Laser Physics Centre, **Machine** VP

Research School of Physical Sciences and Engineering

**Co-Investigators** Jurg Schutz and Doug Body

Laser Physics Centre,

Research School of Physical Sciences and Engineering

**Towards a Modelocked Waveguide Laser**

The Laser Physics Centre has produced waveguides in laser hosts by ion implantation and continuous wave lasers in Neodymium doped, twin core, optical fibres. Our aim is to extend this to producing small lasers (<10cm long), emitting short pulses of light (~1ps) at a high repetition rate (>1GHz). Such devices would be smaller and more robust than those in current use and would have many potential applications, particularly in telecommunications.

The devices under consideration rely on a laser cavity element which has an increasing reflectivity with incident intensity. In our case, this is produced by the change of the coupling of the cores in a twin core fibre or self-focusing in an ion implanted waveguide. Both of these rely on the Kerr Effect (a nonlinear (i.e. light intensity dependent) process)) and lead to the important pulse forming/maintaining behaviour known as Passive Modelocking.

The behaviour of these devices is, however, extremely sensitive to a wide range of design parameters (e.g. laser host material, waveguide dispersion, mirror properties, sources of loss). Many of these properties are essentially fixed at the time of construction and our aim is to understand and model the processes that occur inside these devices. This enables us determine what is likely to work and which properties are expected to be important in building practical devices.

**What are the basic questions addressed?**

What combination of physically realisable device parameters for laser host material, waveguide dispersion, non-linear response and dephasing time will give the most robust, self-starting pulsed laser?

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

Early work looked at the suitability of different laser hosts for producing ion-implanted optical waveguides (particularly in Neodymium doped Yttrium Aluminium Garnets, Nd:YAG) and was concerned with different techniques of achieving passive modelocking in such crystals, with main focus on the Non-Linear Directional Coupler (NLDC). The description of the mode-locking processes in such lasers by an appropriate numerical model has had to evolve in response to experimental results and vice versa. Computer modelling showed that lasers which use Nd:YAG as host material are unlikely to produce the required short pulses because of the narrow bandwidth of the available gain transitions. Experiments aiming to confirm this result will soon be undertaken.

An important laser host to be considered is Neodymium doped silica glass, which can be used with both designs, the ion-implanted work as well as the twin core optical fibre which became available to us from the Optical Communications Group at the University of NSW and from the Optical Fibre Technology Centre (OFTC) at the University of Sydney. Initial modelling showed that the wider bandwidth of Nd in glass should enable the device to produce picosecond modelocked pulses and to self start, that is, to begin producing pulsed laser radiation without any external means.

Several lasers have been built in the laboratory from Nd-doped twin core fibres. These lasers did not produce the desired pulsing, which was to be expected, since the obtainable conditions were far away from the ideal suggested by the models. However, measurements of the output spectrum and the mode dephasing time also produced unexpected results which could not readily be explained. Work is currently under way to look at these effects in more detail.

With the addition of Dr Jurg Schutz to the project we have started to investigate the operation conditions (steady-state) of the twin-core fibre laser in more detail. Numerical calculations have been performed which incorporate the influence of propagation effects, such as fibre nonlinearities (Kerr effect, stimulated Raman scattering) and dispersion (from the host material, waveguide and gain) as well as dissipative processes (linear loss, gain). A considerable amount of time has been spent this year with the construction and the testing of the numerical model and further investigations will begin very soon which cope with experiment-like conditions. For this purpose, other effects like gain saturation and pump depletion will have to be included as well, because they can severely affect the operation conditions of the laser.

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

Two models are under consideration at present. One of them is particularly looking at the self-starting and the dynamics inside the laser in the early stages of lasing and pulse formation. The other one focuses particularly on the effects of the pulse propagation and its long-term stability.

The first model looks at a "window"/sample of the light field in the cavity during a round trip and how this field is modified by the involved processes. During propagation it undergoes intensity dependent and linear loss in time space, where the former is determined by interpolation using results of a set of coupled Ordinary Differential Equations (ODE) which are calculated at the beginning of the computation. In frequency space, frequency dependent gain (modelled by another set of coupled ODEs), gain narrowing and mode dephasing are calculated subsequently. Each round-trip involves a pair of Fourier Transforms to change between these spaces. Self-starting of passively modelocked laser systems has been demonstrated in a variety of different configurations, but little theory has been done on this topic and the fact that such calculations require large amounts of computation power has led to the situation that only crude approximations and special cases have been studied to date. The availability of the supercomputer enables us to have a detailed look at what is happening on a practical time scale.

In the second model, a modified version of the Nonlinear Schrodinger Equation (including higher order dispersion terms, stimulated Raman scattering and gain) is used to describe nonlinear pulse propagation and coupling in the twin-core fibre; the differential equation is solved with the help of the well-known Split-step Fourier Method. The intensity dependent cavity loss, which is responsible for the passive mode-locking in the laser, is established by setting the field in the coupled core to zero, each time the pulse reaches the end of the twin-core fibre cavity, and by leaving the field in the bar core unchanged. This corresponds to the experimental situation, where both ends of the coupled core are non-reflecting and those of the bar core are highly reflective. The supercomputer is required for 2 main reasons :

1. Once the prospective conditions for self-starting are known, it is necessary to determine the corresponding operating conditions of the laser (steady-state) in order to check if they remain within reasonable dimensions. This may require a considerable number of test calculations in order to find appropriate values for intensity and width of the initial seed pulse and for the gain in the fibre, which successfully lead to passively mode-locked laser operation.

2. After the conditions for self-starting and for the steady-state have been determined, it is still necessary to test if these conditions really lead to pulsed laser operation and how many round-trips would be required for building up the laser pulse from the initial noise floor. Preliminary results and experience values from other laser systems indicate, that this process may require several thousand round-trips and 105-106 subsequent Fast Fourier Transforms with about 8192 array points which can only be handled within reasonable time (i.e. hours of CPU time) by a supercomputer. If the procedure which is outlined above does not lead to reasonable results (e.g. if the steady-state pulses owe an extremely high energy) or if self-starting from noise does not occur, the calculations have to be repeated with changed parameters (e.g. lower dispersion).