The average power of fiber lasers is subject to the phenomenon of TMI (transverse mode instability): when the average power exceeds a certain threshold, the thermal effect will cause the high-order mode to couple with the fundamental mode, seriously affecting the quality and stability of the laser. NKT improved the structure of the rod-shaped fiber and increased the TMI threshold by increasing the loss of the high-order mode.

Figure 1 Experimental device［1］

Figure 1 is a schematic diagram of the experimental device, which consists of four parts: front end, main amplification, compression and measurement. The seed source at the front end produces pulses with a center wavelength of 1029 nm, a pulse width of 170 fs, a repetition rate of 40 MHz, and a bandwidth of 6.8 nm. 5 ns with a repetition rate of 750 kHz. Among them, the third-stage amplification (Amp3) adopts 14/135 double-clad optical fiber produced by NKT.

In the main amplification part, rod-shaped optical fibers with a core diameter of 85 μm are used for the fourth and fifth stages of amplification, and the output power of the fourth stage is 25 W. The ytterbium-doped fiber used in the fifth-stage amplification has been specially designed to suppress high-order modes. The average power of the amplified pulse is as high as 248 W, and the pulse energy is 333 μJ. The compression part is composed of four gratings, and the compression efficiency is 80%. Finally, a pulse with an average power of 175 W, a pulse width of 357 fs, and a pulse energy of 233 μJ can be obtained, and M2 is 1.2.

Figure 2 Output beam power and mode field diameter [1]

Figure 2(a) shows the power before and after compression, and the mode field diameter of the output of the fifth stage as a function of the pump power. The slope efficiency before compression is 0.68, and it is 0.52 after compression. Under the influence of thermal lens effect, the mode field diameter decreases from 60 μm to 50 μm. Since the TMI effect is closely related to photon dimming [2], and the influence of photon dimming is reflected in long-term experiments, NKT tested the entire system for up to 4000 hours, as shown in Figure 2(b).

Under the influence of photon darkening, the output power gradually decreased, among which the first 30 hours decreased by 4 W, and the total decreased by 10 W in 4000 hours; the heat generation of the fiber core gradually increased, and the thermal lens effect and photon darkening changed the refractive index Together they lead to a decrease of 2 μm in the mode field diameter, and the change in the mode field diameter reaches saturation in the last 1000 hours.

Fig.3 Spot, spectrum and autocorrelation curve of the output laser［1］

Figure 3 shows the spot before compression, the spectrum after compression and the autocorrelation curve at 0 hour, 2075 hours and 4150 hours, and the hyperbolic secant was used to fit the autocorrelation. The spectrum of the pulse remains basically stable, with an average bandwidth of 5.5 nm and a corresponding transformation-limited pulse width of 330 fs. The spectrum is truncated by the size of the grating in the long wavelength band, and there are some fluctuations in the center, which are caused by nonlinear phase shift and appear as small uncompressed sidelobes in the time domain.

The pulse width is greatly affected by changes in the experimental environment (such as temperature fluctuations, etc.), but it is less than 400 fs in most of the time, and the average value is 357 fs. The shape matches the hyperbolic secant fitting. Before compression, M2 is 1.04×1.04, and after compression it is 1.21×1.17.

At present, the main way to study the phenomenon of TMI is to use a small hole to filter out a small part of the output light, then use a PD probe to measure its power and calculate the standard deviation multiple times, and determine the strength of TMI according to the distribution and change of the standard deviation [3 ]. The author of this article invented a technique called spatial and time-resolved imaging [4] to analyze the beam before compression, using a more complex device, but obtaining more information. This technology uses a high-speed camera to detect the intensity of the overall light field, and after Fourier transform (as shown in equation (1)), it integrates in space to obtain the power spectrum, as shown in equation (2).

Figure 4 Output laser power spectrum and the shape of high frequency components［1］

When the TMI phenomenon occurs, there will be multiple peaks in the range of 50 Hz to 1 kHz in the power spectrum. Figure 4(a) shows the change of the power in the frequency domain before compression within 4000 hours. It can be seen from the figure that There is a series of spikes, two of which are caused by changing the sample time. Figure 4(b) shows the ratio of spectral components higher than 50Hz to DC components. This value is basically lower than 30dBc and relatively stable, indicating that the TMI phenomenon is not serious and is not affected by the degree of photon dimming. Therefore, NKT is aimed at rods. The improvement successfully raised the TMI threshold. Figure 4(c) shows the distribution of light intensity and its phase at some peaks.

In short, NKT has obtained a relatively stable CPA system with a center wavelength of 1030 nm, a pulse width of 357 fs, a repetition rate of 750 kHz, an average power of 175 W, a pulse energy of 233 μJ, and an M2 of 1.2 in a single-core rod fiber CPA system. laser output. The photon darkening effect in the long-term operation of 4000 hours does not lead to the enhancement of the TMI phenomenon, proving that the large mode field diameter rod fiber is an ideal gain medium for generating diffraction-limited megahertz, millijoule femtosecond lasers, and better heat Management and larger core diameters allow for further increases in average power.

References：

［1］ Martin E． V． Pedersen， Mette M． Johansen， Anders S． Olesen， Mattia Michieletto， Maxim Gaponenko， and Martin D． Maack， ＂175 W average power from a single－core rod fiber－based chirped－pulse－amplification system，＂ Opt． Lett． 47， 5172－5175 （2022）．

［2］ Hans－Jürgen Otto， Norbert Modsching， Cesar Jauregui， Jens Limpert， and Andreas Tünnermann， ＂Impact of photodarkening on the mode instability threshold，＂ Opt． Express 23， 15265－15277 （2015）．

［3］ C． Stihler， H．－J． Otto， C． Jauregui， J． Limpert， and A． Tünnermann， ＂Experimental investigation of transverse mode instabilities in a double－pass Yb－doped rod－type fiber amplifier， ＂ Proc． SPIE 10083， Fiber Lasers XIV： Technology and Systems， 100830R （2017）．

［4］ Simon L． Christensen， Mette M． Johansen， Mattia Michieletto， Marco Triches， Martin D． Maack， and Jesper L?gsgaard， ＂Experimental investigations of seeding mechanisms of TMI in rod fiber amplifier using spatially and temporally resolved imaging，＂ Opt． Express 28， 26690－26705 （2020）．