**Principal Investigator**
Barry Luther-Davies **Project **q04

Laser Physics Centre **Machine **VP,CM

Research School of Physical Sciences and Engineering

**Dark Optical Solitons and Soliton Induced Waveguides**

Photonics looks at mechanisms by which one beam of light is able to modify the behaviour of another, without intermediate electronics. By avoiding the conversion light to an electronic signal, photonic devices will able to operate much faster than their electronic counterparts. These devices will then be incorporated into ultra-fast optical computers and high bit rate communication systems.

In this project, photonic interactions which utilise spatial solitons are being investigated. The soliton is stationary pattern of light which propagates through a nonlinear medium in a "particle-like" manner. By inducing a waveguide in the nonlinear medium, the soliton is able to guide a secondary beam of light. It is this guidance, coupled with adjustability of soliton behaviour, that lays the foundation for soliton based photonic devices.

In this year, out computational investigations have examined the behaviour of both dark and bright solitons as they propagate. In particular we have been using our simulations to complement experimental work, which, on its own, is unable to provide a complete three dimensional picture of propagation behaviour.

**What are the basic questions addressed?**

The majority of research into soliton dynamics examines two dimensional systems. With access to super computing power, numerical investigations can be conviniently extended to three dimensions. Using these tools we seek to understand the influence of higher dimensionality on the behaviour of the soliton. By using realistic models for the nonlinear medium, we are also looking at the way deviation from ideal nonlinearity can alter the behaviour of higher dimensional solitons. The kinds of behaviours of interest are those which are potentially useful in all-optical switching configurations, including soliton attraction, repulsion, fusion, splitting and stability.

**What are the results to date and future of the
work?**

Simulation has provided valuable insight into the propagation dynamics of soliton systems. Experimental configurations do not allow propogation dynamics to be observed; only the light intensity in input and output planes can be observed. However, by simulating propagation, such that there is aggreement at both input and output, a picture of the experimental propagtion dynamics can be inferred from its readily disected, numerical equivalent.

Using this technique we have been able to demonstrate the collapse of a perturbed optical vortex into pairs of bright solitons, which can in-turn show attraction and repulsion, depending on the parity of vortex charge. The existence of the stable 3D bright soliton here is due to the saturating nature of the self-focusing nonlinearity, that is, its departure from the ideal (Kerr) case. In addition the dynamics of the well separated solitons was seen to arise from the angular momentum imparted by the vortex initial condition.

As a pair of bright solitons approach and collide in the saturable medium, they are seen to undergo a partial fusion; a third soliton is generated from the collision. This fusion does not occur in the ideal medium, where collisions are elastic. The sequence pictured here shows computed intensity profiles demonstrating evolution of the field from its (charge 2) vortex launching condition to its final, three soliton state. During this evolution, we see several dynamic features demonstrated namely the formation, rotation, attraction, collision and fusion of the solitons.

In other work we have examined the dark soliton behaviour, in the case of self-defocusing nonlinearity. We have found that vortex solitons are readily steered by superimposing weak coherent fields on the vortex launching conditon, as has been verified experimentally. Much work will be done in this area in an attempt to find analytic models for vortex motion in general background fields.

We also used simulation to examine the dynamics of
instability in a quasi 1+1D soliton stripe, observing formation
of vortex solitons as products of the breakup. Our numerical
results were in excellent correspondence with the results of experiment.
Further simulation is expected to show that saturation of the
nonlinearity provides an added mechanism for destabilisation of
the soliton stripe, leading to a quicker transition to transverse
instability.

**Figure 1**

Computed intensity profiles showing propagation dynamics of a charge two vortex in a self-focusing medium. The sequence is from the top left to the bottom right, horizontally.

**What computational techniques are used and why
is a supercomputer required?**

The beam propagation method is used to solve the equations for paraxial light propagation, as derived from Maxwell's equations. In terms of execution time, the beam propagation method is dominated by the two FFTs performed on a complex two dimensional array each iteration. The complex array represents the field cross section and each iteration propagates the cross-section a fixed distance. As this distance goes to zero, so does the computation approach the exact solution. Thus, for high accuracy over reasonable propagation distances the iteration count can be very large. The size of the complex array must also be very large, both for sampling accuracy and to avoid complications as features in the field approach the edge of the grid. On a scalar machine the two dimensional Fourier transform combined with the scalar nature of other matrix operations slows beam propagation computations to unworkable running times. Since each computational step comprising a single iteration is an operation on the field matrix, the code is highly vectorizable and runs extremely efficiently on vector supercomputers. Run times for 10000 iterations using a 512 x 512 grid are only around 40 minutes with 97% vectorization on the VP2200. Performance, in terms of execution time, is similar on the CM5.

**Publications**

*Spiralling Bright Spatial Solitons Formed by the
Breakup of and Optical Vortex in a Saturable Self-Focusing Medium*
, V. Tikhonenko, J. Christou, B. Luther-Davies, Journal of the
Optical Society of America **B 12** 2046-2052 (1995)

*Three Dimensional Bright Spatial Soliton Collision
and Fusion in a Saturable Self-Focusing Medium*,V.
Tikhonenko, J. Christou, B. Luther-Davies, Physical Review Letters
**76 **2698-2701 (1996)

*Observation of Vortex Solitons Created by Dark
Soliton Stripe Instability,* V. Tikhonenko,
J. Christou, B. Luther-Davies, Yu. S. Kivshar, Optics Letters,
in press

*Creation of Vortex Pairs via Transverse Instability
of Dark Solitons*, V. Tikhonenko, J. Christou,
B. Luther-Davies, Yu. S. Kivshar, The Twentieth Australian Conference
on Optical Fibre Technology (ACOFT '95), Proceedings 51-58,(1995).

*3D Spatial Soliton and Collision and Fusion,*
V. Tikhonenko, J. Christou, B. Luther-Davies, The Twentieth Australian
Conference on Optical Fibre Technology (ACOFT '95) Proceedings
184-187, (1995)

*Interacting Bright Spatial Solitons formed by
Optical Vortex Breakup in a Saturable Self-Focusing Medium*
, V. Tikhonenko, J. Christou, B Luther-Davies, The Tenth Conference
of the Australian Optical Society (AOS 10), Book of Abstracts,
33 (1995).