**Principal Investigator**
Barry Luther-Davies **Project **p59

Laser Physics Centre, **Machine **VP

Research School of Physical Sciences

**Towards a Modelocked Waveguide Laser**

The Laser Physics Centre has produced CW lasers in the infra-red region of the spectrum in Neodymium (Nd) doped glass fibre, in waveguides produced by ion implantation into the common laser crystal Nd doped Yttrium Aluminium Garnet (YAG) and in the bulk laser host Nd doped Yttrium Orthovanadate (Nd:YVO4). 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 .

We want to produce the pulses by taking advantage of the nonlinear (ie. intensity dependent) interaction of two optical waveguides placed less than 0.015mm apart. Such a device, called a Non-Linear Directional Coupler (NLDC), can be constructed so that it has increasing reflectivity with increasing intensity and this leads to pulse formation within the laser in a process known as passive modelocking. We also want the device to be self-starting ie. to start pulsing when turned on, rather than relying on an external stimulus.

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 fixed at the time of construction and our aim is to model and understand the processes that occur inside the device. This enables us to 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, waveguide loss, waveguide length and dephasing time will give the most robust, self-starting pulsed laser?

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

Early work looked at the suitability of different laser hosts for producing ion-implanted optical waveguide lasers (particularly in Neodymium doped Yttrium Aluminium Garnets, Nd:YAG) and was concerned with different techniques of achieving passive modelocking in such crystals, with the main focus on the 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. For example, computer modelling showed that lasers that use Nd:YAG as host material are unlikely to produce the required short pulses because of the narrow bandwidth of the available gain transitions and so other laser hosts needed to be examined.

Next we considered Nd doped silica glass, as this was available to us in the form of optical fibre from both the Optical Communications Group at the University of NSW and the Optical Fibre Technology Centre (OFTC) at the University of Sydney. Simulations showed that for lasing at 1055nm there was a space of realisable parameters in which the laser would self-start and produce picosecond pulses.

However, for the device to behave correctly it is necessary to produce a fibre that has two cores that are identical to each other for an appreciable distance (>5cm). To date neither laboratory has been able to do that for us at 1055nm. Fibre has been given to us that does have the desired properties at 1342nm and this has led to the need to study a new host, Neodymium Yttrium Orthovanadate (Nd:YVO4) which lases as this wavelength. Data about material parameters has been recently collected from experiments on the host itself and work is under way to see how it should respond.

With the addition of Dr Jurg Schutz to the project we have been able 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 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 different elements of the laser. 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 experimental 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. Due to the random nature of the starting noise and spontaneous emission processes in our laser model, each simulation is a "special case" and so we have been expanding the work to do a number of simulations for each set of parameters and averaging the output to improve the statistical accuracy of the results.

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 supercomputer is required for two 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 requires 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
that can only be handled within reasonable time (i.e. hours of
CPU time) by a supercomputer. If the procedure that 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).