Increased mode instability thresholds of fiber amplifiers by gain saturation

We show by numerical modeling that saturation of the population inversion reduces the stimulated thermal Rayleigh gain relative to the laser gain in large mode area fiber amplifiers. We show how to exploit this effect to raise mode instability thresholds by a substantial factor. We also demonstrate that when suppression of stimulated Brillouin scattering and the population saturation effect are both taken into account, counter-pumped amplifiers have higher mode instability thresholds than co-pumped amplifiers for fully Yb$^{3+}$ doped cores, and confined doping can further raise the thresholds.Comment: 13 pages, 8 figure

Frequency dependence of mode coupling gain in Yb doped fiber amplifiers due to stimulated thermal Rayleigh scattering

Using a numerical model we study the frequency dependence of mode coupling gain due to stimulated thermal Rayleigh scattering in step index, Yb doped, fiber amplifiers. The frequency at the gain peak is shown to vary with core size, doping size, population saturation, thermal lensing, fiber coiling, direction of pumping, photodarkening, and pump noise spectra. The predicted frequencies are compared with measured values whenever possible.Comment: 13 pages, 12 figure

Maximizing the mode instability threshold of a fiber amplifier

We show by detailed numerical modeling that stimulated thermal Rayleigh scattering can account for the modal instability observed in high power fiber amplifiers. Our model illustrates how the instability threshold power can be maximized by eliminating amplitude and phase modulation of the signal seed and the pump, and by careful launch of the signal seed. We also illustrate the influence of photodarkening and mode specific loss on the threshold.Comment: 7 pages, 7 figure

Modeled fiber amplifier performance near the mode instability threshold

We numerically model fiber amplifier performance near and slightly above the mode instability threshold. These results are compared with recently published experimental work. Using weakly amplitude modulated pump light we obtain qualitative agreement with the measured instability thresholds, mode switching ranges, pixel power modulations, and modal amplitude modulations.Comment: 8 pages, 5 figure

Spontaneous Rayleigh seeding of stimulated Rayleigh scattering in high power fiber amplifiers

We estimate the Stokes wave starting power for stimulated thermal Rayleigh scattering (STRS) produced by thermal fluctuations in the fiber core that transiently alter the refractive index profile in the core. A transverse temperature gradient creates a transverse refractive index gradient via the thermo optic effect, and if the fluctuation frequency lies in the STRS gain band, it can couple light from mode LP$_{01}$ to LP$_{11}$ to seed STRS. This spontaneous Rayleigh seed may be stronger than the quantum background and may affect the mode instability thresholds of fiber amplifiers. This new seed estimate can be incorporated in STRS models to improve threshold calculations.Comment: 7 pages, 1 figure. Accepted for publication by IEEE Photonics Journa

Steady-periodic method for modeling mode instability in fiber amplifiers

We present a detailed description of the methods used in our model of mode instability in high-power, rare earth-doped, large-mode-area fiber amplifiers. Our model assumes steady-periodic behavior, so it is appropriate to operation after turn on transients have dissipated. It can be adapted to transient cases as well. We describe our algorithm, which includes propagation of the signal field by fast-Fourier transforms, steady-state solutions of the laser gain equations, and two methods of solving the time-dependent heat equation: alternating-direction-implicit integration, and the Green's function method for steady-periodic heating.Comment: 19 pages, 2 figure

Influence of signal bandwidth on mode instability threshold of fiber amplifiers

We show how signal linewidth affects the gain of stimulated thermal Rayleigh scattering (STRS) which is responsible for mode instability in fiber amplifiers. The gain is reduced if the coherence time of the signal is less than the group velocity induced walk off between modes LP$_{01}$ and LP$_{11}$. We derive equations for short pulses, linear chirps, and general periodic cases.Comment: 3 figure

When Ideal-based Zero-divisor Graphs are Complemented or Uniquely Complemented

Let $R$ be a commutative ring with nonzero identity and $I$ a proper ideal of $R$. The {\it ideal-based zero-divisor graph} of $R$ with respect to the ideal $I$, denoted by $\Gamma_I(R)$, is the graph on vertices $\{x \in R\setminus I \mid xy\in I$ for some $y\in R\setminus I \}$, where distinct vertices $x$ and $y$ are adjacent if and only if $xy\in I$. In this paper, we classify when an ideal-based zero-divisor graph of a commutative ring is complemented or uniquely complemented.Comment: 6 Page

Mode instability thresholds for Tm-doped fiber amplifiers pumped at 790 nm

We use a detailed numerical model of stimulated thermal Rayleigh scattering to compute mode instability thresholds in Tm$^{3+}$-doped fiber amplifiers. The fiber amplifies 2040 nm light using a 790 nm pump. The cross-relaxation process is strong, permitting power efficiencies of 60%. The predicted instability thresholds are compared with those in similar Yb$^{3+}$-doped fiber amplifiers with 976 nm pump and 1060 nm signal, and are found to be higher, even though the heat load is much higher in Tm-doped amplifiers. The higher threshold in the Tm-doped fiber is attributed to its longer signal wavelength, and to stronger gain saturation, due in part to cross-relaxation heating.Comment: 18 pages, 11 figures, 3 table

Thermo-optic and thermal expansion coefficients of RTP and KTP crystals over 300-350 K

We report new measurements of the thermal expansion and thermo-optic coefficients of RbTiOPO$_4$ (RTP) and KTiOPO$_4$ (KTP) crystals over the temperature range 300-350 K. For RTP/KTP our coefficients of linear thermal expansion at 305 K are: $\alpha_x=9.44/7.88\times 10^{-6}$/K, $\alpha_y=12.49/9.48\times 10^{-6}$/K, $\alpha_z=-4.16/0.02\times 10^{-6}$/K. Our normalized thermo-optic coefficients $\beta=(1/n)dn/dT$ at 632.8 nm and 305 K are: $\beta_x=5.39/3.78\times 10^{-6}$/K, $\beta_y=7.11/5.24\times 10^{-6}$/K, $\beta_z=12.35/9.34\times 10^{-6}$/K.Comment: 12 pages, 5 figures, 9 table