Propuesta de ampliación del territorio Barí

P B M

λ

where P is the power emitted from the laser, M2 is the beam propagation factor and

λ

Finally, there is another common term, which is used to quantify the beam quality of a laser source, called the “beam parameter product” or BPP. It is defined as:

2 0 4 D BPP M

λ

π

Other definitions may exclude the factor of 1/4. In contrast to the M2-parameter, the BPP directly tells us how tightly a beam can be focused (at a certain numerical aperture), without any explicit dependence on the wavelength.

2.2

Double-clad fibres

The breaktrough RE-doped fibres realised in the mid-1980s were single- or few-moded devices that were pumped in the core. They generally relied on single-mode pumping, which limited their scope for brightness-enhancement. Their potential for power-scaling was also limited, since suitable single-mode pump-laser diodes are still limited in power to the watt-level. To overcome these limitations we would like to break the constraint of single-mode pumping

and to allow greater amounts of pump power to be coupled into the fibre, while at the same time retain a diffraction-limited output beam. A solution was proposed in 1989 by Po et al. [4] which consisted of a fibre whose cladding is surrounded by a lower index outer cladding which then forms a waveguide, outside of the primary core waveguide. The pump light can be introduced into the inner cladding and can propagate along the fibre, interacting with the rare-earth doped core as shown in figure 2.3. Such a fibre is called a double-clad fibre [5]. Since the core is often single-moded, a diffraction-limited output is obtained even with high-power multi-mode pumping.

Figure 2.3: Working principle of a double-clad fibre laser. The pump light (in blue) from

a laser diode propagates in the inner cladding of the double clad fibre, while lasing (in red) occurs in the core in a cavity formed by two embedded fibre gratings.

In order to maximize the amount of pump power that can be launched, the second cladding must have a refractive index as low as possible, to yield an NA of the inner cladding that is as high as possible. The inner cladding can also have a significantly larger area than the core. Consequently, with a typical value for silica face damage of about 10 W/µm2 at around 980 nm, more than 1.256 MW could theoretically be launched into a 400 µm diameter circular fibre. Unfortunately, although a larger inner-cladding enables more pump power to be coupled into the fibre structure, as long as the core design is fixed with a fixed RE-ion concentration, the pump absorption decreases as the interaction between the pump and the core is reduced (the overlaps between the modes of the inner cladding and the core decrease). Nonetheless this can be compensated with a longer fibre length, up to limits set by background loss and non- linearities. In addition, the pump power coupled into the fibre can be further increased with spectral and spatial multiplexing of multi-mode pump sources such as laser diodes stacks, diode bars or multiple single laser emitters. Therefore, from the development of the double-clad fibre, a new class of high power high-brightness laser sources emerged: the fibre laser.

2.2.2 Cladding designs

Double-clad fibres have a secondary lower index, outer, cladding. There are three types of outer cladding. Firstly, the cladding can be composed of a low-index glass. For example, fluorine doped silica yields a numerical aperture of typically about 0.2 to 0.3 for a pure-silica inner cladding. Such double-clad fibres are also called all-glass double-clad fibres. Advantages include a high thermal resilience and low propagation loss. It is based on well-known technology used for the fabrication of large-core fibres, but then with a large pure-silica core surrounded by a fluorosilicate cladding. The double-clad fibre design would introduce a (primary) RE-doped core into the pure-silica core of such a fibre. Secondly, the outer cladding can consist of a polymer or polymer-like coating, e.g., a fluoro-acrylate or a silicone. In this case, the NA (relative to a pure-silica inner cladding) can become 0.4 – 0.5. This is the most commonly used approach because the fabrication is straightforward and the cladding can be easily removed and the fibre easily cleaved. Figure 2.5 shows a cleaved end-face of D-shaped double-clad fibre which was coated with a low index polymer. Finally, the secondary cladding can consist of air holes in a silica fibre as shown in figure 2.4, such fibres being known as all- glass air-clad fibre (also Jacketed Air-Clad fibre). The numerical aperture depends on the structure. Values approaching unity have been reported [6], but are difficult to realise and to work with in practice. Typical values are lower, e.g., about 0.6 [7]. This is much higher than the other fibre designs due to the high refractive index contrast between silica and air. Still JAC fibres are challenging to fabricate and to handle and, therefore, are only occasionally used.

Figure 2.4: Jacketed Air-Clad fibre whose

outer cladding is formed by air-holes (here, the inner-cladding diameter is ~ 30µm)

[7].

Figure 2.5: D-shape double-clad fibre with a

Another important aspect of the cladding design is its shape, which influences the interaction between the pump light and the doped core [8 - 11]. For example, in fibres with circular symmetry, there are skew modes, which never overlap with the core. In a step-index structure, these correspond to higher-order Bessel functions, which vanish in the centre. Only J0

is non-zero in the centre, and the corresponding modes will see a high absorption. In contrast, the pump power contained in skew modes cannot interact efficiently with a core in the centre of the fibre. A large part of it is simply lost, without contributing to the amplification process. In the case of circular fibre, bending the fibre can induce some pump mode mixing. Thus, for example, pump power can be transferred into the J0-modes and prevent these from being

depleted. Therefore bending is commonly used to increase the pump absorption in circularly symmetric fibres. A more robust and repeatable alternative is to use cladding designs that do not support skew modes [12, 13] as shown in figure 2.6. For example, fibres with a rectangular inner cladding have shown an increased pump absorption over circularly symmetric fibres [14 - 16]. An off-centre core is another way of breaking the symmetry of circular fibres.

Figure 2.6: Common shapes of the inner cladding of double-clad fibres: a) circular, b) square,

c) rectangular, d) hexagonal, e) flower shape, f) D-shape [17].

2.2.3 Light injection methods

The injection of the pump light into the inner-cladding of the DCF can be achieved through various means, partly depending on the fibre geometry. The choice of the injection method is important as it, together with the pump brightness, determines the maximum permissible pump power, which can be coupled into a DCF. In many cases, this determines the performance that can be reached with a high-power fibre laser. The pump injection methods can be divided in two groups according to the location of the injection point along the double-clad fibre: end-pumping and side-pumping. There are also hybrid schemes, in which the pump power is first launched into a passive fibre through its sides. The pump power is, then launched into the active fibre through its end, by splicing the passive fibre to the active one.

The simplest method is to launch the pump directly into the inner cladding of the active fibre through one or both of the fibre ends using free-space coupling optics. Free-space end- pumping is easy to implement in an experimental set-up and the launch efficiency is generally good (e.g., 80%) if the beam quality of the pump source is sufficiently high. An additional advantage of free-space end-pumping is that the pump power can be scaled using diode bars or diode stacks whilst maintaining a high launch efficiency. Sometimes, free-space end-pumping is the only practical brightness-preserving solution when the source and fibre NA are very different, for example, in the case of high-NA, small inner-cladding fibres such as jacketed air clad fibres which have down to 30 µm inner cladding diameters [7]. However, the launch optics require precise and stable alignment. Furthermore, the fibre ends are not accessible for splicing which means that the signal has to be accessed with free space optics (at least with double- ended pumping). However, in commercial products all-fibre pumping schemes are preferred as it reduces or replaces a number of bulk optic components, enabling the construction of monolithic fibre laser sources in which the light propagates within the fibre. For example, fused components and fibre splices cannot be misaligned (although they can still suffer from excess accumulated heat in some cases).

Therefore, tapered fibre bundles (TFB) with signal feed-through [18, 19], which are only recently becoming commercially available, are commonly used in fibre laser. A tapered fibre bundle combines a fibre with a signal-guiding core and a number of pump fibres into a single double-clad fibre, guiding both the signal in its core and the pump in the inner cladding. Typically, the common double-clad fibre is not RE-doped, but is spliced to an active double- clad fibre. However, with a passive TFB that is spliced to the end of an active fibre, this effectively becomes an end-pumping method. As such, the maximum number of injection points is limited to the two fibre ends. In addition, in high power applications, the high pump power intensity at the injection points can lead to thermal loading at the fibre ends and special cooling arrangements must be then implemented to reduce fibre damage.

The second group of injection methods utilise some coupling mechanism that takes place on or along the side of the double-clad fibre. The notch coupling invented by Goldberg et al. [20] consists of a V-shaped groove cut into the fibre inner-cladding which is used to reflect the pump. V-groove side pumping allows for multiple injection points along the fibre with a typical launch efficiency of 75% [21]. However, the power scaling ability is poor because the number of V-grooves increases with power and the output power of laser diodes chips remains quite limited. Other side pumping methods consist of injecting the pump light through a side fibre in optical contact with the inner-cladding [22, 23]. This co-linear coupling is basically a long coupler, extended over the whole fibre where the pump and signal fibre are independently free and share a common low index cladding. This coupling mechanism is less prone to high

thermal loading because the pump power is slowly distributed to the active fibre inner-cladding [24]. Another side coupling method is the fused taper side-coupling invented by Samartsev et al. [25]. Little is really known about the power handling capability of this method, but in its design it is quite similar to the tapered fibre bundle and should have comparable power handling capability.