ACTIVE STABILIZATION OF MODE INSTABILITIES IN OPTICAL WAVEGUIDES

Abstract

A method of propagating a laser signal through an optical waveguide and a waveguide laser system provide a novel way of stabilizing the beam emitted by a fiber laser system above the mode instability threshold wherein the beat length of two or more interfering transverse modes of the laser signal in the optical waveguide is modulated in time.

Claims

1. A method of propagating a laser signal through an optical waveguide, wherein the beat length of two or more transverse modes of the laser signal in the optical waveguide is modulated.

2. The method of claim 1, wherein the frequency of the modulation of the beat length is close to the inverse of the thermalization time of a core of the optical waveguide.

3. The method of claim 1, wherein the frequency of the modulation of the beat length is close to the time of fluctuations of the laser beam observed at the output of the optical waveguide.

4. The method of claim 1, wherein the beat length of the transverse modes is modulated with a frequency below 100 kHz, preferably below 10 kHz.

5. The method of claim 1, wherein the optical waveguide is optically active and is optically pumped to amplify the laser signal while propagating through the optical waveguide.

6. The method of claim 5, wherein the modulation of the beat length of the transverse modes is achieved by modulating the pump power.

7. The method of claim 6, wherein at least two pump sources are used, wherein the pump radiation of one of the pump sources propagates in the co-propagating direction and the pump radiation of another one of the pump sources propagates in the counter-propagating direction with respect to the laser signal through the optical waveguide.

8. The method of claim 7, wherein the modulation of the pump power of the pump sources is synchronized to achieve a constant power of the laser signal at the output of the optical waveguide.

9. The method of claim 5, wherein the modulation of the beat length of the transverse modes is achieved by modulating the power of the laser signal coupled into the optical waveguide.

10. The method of claim 5, wherein a modulated auxiliary signal is coupled into the optical waveguide in addition to the laser signal, wherein the wavelength of the auxiliary signal falls within the amplification bandwidth of the optical waveguide.

11. The method of claim 5, wherein the optical waveguide comprises an absorbing material which is illuminated by an external modulated radiation source at an absorption wavelength of the absorbing material, wherein the absorption wavelength is outside of the pump absorption bands and amplification bands of the optical waveguide.

12. The method of claim 11, wherein the absorbing material is the host material of the optical waveguide.

13. The method of claim 1, wherein two or more electrodes are incorporated into the optical waveguide, wherein a modulated voltage is applied to the electrodes to dynamically modify the refractive index profile of the optical waveguide via electrostriction.

14. The method of claim 1, wherein the optical waveguide is doped with rare-earth ions.

15. The method for mitigation of mode instabilities according to claim 1, in which the amplitude, frequency, and/or temporal shape of the modulation of the beat length of the transverse modes is controlled by a feedback loop which monitors the laser signal at the output of the optical waveguide.

16. A waveguide laser system comprising an optical waveguide, through which a laser signal is propagated, and a modulator, which modulates the beat length of two or more transverse modes of the laser signal in the optical waveguide.

17. The waveguide laser system of claim 16, wherein the modulator is configured to modulate the beat length of the transverse modes.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The enclosed drawings disclose preferred embodiments of the present invention. It should be understood, however, that the drawings are designed for the purpose of illustration only and not as a definition of the limits of the invention. In the drawings:

[0018] FIG. 1 shows a schematic illustration of the origin of mode instabilities;

[0019] FIG. 2 shows schematically the impact that changing the beat length of the fiber modes between two states (state 1 and 2) has on the thermally-induced index grating (n);

[0020] FIG. 3 illustrates the impact of a dynamic modulation of the beat length at a frequency similar to that of the beam fluctuations during mode instabilities;

[0021] FIG. 4 shows the impact of a dynamic modulation of the pump power of a fiber laser system on the longitudinal temperature gradient and on the thermally-induced index grating;

[0022] FIG. 5 schematically illustrates the impact of the absorption of an external radiation in an absorbing region of the fiber;

[0023] FIG. 6 shows a cross section of a fiber containing two electrodes used to modulate the transverse index profile of the fiber; and

[0024] FIG. 7 schematically illustrates the incorporation of a feedback control loop to achieve a long term stabilization of the beam fluctuations using the embodiment with the modulation of the pump power.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0025] As schematically illustrated in FIG. 1, when two transverse modes are simultaneously excited in an optical fiber (constituting an optical waveguide within the meaning of the invention), they propagate giving rise to a three dimensional interference intensity pattern. This, in turn, gets imprinted in the inversion profile generating a heat load that mimics the interference pattern. Such situation results in a temperature profile with periodic features in it that, via the thermo-optic effect, is translated into a quasi-periodic refractive index change, i.e. a thermally-induced index grating. Such grating has characteristics in terms of symmetry and periodicity to potentially transfer energy between the interfering modes, thus giving rise to the observed phenomenon of mode instabilities. For the sake of simplicity, the three dimensional patterns (intensity, inversion, heat-load, temperature and index change) will be represented in the following by their projections along the axis of the fiber (dashed lines in FIG. 1), thus reducing them to two-dimensional functions (which in the simplest case will resemble a sinusoidal function).

[0026] It is important to realize that the period of the thermally-induced index grating at each point along the fiber is determined by the local beat length between the interfering fiber modes. Thus, as schematically illustrated in FIG. 2, by changing this beat length (i.e the period of the modal interference intensity pattern), it will be possible to influence the thermally-induced index grating (represented by n in FIG. 2). However, the index grating n requires a certain time (related to the thermalization time in the fiber core) to adapt itself to the new situation (i.e. heat-load). This reaction time is approximately given by the inverse of the frequency of the beam fluctuations during the instabilities, and it can be roughly estimated by the thermalization time in a rod geometry:

[00001]${}_{\mathrm{th}}=\frac{C.Math..Math.M.Math..Math.F.Math..Math.D^2}{4.Math..Math.}$

where C is the heat capacity, is the density and is the thermal conductivity of the core material. Additionally MFD represents the mode field diameter of the light in the fiber. Depending on the size, and according to the formula given above, the fluctuations of mode instabilities have a characteristic frequency <100 kHz, even though for the conventional fibers used in high average power systems this frequency is usually <10 kHz.

[0027] As indicated in FIG. 3, if, once that the mode instability threshold has been reached, the beat length of the fiber is modulated with a frequency close to that of the beam fluctuations of the free-running system, the thermally induced index grating n will not be able to fully adapt itself to the changing situation. As a consequence it will adopt a profile that is the superposition of the different states forced by the modulation. In other words, the thermally-induced index grating will be washed out. Hereby, the ability of the grating to transfer energy between the fiber modes will be weakened and the beam will be stabilized.

[0028] The beat length L.sub.b of two fiber modes is given by:

[00002]$L_b=\frac{}{n_{\mathrm{eff}.Math..Math.1}-n_{\mathrm{eff}.Math..Math.2}}$

[0029] Where is the wavelength of the signal and n.sub.effi represents the effective refractive index of the i.sup.th mode. Therefore, in order to modulate the beat length for a constant signal wavelength according to the invention, it is necessary to change the difference between the effective refractive indexes of the fiber modes. There are several ways to accomplish this, which corresponds to different embodiments of this invention. These will be detailed in the following.

[0030] The beat length of two fiber modes depends on the temperature gradient of the fiber, which may be controlled by the pump power. As illustrated in FIG. 4, if the pump power is modulated (having a highest power level of {circumflex over (P)} and a lowest power level of {hacek over (P)}), the temperature distribution along the fiber can be changed. Since the beat length of the modes in a fiber is usually shorter the higher the temperature (or, more correctly, the higher the transverse temperature gradient), modulating the pump power has the effect of also changing the beat length along the fiber. However, since in a real active fiber there is usually a longitudinal temperature gradient, the beat length for any given pump power is not constant along the waveguide which, as illustrated at the bottom of FIG. 4, results in a thermally-induced index grating that is not homogeneous along the fiber length. In spite of this, modulating the pump power still has the desired effect of shifting the maxima and minima of the thermally-induced index grating in the axial direction of the fiber. This, when done at the proper modulation frequency, will result in an equilibrium state with a significantly weaker thermally-induced grating and, correspondingly, less mode instabilities.

[0031] This approach has the advantage of an easy and convenient integration in existing fiber laser systems, which makes it very attractive from the practical point of view. The drawback, however, is that the pump modulation will be translated into a modulation of the output power of the fiber system. This modulation will usually be in the range of some 100 Hz to a few kHz (typically below 10 kHz). Whereas such a fast modulation will not be noticeable for many application, there are some that are definitively sensitive to it. Therefore, in order to solve this potentially detrimental side-effect of the proposed embodiment of the invention, it is suggested by the invention to use at least two modulated pump sources (which, without any loss of generality may have different wavelengths): with at least one in the co-propagating direction and at least one in the counter-propagating direction (with respect to the laser signal propagating in the fiber). In the easiest implementation, these pump sources will emit exactly the same average power. The modulation of these two pump sources should be synchronized and have a 7-phase shift relative to each another. This implementation results in a longitudinal shift of the maxima and minima of the thermally-induced index grating without any power fluctuation of the output signal.

[0032] In a different embodiment, the modulation of the beat length of the fiber modes can be achieved by modulating the seed signal power, i.e. the power of the laser signal propagating through the fiber. This, when choosing the correct parameters in terms of modulation amplitude, frequency and function, will lead to similar stabilization results as those obtained with the modulation of the pump power. This approach has the same disadvantage as the one described previously, that is: the output signal power will fluctuate at a frequency corresponding to the modulation. In order to prevent this from happening, both approaches can be combined. In this way it becomes possible to realize a fiber system which is end-pumped only from one side with a modulated pump and which is seeded by a modulated (seed) laser signal. By choosing the right modulation parameters for both the signal and the pump (usually this will lead to using the same modulation frequency and a -phase shift between the modulation patterns of signal and pump), it is possible to stabilize mode instabilities and to obtain a signal at the output which shows no power fluctuations.

[0033] In yet another embodiment of the invention, it is possible to inject a secondary auxiliary signal into the system, which will have a different wavelength from that of the main useful laser signal and which is modulated. In the preferred embodiment, the wavelength of this auxiliary signal will fall within the amplification bandwidth of the fiber system. Again, the modulation of this auxiliary signal with the right parameters will lead to a weakening of the thermally-induced index grating and to a stabilization of mode instabilities. As before, this embodiment can be combined with any of the previous ones to obtain a stabilized beam with no power fluctuations at the output.

[0034] Another way of changing the beat length of two modes in a fiber is by generating heat inside of the waveguide. Such an internal heat source leads to a change of the refractive index profile of the fiber which, in turn, results in a modification of the effective refractive indexes of the fiber modes and, therefore, of their beat length. One way of modulating the internal heat generated in a fiber is by incorporating an absorbing medium into the optical waveguide and by illuminating it by an external radiation source (usually, but not necessarily, light) which has a wavelength that is outside the pump absorption and gain bands of the fiber. This is schematically illustrated in FIG. 5. Following this approach, a modulation of the external radiation will lead to a modulation of the modal beat length in the fiber and, as explained above, when done with the right frequency, to a weakening of the thermally-induced index grating.

[0035] A particularly simple embodiment of this approach is to use the host material optical fibers are made of (usually silica) as the absorbing material. Thus, in the case of silica, the OH absorption peaks situated around 1400 nm or 2000 nm could be used. Likewise, the silica fiber can be irradiated by an external radiation source emitting at a wavelength longer than the transparency edge of silica (located around 2.2 m). By doing so and by performing a transversally inhomogeneous illumination of the fiber with the external radiation (e.g. concentrating this radiation exclusively in the fiber core), it will be possible to generate an extra heat source in the fiber that controls the beat length of the fiber modes.

[0036] Another simple embodiment of this approach, particularly useful in Yb-doped fibers, exploits the photo-darkening effect in these kind of systems. Photo-darkening is an effect by which a photo-degradation of the fiber is observed, which manifests itself in the appearance of strong absorption peaks in the visible part of the electromagnetic spectrum. Thus, these peaks can be used to generate heat in the fiber by illuminating it with radiation between 300-700 nm. The advantage of this embodiment is that the absorption peaks only appear in the fiber regions doped with Yb, which automatically leads to the generation of a transversally inhomogeneous heat load and, therefore, to the modification of the beat length even if the whole fiber is illuminated with the external radiation.

[0037] Even though the absorbing material has been considered to be located in the core of the fiber in the examples discussed above, in general it can be placed anywhere in the fiber (related to both its cross-section and its length). Placing this absorbing material outside of the core might be advantageous since it may allow, for example, injecting the external radiation to be absorbed from the side of the fiber, i.e. transversally to the fiber axis. Placing the absorbing material in the cladding can be particularly effective in waveguide designs which effective single-mode operation is based on the concept of delocalization. In these waveguide the inner structure results in the higher-order modes having most of their energy located outside of the central core. In such a situation these modes are extremely sensitive to changes in the cladding portion of the waveguide and, therefore, modulating the heat load there can lead to strong changes of the modal beat length and, ultimately, to the stabilization of the beam fluctuations above the mode instability threshold.

[0038] Yet another approach to change the beat length of the fiber modes is the direct modification of the refractive index profile of the fiber. A possible embodiment of this idea is, as schematically shown in FIG. 6, to incorporate two or more electrodes in the cross-section of the fiber outside of the fiber core. Then, by applying a voltage difference between the electrodes, an electric field is created that, through electrostriction, can lead to the change of the index profile of the fiber. A modulation of this electrical signal can, then, result in a modulation of the beat length of the modes and, in turn, to a weakening of the thermally-induced grating.

[0039] Regardless of the particular embodiment, a feedback control loop should be used that analyzes the stability of the output laser signal and adjusts the frequency, amplitude and modulation function to adapt itself to possible drifts of the system. This approach is exemplarily illustrated in FIG. 7, for the embodiment in which the pump power is modulated.

[0040] Even though most of the embodiments described above will typically be realized with rare-earth doped fibers as optical waveguides, the embodiments can also be applied to fiber amplifiers based on inelastic scattering (Brillouin and Raman) or on parametric processes (such as four-wave mixing).

REFERENCES

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