Applications

Fiber sources could potentially be used in many fields:

Some applications such as LIDAR or coherent communications required narrow linewidth sources. Low power DFB erbium doped fiber laser can be used as injectors for MOPA architectures. Today these lasers can reach 2kHz to 15kHz linewidth [9][10]. Their RIN is characterized by a peak at a relaxation frequency near 1MHz. It then quickly decreases below –14dB/Hz after a few MHz. The ONERA is currently working on wavelength locking on a Rubidium line of an Erbium/Ytterbium fiber laser. This laser (built by Koheras/IDIL) exhibit a very low RIN above 10MHz (<160dB/Hz, measurement done by ENSSAT in Lannion - France) (Fig. 1)

Fig. 1

RIN spectrum of the Erbium-Ytterbium fiber laser for wavelength locking at the ONERA.

In cooperation with Thales/Avionics, the ONERA/DOTA built a 1.5 μm LIDAR demonstrator. This MOPA continuous coherent fiber LIDAR is built around a 30 dBm Keopsys amplifier and is designed for use on board a helicopter. Its good vibrations handling capacity illustrates the robustness of fiber sources.

2.1

1^st cladding geometries

Pump light is only absorbed when the rays occasionally cross the doped single-mode core. Due to the small area ratio A_core/A_clad, the coupling of the pump light from the to the doped core is relatively weak. The pump absorption is strongly determined by the l^st-cladding geometry.

The pump cladding absorption can be expressed as:

where α_core and α_clad are the absorption in the core and the cladding respectively and K < 1. If the pump field was uniformly distributed across the first cladding, we would have K = 1. Due to the propagation of helical fiber modes only a fraction of the pump light can be absorbed in a circular cladding DC fiber and K < 1 [15]. Special cladding geometries were studied to offer both high K factor and good mechanical properties [16]. The usual cladding geometries proposed by specialty fibers manufacturers are: flower (OFS), hexagonal (INO, …), rectangular (Polaroid, Highwave, …), D-shaped. Theses types of DC fibers can be spliced using automatic splicers. At very high pump power, special geometries including several layers improve the thermal behavior.

2.2

Pump injection solutions

Different techniques for DC pump injection have been proposed in the literature. We describe here the more reliable solutions for high power amplifiers design. Essentially, three clad pump techniques have are used in commercially available systems:

2.3

Erbium/Ytterbium codoping

The Erbium ions concentration in the core is limited by clustering effect [21]. The maximum pump absorption cross-section is about 2x10^-25 ions.m^-3. Therefore the effective pump absorption of a pure Erbium doped fiber would be pretty low.

The Ytterbium ions concentration can be several tens times higher. Moreover the 977 nm pump peak absorption is twice larger than with 975 nm Erbium. The proximity between the transitions 2F_7/2 to 2F_5/2 and 4I_15/2 to 4I_11/2 allows resonant coupling between Ytterbium and Erbium ions. Thus pump power can be absorbed by Ytterbium with high rate an transferred to Erbium to benefit from high absorption and 1,55μm band.

Power scaling of lasers and amplifiers at 1,55 μm thus quickly directed towards Erbium-Ytterbium fibers (Fig. 2). It should be however noted that these fibers are more challenging to make: not only have Erbium and Ytterbium concentration to be tuned to get a good transfer rate, but Aluminum and phosphorous have to be introduced too. Aluminum is required to increase rare earth solubility and avoid clustering ; phosphorous is added to reduce the Erbium 4I_11/2 excited level lifetime and thus reduce the backtransfert from Erbium to Ytterbium.

Fig. 2

The Erbium-Ytterbium energy diagram

The basic equations for the modeling of Erbium- Ytterbium system can be found in several papers [22, 23].

3.1

Maximum extractable energy

If continuous wave amplifiers performances are now well-known and modeling, amplifiers in pulsed regime have a more complex behavior.

Aside numerical models, we use a semi-analytical model which provide great insight in the physics of pulsed amplifiers. We adopt the following hypothesis:

We the define the saturation energy at the signal wavelength by :

Γ is the overlap factor at the signal wavelength between the signal mode and the doped zone, hν is the photon energy, σ^e and σ^a are the emission and absorption cross-section at the signal wavelength and A is the area of the doped zone. For a usual telecom fiber, E_sat<5 μJ.

We then assume that pulses whose peak power is high compared to the saturation power enter the amplifier. The gain can then be analytically computed during the pulse [23]:

where G_o is the amplifier gain just before the pulse arrival, corresponding at t = 0, E_in(t) is the energy which entered the amplifier. This expression is called the Franz-Novdik relation for an amplifier [24].

It can then be shown that the output energy per pulse does not depend on the pulse shape:

When E_in>>E_sat, The output energy can be simply Signal wave expressed as:

G_o is the only parameter to estimate. At low pulse repetition rate or very high repetition rate, it can be computed using a continuous wave model assuming that the input power is the average input power in the real situation. Figure 3 shows the excellent agreement at low pulse rate between this model and a full numerical one.

Fig. 3

Comparison between (3) and a numerical model for pulse amplification at 1 kHz repetition rate.

Using (4), we estimated the extractable energy for several fibers (Fig. 4). As the saturation energy scales with the doped area, we can see that large pulse energy requires fiber with large doped core.

Fig. 4

Extracted energy by 100 μJ from a 3m fiber amplifier.

Solid state lasers can be seen as a limit of this scaling process.

3.2

Non linear effects

The efficiency of fiber lasers and amplifiers comes from the tight confinement of the optical mode into the core. However, the resulting small mode field diameter is also the source of limitations due to non-linear effects.

Non-linear effects arise from the change in the silica properties by high intensities. Their threshold thus scales with the ratio L_eff/A_eff where Leff is an effective length and Aeff is the effective area of the fundamental guided mode (A_eff = πω² in gaussian field approximation where ω is the mode field diameter)

For narrow linewidth sources, the first non-linear effect to appear is the Stimulated Brillouin Scattering (SBS) [25].

SBS originates from the interaction between the signal and acoustic waves in the fiber (Fig. 5). A small fraction of the pump is scattered in a counterpropagating beam called the Stokes wave. When the signal reaches a threshold, the process becomes stimulated and the Stokes wave is amplified until complete depletion of the signal. The Stokes wave is downshifted by ~ 11 GHz.

Fig. 5

Stimulated Brillouin Scattering principle.

The Stokes wave can be powerful enough to be scattered into a second order. The total spectrum will thus be spread over several GHz. In an amplifier, every scattering will act as a (distributed) mirror and every Stokes order will be amplified up to be several times more powerful than the signal itself. It can be strong enough to destroy optical components such as isolators. In the time domain, the signal power drops periodically (Fig. 6). The period is the round-trip time of light in the fiber. A numerical model is developed at the ONERA/DOTA including SBS and gain dynamic to get greater insight into the amplifier behavior [26].

Fig. 6

Amplification of rectangular pulses by a 1 W amplifier for three increasing input peak power (a) below threshold. (b) above threshold. (c) above the 2^nd order threshold.

A rule of thumb can be derived to estimate the SBS threshold using the Smith relation [27]:

where g_B ≈3x10^-11 m^-1.W^-1 is the Brillouin gain in silica fibers, Aeff is the fiber effective area and Pth is the threshold power at the output of the amplifier, χ is a unitless number which changes slowly with the amplifier gain, length and effective area. L_eff=L_physical/ln(G) with G the amplifier gain and Lphysical its length.

This relation was derived for passive fibers as long as several kilometers. In that case, χ is closed to 21. For active amplifiers (6) holds with a χ slightly different which can be numerically estimated [27].

Using this rule, it appears that double-clad fibers should have a large core and a small 1^st-cladding to core ratio. It would indeed allow to reduce A_eff and L_eff as the pump would be absorbed on a shorter length. The reduction of the 1^st-cladding is only possible now with the availability of high brightness pump diodes which can be coupled into 100 μm fibers. A threshold several dB higher is thus forecast. The Kerr effect is another relevant effect. The nonlinear Kerr parameter of a Er³⁺/Yb³⁺ co-doped fiber has been measured using the FWM method[28]. The FWM products are generated by a two co-propagated signal pumps with co-linear polarization arrangement. These two pumps can be degenerated. The Kerr non-linear coefficient Υ_ErYb of the Er³⁺/Yb³⁺ co-doped fiber is evaluated ~ 15 W^-1km^-1 which is somewhat higher than in undoped fiber. Kerr effect in fibers is responsible for FWM, SPM and XPM which would be relevant in a context of spatial optical communications [24]. In the context of high power pulse generation, FWM is the most relevant non-linear effect as it is responsible for optical parametric amplification [24]. Using a simple 1 W amplifier with a mode area of 50 μm², we observed OPA which impairs the spectral purity of the signal below 1 kW.

As with SBS, an increase in the core diameter and a decrease in the fiber length should help to enhance the SBS threshold by several decibels.