Retroreflecting Light with Modematching Sample

One common task in optics experiments is to set up a mirror to retroreflect light. In its simplest form that just means taking light that's coming in one direction and placing a mirror such that it returns along the same path in which it came. Sometimes that's not enough though. Sometimes we also need to make sure that the curvature of the mirror is matched to the curvature of the wavefront so that the beam at any point is at the same size, whether it's going or coming. If we retororeflect the beam, making sure to match the sizes of the input and output beams, then we can build things like Michelson interferometers or Twyman-Green interferometers where we have light traveling different paths and recombining, and regardless of the length of those paths we can ensure that the recombined beams have the same spot size so that we get good interference contrast. Let's look at how to retroreflect a beam, ensuring the return spot has the same size as the input spot. Here is set up a simple system with a laser and since we're going to be sending the light back in towards the laser, I have put a Faraday isolator here to block the retroreflected beam so that it doesn't destabilize my laser. So this system is my light source, I've then got a beam expander here and a mirror to reflect the light. There's a couple of additional optics that I've added to this system that are going to be critical for understanding when we have the beam properly retroreflected. One is a pinhole at the focus of this microscope objective. That microscope objective together with this lens forms an expansion telescope that expands the size of my beam. Putting a pinhole at the focus does two things: The most common reason we would do that is to remove the high spatial frequency noise on the light - basically get a very clean output of my light, so that if I'm using the light in an interferometer for example, I've got a nice uniform wavefront. The reason I'm using it today is because it provides a very small target that the input beam will go through. If I've properly mode-matched my reflected light to the input light, then the reflected light will also get through that pinhole. i can measure the retroreflected light that makes it back through the pinhole, and use that as a quantitative way to to determine how good a job I've done at matching the input and output modes from the retroreflecting mirror. Now in order to observe the power that's gone back through the pinhole, I've placed in this beamsplitter such that the retroreflected light can be separated from the input light and measured independently without blocking the laser beam. So the first thing I'm going to do is align my spatial filter Once my pinhole is aligned I've got a nice clean output beam here and with a flat mirror I need that light to be collimated at the mirror such that when it retroreflects it has the same outgoing mode as it had as the ingoing mode. So the first step in retroreflecting my light is to make sure that the path that the return light takes matches the input path. For that I'll take a card with a hole punched out of it. I'll place it in the path of the input light such that some of the light passes through that hole. I then want to adjust the orientation of my retroreflecting mirror so that the position of that return spot overlaps with that of the input spot. Now Ive aligned the optical axis of the return beam to that of the input beam. I still haven't done anything to make sure the mode of the return beam matches the mode of the input beam. To provide mode-matching I'm going to take a lens and place it one focal length away from my retroreflecting mirror. This happens to be a 50mm lens (or about 2 inches) so I've roughly positioned it 2 inches away, and I've mounted it on this translation stage which will allow me to change that position and very precisely locate the lens so that it is one focal length away. Once I've positioned the lens at the appropriate location, the light at the mirror will be a waist of the beam. A waist of the beam is where the wavefronts are flat and therefore they will match that of the mirror causing the return light to have exactly the same shape - the same mode - as as the input light. I could look at the light that's returned through the system reflected off my beam splitter and come out and measure that amount of power and use that as a measure of how good the position of my lens is. When the lens is properly positioned, that power should be maximized. I can use a photodetector for this but for the purpose of this demonstration I'm going to use a CCD camera and I've got the image shown here. Mostly what we see is is a lot of background light that is caused by the light that hit the front surface of this microscope objective, scattering back, or some of the light which reaches the pinhole, scattering back. So that's not light which has hit my retroreflecting mirror and is not the light that I'm attempting to observe. rather in the middle of this pattern I see a little bit of motion, or a little bit of variation in the intensity and as I block and unblock the arm I can see additional power at the center of the frame goes away and comes back. So this central region of my frame represents the power that's been retroreflected back through the pinhole. Now by adjusting the translation stage to move the lens back and forth I can attempt to find the point where that retroreflected power is maximized with the camera I'll observe how much change in intensity there is when I block and unblock the light but it's best to use a photodiode here to measure the total power reflected from my system observed on an oscilloscope. I can then maximize that signal as I adjust the translation stage to bring the lens precisely into the position where the light gets retroreflected.