. Filling in of the nulls would occur if the amplitudes of the two sources were unequal.
The best mental picture for all these questions is surely to use two radio frequency antennae, fed from the same source and with amplitude / phase knobs. (But then I may be biassed here.)

 

[tech99]

The simplest method must be to rotate the plate so that one slit is half a wavelength in front of the other.
As we do not routinely set up this experiment with micron precision, it shows that we are never sure anyway what we are actually looking at, and it makes almost no difference. The whole pattern is just shifted by half a fringe spacing.

 

[Marco Masi]

Yes, I realize now the image would not be blurred, it is just one beam phase shifted, no blurring. But also the fringes are not shifted. The maxima decrease to zero while the minima grow up to maxima. In between they sum up to the Gaussian. Indeed, rotating the plate in front of one slit is the simplest method to illustrate it. As I understand it it must be a half-wavelength plate, which causes for half rotation a 360° shift?

 

[sophiecentaur]

The simplest method must be to rotate the plate so that one slit is half a wavelength in front of the other.
As we do not routinely set up this experiment with micron precision, it shows that we are never sure anyway what we are actually looking at, and it makes almost no difference. The whole pattern is just shifted by half a fringe spacing.

it may be more convincing to leave the slits and screen in the same orientation and move the source to one side (doing the geometry right) so that the waves arrive at the back of the slits in the relative phase you wanted.

As I understand it it must be a half-wavelength plate, which causes for half rotation a 360° shift?

I'm not sure what you mean here and in this context. Isn't a half wave plate a component in polarisation experiments? You need a path length change of a half wave in one path.

 

[Julian Phillips]

Increasing the number of slits effectively produces a phased array, and a stearable beam. A concept that has real world applications in radar and ultrasound.

 

[synch]

Is an anti-fringe, where there is destructive interference and so decreased visibility? Is it visible by itself?

 

[sophiecentaur]

Increasing the number of slits effectively produces a phased array, and a stearable beam. A concept that has real world applications in radar and ultrasound.

You would need to change the thickness if you wanted to 'steer' the beam. It would be more of a 'tilted' beam. This is nothing unusual.
But we are missing the fact that there is a path from 3 to 1, as well as a path from 1 to 3. In terms of multiple element antenna arrays, it would be the equivalent to weighting the outside elements (Amplitude and phase) differently. That could broaden or narrow the beam marginally.
I guess what's special about this effect is that it operates between alternate slits; there is no one way path from 1 to 2 or 3 to 3.