Some more non-linearity

In recent times I have focused my blogposts on events that I attended.

Today I feel some pleasure in going back to writing a bit about my research.

In a recent journal article that we published we explored how an ultra broadband Supercontinuum in the mid Infra Red part of spectrum can be efficiently generated in spiral chalcogenide PCF.

We showed by numerical simulations an SCG spectra that spanned more than 3 Octave from 1.3-11 micron and beyond. The difficulties in generating SCG in these wavelength regimes include lack of sources at appropriate pump wavelengths, such sources of sufficiently high power, as well as waveguides that have zero and flat dispersion near the pump.

With the Equiangular Spiral PCF,  it is possible to modify both the dispersion (making it flat and close to zero @ the choice of pump wavelength)  as well as have a well confined modal field with large non-linearity.

What this work offers along with Disperison and nonlinearity control is the additional control of absorption: possibility  of a cladding  made of the same material as the core (only airholes are introduced for guidance) which overcomes the problem of absorption seen in other proposed/fabricated planar waveguide and step index chalcogenide based designs.

It goes without saying that the results were exhilarating and I now look forward to taking this work further, preferably with someone who can fabricate and test the design!

So if you want to collaborate do get in touch!

Lazy days in Delhi

I am in Delhi right now – part work and partly a holiday. The work bit is attending the Workshop on Recent Advances in Photonics (WRAP) at IIT Delhi, my alma mater.

Its been a great opportunity to hear some brilliant speakers- David Payne, Govind Agrawal, Wolfgang Freude, C. Jagdish, Kent Choquette, and others. The networking is also brilliant- I have had a chance to meet several young researchers in leading institutions in India who are setting up new labs in Photonics and opening up new areas of research. Then there is the connecting with old colleagues and friends from my student days.

One would think that attending a workshop while on holiday would be a drag. Surprisingly, its been anything but. I have had so much fun catching up with friends and colleagues, over tea breaks in the weak sunshine…talking about our teachers, exchanging gossip and life stories. It has made me feel both relaxed and lazy – a combination one rarely associates with attending a conference.

One thing that i really liked about the workshop was that it brought together students and researchers from across India, many of whom would not be travelling to many larger international conferences, and gave them an opportunity to hear the latest work in the field from globally leading figures. On the other hand many of the young attendees had out up posters and were able to get feedback on their work and ideas from these leading figures in a relatively relaxed and stress free environment. This kind of exposure can be invaluable and inspiring.

Lest you think i haven’t heard a single talk and only chatted with friends, i will summarise two of my favourite talks from the workshop:

The first by Govind Agrawal was about adiabatic wavelength conversion in resonators. The key idea is that the wavelength (or frequency) modes of a resonator depend on the refractive index
and length of the cavity. By changing the refractive index, the resonant frequency changes and this causes the energy stored in the resonator to transfer to the new resonant frequency.
This fairly simple principle was applied and experimental results were presented as corroboration.

The second talk that i enjoyed tremendously was by Sidharth Ramanchandran on optical fibers with an annular refractive index profile, exhibiting modes with Orbital Angular Momentum (OAM) that does not change as the modes propagate. The phase or OAM shows a spiral dependence (looks like an archimedean spiral to me!).

Now I shall endeavour to follow up on the contacts I made and enjoy a coffee with my teachers from my graduate days.

Supercontinuum generation with spiral fibers

In previous posts (Stacking the spiral, magic of equiangular spirals, my research) I have talked about the properties of spiral PCF focusing especially on the modal properties which gives us dispersion tunability as well as great confinement (hence large non-linearity). This has applications for Supercontinuum Generation (SCG) and Second Harmonic Generation (see another paper).

In this post I talk a little about studying SCG in the Equiangular Spiral PCF (ES-PCF) with numerical simulation (see the paper).

To begin with we used the Finite Element Method (FEM) to design and optimize the ES-PCF. We changed the spiral properties and ran simulations to get a design with very low dispersion (the total dispersion from 1.5 μm – 2.3 μm, varies very little, in the range of ±4 ps/nm/km. In addition, the ES – PCF exhibits three ZDWs at 1.52, 1.88 and 2.22μm which can make multi – wavelength pumping possible).

The next big step was to simulate SCG by solving the Generalised Non Linear Schrodinger Equation (GNLSE) using a split-step Fourier method. This allows us to look at how the SCg evolves in the ES-PCF as a function of a) pump power b) fiber length c) pumping at different wavelengths. We found that for the pump wavelength at 1557 nm and average pump power of 11.2 mW, SCG bandwidth > 3 µm (970 nm – 4100 nm) at 40 dB below the peak spectral power. In the same fiber, at pump wavelength 1930nm and average pump power of 12mW the SC bandwidth was more than 2 octaves (1300 nm – 3700 nm).

The paper can be accessed here.

The importance of this paper is on more than 1 count:

1. It shows a fiber design that has flat dispersion over a very large wavelength range: 1800nm
2. This fiber has the potential of multi wavelength pumping for SCG.
3. The sueprcontinuum generated is broadband and flat, at much lower pumping powers than reported in several studies
4. Through numerical simulation we can help design and characterize optical components, reducing time and money in the fabrication cycle.

I feel that when experimental and theoretical work goes hand in hand the gains are far more than the sum of the individual parts!
So I would be really happy to work with an experimental group on this!

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 Hexagonal CLose Packed layers of spheres 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.

Giant's Causeway: HCP in action 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…

The magic of Equiangular Spirals

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

schematic of an equiangular spiral curve

Fig. 1: Schematic of an equiangular spiral curve

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?

The ES curve grows continuously and is defined by the equation: equiangular spiral equation

where

definiton of alpha

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

Fig. 2: schematic of the ES-PCF

Fig. 2: schematic of the ES-PCF

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

Fig.3: Schematic of the Hexagonal PCF
Fig.3: Schematic of the Hexagonal PCF

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.