There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The rise in output power from rare-earth-doped fiber sources over the past decade, via the use of cladding-pumped fiber architectures, has been dramatic, leading to a range of fiber-based devices with outstanding performance in terms of output power, beam quality, overall efficiency, and flexibility with regard to operating wavelength and radiation format. This success in the high-power arena is largely due to the fiber’s geometry, which provides considerable resilience to the effects of heat generation in the core, and facilitates efficient conversion from relatively low-brightness diode pump radiation to high-brightness laser output. In this paper we review the current state of the art in terms of continuous-wave and pulsed performance of ytterbium-doped fiber lasers, the current fiber gain medium of choice, and by far the most developed in terms of high-power performance. We then review the current status and challenges of extending the technology to other rare-earth dopants and associated wavelengths of operation. Throughout we identify the key factors currently limiting fiber laser performance in different operating regimes—in particular thermal management, optical nonlinearity, and damage. Finally, we speculate as to the likely developments in pump laser technology, fiber design and fabrication, architectural approaches, and functionality that lie ahead in the coming decade and the implications they have on fiber laser performance and industrial/scientific adoption.

High power fiber lasers: current status and future perspectives [Invited]

Recently there has been a remarkable synergy between the technologies of precision laser stabilization and mode-locked ultrafast lasers. This has resulted in control of the frequency spectrum produced by mode-locked lasers, which consists of a regular comb of sharp lines. Thus such a controlled mode-locked laser is a ``femtosecond optical frequency comb generator.'' For a sufficiently broad comb, it is possible to determine the absolute frequencies of all of the comb lines. This ability has revolutionized optical frequency metrology and synthesis. It has also served as the basis for the recent demonstrations of atomic clocks that utilize an optical frequency transition. In addition, it is having an impact on time-domain applications, including synthesis of a single pulse from two independent lasers. In this Colloquium, we first review the frequency-domain description of a mode-locked laser and the connection between the pulse phase and the frequency spectrum in order to provide a basis for understanding how the absolute frequencies can be determined and controlled. Using this understanding, applications in optical frequency metrology and synthesis and optical atomic clocks are discussed. This is followed by a brief overview of how the comb technology is affecting and will affect time-domain experiments.

https://www.reading.ac.uk/physicsnet/units/4/4phla/Papers/RMP03_FemtosecondCombs_Cundiff.pdf

Colloquium: Femtosecond optical frequency combs

We review some basic techniques for laser-induced adiabatic population transfer between discrete quantum states in atoms and molecules.

Laser-induced population transfer by adiabatic passage techniques.

In this paper, we summarize the fundamental properties and review the latest developments in high power fiber lasers. The review is focused primarily on the most common fiber laser configurations and the associated cladding pumping issues. Special attention is placed on pump combination techniques and the parameters that affect the brightness enhancement observed in single-mode and multimode high power fiber lasers. The review includes the major limitations imposed by fiber nonlinearities and other parasitic effects, such as optical damage, transverse modal instabilities and photodarkening. Finally, the paper summarizes the power evolution in continuous-wave and pulsed ytterbium-doped fiber lasers and their impact on industrial applications.

High Power Fiber Lasers: A Review

We compare frequency doubling of broadband light in a single nonlinear crystal with doubling in five crystals with intercrystal temporal walk-off compensation and with doubling in five crystals adjusted for offset phase-matching frequencies. Using a plane-wave dispersive numerical model of frequency doubling, we study the bandwidth of the second harmonic and the conversion efficiency as functions of crystal length and fundamental irradiance. For low irradiance, the offset phase-matching arrangement has lower efficiency than a single crystal of the same total length but gives a broader second-harmonic bandwidth. The walk-off-compensated arrangement gives both higher conversion efficiency and broader bandwidth than a single crystal. At high irradiance, both multicrystal arrangements improve on the single-crystal efficiency while maintaining a broad bandwidth.

/pdf/frequency-doubling-broadband-light-in-multiple-crystals-4nz14rnxh0.pdf

Frequency Doubling Broadband Light in Multiple Crystals

Our objective is to understand the mechanism that generates catastrophic optical damage in pulsed fiber amplifiers. We measured optical damage thresholds of bulk fused silica at 1064 nm for 8 ns and 14 ps pulses. The 8 ns pulse is single longitudinal mode from a Q-switched laser, and the 14 ps pulse is from a Q-switched mode-lock laser. The beams in both cases are TEM 00 mode, and they are focused to a 7.5 μm spot inside a fused silica window. The pulse-to-pulse energy variations are 1% for 8 ns pulses and 5% for 14 ps pulses. Under these conditions optical damage is always accompanied by plasma formation at the focal spot; we found the damage threshold fluences are 3854 ± 85 J/cm 2 for the 8 ns pulses and 25.4 ± 1.0 J/cm 2 for the 14 ps pulses. These fluences are corrected for self focusing. Both damage thresholds are deterministic, in contrast to the claim often made in the literature that optical damage is statistical in the nanosecond range. The measured damage threshold fluences for 8 ns and 14 ps pulses do not fit a square root of pulse duration scaling rule. We interpret the damage in terms of plasma formation initiated by multiphoton ionization and amplified by an electron avalanche. The damage threshold irradiance can be matched with a simple rate equation model that includes multiphoton ionization, electron avalanche, and electron-hole recombination. The damage morphologies are dramatically different in the nanosecond and picosecond cases because of the large difference in deposited energy. However, both morphologies are reproducible from pulse to pulse. We also measured surface damage thresholds for silica windows polished by different methods. We find that cerium oxide polished surfaces damage at approximately 40% of the bulk threshold, with a large statistical spread. Surfaces prepared using an Al 2 O 3 polish damaged between 50% and 100% of the bulk damage limit, with a substantial fraction at 100%. Surfaces polished using first the Al 2 O 3 polish and then an SiO 2 polish exhibit surface damage values equal to the bulk damage value at nearly every point. We also measured damage thresholds for different sized focal spots. Some earlier reports have claimed that damage thresholds depend strongly on the size of the focal spot, but we find the surface threshold is independent of the spot size.

Rate equation model of bulk optical damage of silica, and the influence of polishing on surface optical damage of silica

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.

Maximizing the mode instability threshold of a fiber amplifier

We have generated the second, third, fourth, and fifth harmonics of the output of a Yb-doped fiber amplifier seeded by a passively Q-switched Nd:YAG microchip laser. The fiber amplifier employed multimode fiber (25 μm core diameter, V ~ 7.4) to provide high-peak-power pulses, but diffraction-limited beam quality was obtained by use of bend-loss-induced mode filtering. The amplifier output had a pulse duration of 0.97 ns and smooth, transform-limited temporal and spectral profiles (~500 MHz linewidth). We obtained high nonlinear conversion efficiencies using a simple optical arrangement and critically phase-matched crystals. Starting with 320 mW of average power at 1064 nm (86 µJ per pulse at a 3.7 kHz repetition rate), we generated 160 mW at 532 nm, 38 mW at 355 nm, 69 mW at 266 nm, and 18 mW at 213 nm. The experimental results are in excellent agreement with calculations. Significantly higher visible and UV powers will be possible by operating the fiber amplifier at higher repetition rates and pulse energies and by further optimizing the nonlinear conversion scheme.

Efficient visible and UV generation by frequency conversion of a mode-filtered fiber amplifier

We show that nanosecond optical parametric oscillators pumped well above threshold by single-longitudinal-mode pulses produce signal and idler light that is nearly purely phase modulated under a variety of conditions, including both seeded and unseeded operation.

Arlee V. Smith

Papers

Frequency Doubling Broadband Light in Multiple Crystals

Rate equation model of bulk optical damage of silica, and the influence of polishing on surface optical damage of silica

Maximizing the mode instability threshold of a fiber amplifier

Efficient visible and UV generation by frequency conversion of a mode-filtered fiber amplifier

Tendency of nanosecond optical parametric oscillators to produce purely phase-modulated light