In this series of posts I’ll be writing in more detail about the spiral PCF that I enjoy working on. An introduction and overview on spiral PCF can be found on the My Research page.
So, back to Equiangular Spiral PCF or ES-PCF
Equiangular spirals or logarithmic spirals are self similar curves: as the curve grows, the shape remains unchanged. We see them in nature in snails, shells, plants, galaxies and in many other places.
How is the ES design adapted for PCF?
and θ is the angle between the radius of the ES and tangent at the end point of the radius; rspiral is the distance at any point along the spiral arm from the centre of the structure.
To adapt the design for a PCF, we choose the parameters, ro,, θ , which decide where the air holes will fall (alo
ng the ES curve). Several such independent ES patterns of holes can be arranged around a central core to form a cladding with microstructure of air holes. The average refractive index in the cladding region is lower than the core, similar to standard PCF, and hence Total Internal Reflection (TIR) is the guiding mechanism for light. The cross section of an ES-PCF can be seen in fig. 2.
What makes the ES-PCF so unique and useful?
A number of things:
a) The number of parameters to play around with and optimize performance is bigger than most traditional PCF. We can change the number of ES arms, number of holes per arm, the radius of the arm, angular increment and finally air hole radius.
b) The air holes in the second ring are closer to the core than in a traditional Hexagonal PCF. For the same distance from origin to centre of first air hole (ro), in the ES-PCF the centre of the air holes in the 2nd ring are roughly 0.45 ro away from 1st ring, while this distance is about 0.87 ro or Hex PCF (see Fig. 3). This means the optical field can be squeezed more tightly into the core by the air
holes resulting in properties such as large non-linearity.
What does this give us?
Just be squeezing the field more effectively into the core, we can significantly improve modal properties:
1) Higher non-linearity (see
2) Lower bending loss
3) Flat dispersion
4) Ability to optimize performance over more than 1 parameter simultaneously
What is the catch?
The catch is that such designs have not been made yet. Feasible fabrication remains the biggest stumbling block for such quasi-crystal designs.
Is there a solution?
Yes. Techniques such as extrusion or drilling can be used to make unconventional PCF designs, so these offer one possibility. Another is to adapt the ‘stack and draw’ technique which is primarily used for hexagonal PCF. In another post I’ll explore how some very elegant mathematics gives us a way to do the latter.