Stacking the Equiangular Spiral!

What a thrill!

Coming up with the idea of the ES design was a lot of fun and working with it, discovering the optical properties (see my papers) that we could get from it has been an addiction! I know addiction is not a word used with work very often, but this work has had me hooked. You can probably guess that by reading my previous posts: the magic of equiangular spirals and my research page.

Now I am writing about something that topped all that went before.

How to make the spiral!

Brilliant theoretical ideas, flights of fancy and exotic designs are not new in research. From that perspective the spiral PCF designs that I work on can be regarded as yet another cool idea that may not survive the first big hurdle: how do you make it real? If a design cannot be fabricated then it may get lost forever in the dusty past issues of a journal. However, if it can be made, tested and used, then the story might be different.

When some colleagues at the University of Nottingham, asked me how the ES design  could be fabricated, initially I was stumped. I thought, “that’s the work of the fabrication experts surely?” On second thoughts, no! Some introspection showed me that making the ES design was not about changing the temperature settings in the oven. There was some beautiful science involved. And this post gives some insight into that.

There is more than 1 fabrication technique that could be employed for the ES design: extrusion, drilling and Stack-and-Draw (SaD). The first two are more recent, while the third is the most mature and used the world over. For that reason, I focused on developing an algorithm that could fabricate the ES PCF using the Stack-and-Draw  technique.

The SaD method is essentially a 2D form of Hexagonal Close Packing (HCP). HCP is a method of placing spheres on top of each other in 3D in way that maximises packing density. It results in spheres in 1 layer being placed in the depressions left from the spheres in the layer below. This leads to a hexagonal arrangement of spheres.

 In PCF fabrication, we stack long cylindrical glass tubes/capillaries such that each layer of capillaries lies on the depressions left from the layer below. This naturally gives us a hexagonal arrangement of capillaries. Deviations from this arrangement are impossible using stacking (some what similar to this picture of the Giant’s Causeway)!

Then how can we use stacking to change the angle from 60 degrees, or the position of a capillary?

That’s where the beautiful Science comes in!

We recognise that the packing of capillaries is like 2D packing of circles. I found that using the concept of Steiner chains we could stack capillaries to form equiangular spirals. This work is discussed in my latest paper, available as a free preprint or from the IEEE website. In this paper, I’ve explained the algorithm and given some simulation results to show that there is a way. So if you are interested in making it, please get in touch!

Of course, the story doesn’t stop here. Now I am wondering if the Golden Spiral PCF can be made with this technique. Apart from other cool things that can be done with spirals…