Q:

Can you propagate electromagnetic waves confined to a plane?

I am a newbie on Electromagnetism and its principles.
Can we possibly propagate the waves in a planar direction? I am working on a project where I have a receiver and transmitter. The receiver needs to detect the  direction of the transmitter (boolean whether receiver is in planar direction or not) and the distance from the transmitter.
The transmitter should propagate planar waves eg. in XY plane and the receiver should receive it only when it is in the same XY plane as the transmitter.
Can this be done? If Yes,

Can I also measure the strength?
Will the presence of obstructions like human beings, wood, etc. lead to distortion of the plane? I understand that obstructions will definitely reduce the strength. Will the receiver still receive the waves?

A:

If by this

the receiver should receive it only when it is in the same XY plane as the transmitter

you mean that the receiver should intersect some predefined strict, mathematical, infinitely thin plane, then no, it cannot be done.
For starters, keep in mind that you cannot confine light in free space to dimensions smaller than its wavelength. For e.g. WiFi signals, this is in the ~10cm range.
Similarly, the propagation of waves outwards from a confined source is always subject to diffraction. This means that the waves will also come out at an angle $\theta$ above and below the plane, and this will be roughly limited by the size of the transmitter: if $d$ is the length of the transmitter along the direction normal to the plane, then $\theta\sim \lambda/d$ is a rough estimate for the limits on $\theta$. The smaller the wavelength as compared to your transmitter, the more you can keep the waves in plane.
In the radio domain, this is a problem, because the wavelengths are large and if you're e.g. a cellphone company, you don't want to be beaming most of your power into the sky, so that's why we have things like collinear antenna arrays among other fancier antenna technologies.
If you don't have any wavelength restrictions, then yes, this can of course be done - just use a sheet of light. In the radio domain, though, you might be better off implementing some kind of electromagnetic ranging system.

