# User:Andy Maloney/Notebook/Lab Notebook of Andy Maloney/2009/04/01/Optical tweezers

## Collimation

Collimation has proven to be quite difficult. Let me run through some of the points that have proven to stretch my capabilities.

#### Table Space

This is a big issue for me. The laser diode is between the microscope and the corner of the table. Thus, there is limited usable table space to put the necessary components. So far, these components include 4 translation stages, 2 cylindrical lenses, 2 spherical lenses and a rail. I believe I have about a 10" x 10" square of useful space on the table for these things. It's cramped, and I can't do anything about it.

#### Diode placement in the cooler

The aspheres we purchased have focal lengths of 3 mm roughly. This is small. It's small because I was anticipating the LD to have a large NA. I tried to get a large enough asphere with a decent NA to accept all the light from the diode but as it turns out, I was unable to get the aspheres to collimate the laser.

The first question I need to ask myself is, Why was I not able to collimate with this asphere? The answer is, I just don't know exactly. To use the asphere, I had to use an adapter to thread into the tapped hole the LD is mounted in. Doing so made me lose the ability for precise positioning of the asphere for collimation. I think this is why I couldn't get it to work but it may not be the only reason.

Abandoning the asphere, I moved to collimating the laser with a set of cylindrical lenses. This made sense to me because the beam from the LD is elliptical (i.e. a line) and the best way to image lines is with cylindrical lenses. I purchased 3 cylindrical lenses from Thorlabs with my GRD funds. They include 2 10 mm and 1 30 mm focal length lenses. I'm pretty sure I purchased these because of the LD quoted diffraction angles. I calculated the beam size after using the 10 and 30 mm cylindrical lenses and the size works for the input into our anamorphic prisms. (I think I conveniently forgot this.) At any rate, this is great because I now have a way to collimate the beam. Unfortunately when I went to use the 10 mm cylindrical lens to focus the parallel axis, I noticed that I was unable to get the lens close enough to the LD. This is because I forgot where the focal planes of a cylindrical lens are and, I also did not account for the lens mount to take up as much space as it did. So, it just didn't work and I had to abandon this method. Another reason to abandon this is because I can't use the shutter I purchased in this setup.

#### LD diffraction angles

Ant and I measured the diffraction angles for the perpendicular and parallel directions of the LD just to check. The perpendicular diffraction angle is 1˚ thanks to the FAC collimation on the diode and the parallel diffraction angle is 10˚. Well, I'm not so sure about the parallel direction. I think it's more.

The diffraction of the LD is great enough to make using the awesome manual shutter I have useless because the shutter basically turns into an aperture cutting off the beam at the shutter's edges. This is no good if we want to maintain power and beam quality.

#### LD emmision

The LD is also not emitting in the center of the tapped hole it is mounted in. If it did, then using a cage system would be viable but, I just can't seem to get the cages to work properly. Plus, the cage system is not setup properly for using cylindrical lenses. Plus, Thorlabs doesn't sell anything close to a proper mount for these types of lenses in a cage system.

I think I'll draw something up and suggest it to them.

#### Imaging the LD element

So, I cannot use an asphere to collimate the LD beam because I cannot control the position of the lens precise enough for collimation. I cannot use the sets of cylindrical lenses we own because I cannot get the 10 mm lens close enough to the LD for collimation. If I use the 30 mm lens to collimate the parallel axis, I would have to use a 50 mm lens to collimate the perpendicular axis. Using this combination means that I am pushing the limits for the input of the anamorphic prisms. Plus, by the time the beam reached the 30 mm focal length lens, part of the beam would not hit the lens thus clipping it. Also, I still haven't taken into consideration the fact that the shutter clips the beam.

Well, Koch suggested I try imaging the LD element out of the cooling unit. This is a great idea and is easily done but, it still didn't fix the shutter clipping problem. Plus, when I set this up scenario up, another problem occurred.

Since I am limited on space, I had to use 2 25 mm focal length lenses. Imaging the element was easy and getting the 10 mm cylindrical lens in place was a breeze for parallel collimation. Except for the fact that the beam coming out of my 1:1 image system diverged quickly and thus was being clipped by the size of the cylindrical lens. Also, the shutter still clipped the beam out of the cooling unit. And also also, I mounted the 1:1 imaging system in lens tubes. Since the lens tubes are centered with respect to each other and the LD beam does not emerge centered with respect to the tubes, the beam had major aberrations.

#### Conclusions

Just to catalog my problems, they include:

1. Table space.
2. Inability to precisely position an asphere for collimation.
3. Diffraction angle of the LD beam.
4. Funky angle of emission from the LD.
5. Problems with the shutter clipping the beam.
6. Issues imaging the LD element out of the cooler.

## New idea

It's clear that I need a fresh start with this collimation problem. So, I'm going to propose an idea here. I'm going to talk to myself in the following dialog. I know it's weird, but it helps me think. If you don't like stream of consciousness, then you should stop reading.

I really like the idea of imaging the LD element out of the cooling unit. It's a great idea and I cannot believe I didn't think of it before. I guess I was hung up on an idea in my mind and refused to try something else until what I wanted to work, worked. That's bad and I need to not do that in the future.

At any rate, if I image the element out of the cooling unit, I need to take into consideration the size of the shutter, and the diffraction of the image out of the unit so that I can use the 10 mm cylindrical lens without clipping the beam. This is easily done by using a lens to make a virtual image of the element. Where my virtual image is will also tell me where how fast the beam will diverge. This is kind of cool. We all know the paraxial approximation for lenses

$\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}$

where f is the focal length of a lens and di and do are the image distance and object distance respectively. But, if f and do are known and you are looking for the image distance, then

$\lim_{d_o\rightarrow f}\frac{d_of}{d_o-f}\rightarrow-\infty$

This is great because as do approaches f from the left (do < f) a virtual image goes to negative infinity. This is just the opposite for real images. That's a cool symmetry I never realized. Of course this means that the farther away the virtual image is, the less divergence angle it will have and thus will clear the aperture without clipping it. Score +1.

Now all I need to do is turn the virtual image into a real one with another lens. The focal length of the other lens will depend on where I put the virtual image but I hope we have a lens that will work. So, I need to put the virtual image somewhere so that the divergence angle clears the aperture and will not overfill the cylindrical lens. Plus it needs to correspond to a focal length lens we have to make it real again. "I'm a real boy!"

I did try this a little before leaving and yep, it does work. I just need to tweak it so that it works completely. I guess I could try and dust off the old cogs in my head and do a real matrix calculation for the optical setup, but that will take time and I'll only do it if I have down time or if my approximations are grossly overstated.

Great. I can use the 10 mm and 30 mm cylindrical lenses as well to make a 1 mm x 4 mm beam to input into the anamorphic prisms. The only problem that remains is finding a way to mount the lenses so that the beam goes through the center of them and table space issues.

I'm going to have to move everything again...

## Enclosure

Before I forget. The helium filled enclosure. We don't have to have it enclose a lot because if we use a spatial filter, the only thing that needs to be enclosed is the spatial filter. Since the filter will get rid of all extraneous gunk that happens to the beam before it, it's only the filter that needs to be enclosed. Boy I hope that pinhole will take the laser power. We will definitely want to spring for expensive optics for this.