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supplementary materials (4 parts)

In recent years, picosecond laser in ultraviolet (UV) has manifested great importance for applications both in science and industry, such as biomedical research, micro machining, etc. Now, the well proven approach to generating ultra-short UV pulses is extra-cavity frequency conversion based on nonlinear optical (NLO) crystal, due to the lack of suitable laser sources directly generating UV laser. In this process of harmonic generation, the length of nonlinear crystal is an important factor affecting the conversion efficiency and beam-quality. The optimal length of the nonlinear crystal is influenced by incident laser parameters and crystal absorption coefficient. At present, for the UV 355 nm picosecond laser generated from extra-cavity sum frequency, published are few reports about detailed analysis and research on the influence of photon ratio of the incident laser beams and nonlinear crystal absorption on optimal length of sum frequency crystal. In this paper, the steady-state solutions with the highest conversion efficiency under different incident conditions are obtained by theoretical analysis and numerical simulation of the three waves coupling equations. The effects of different photon ratios and absorption effect of the sum frequency crystal on the optimum crystal length are analyzed. We propose a solution based on the fundamental frequency laser amplified to shorten crystal length and improve conversion efficiency. In this scheme, the 532 nm second harmonic laser with a high conversion efficiency over 65% can be achieved by LiB3O5 crystal. After that, the 1064 nm fundamental frequency laser is separated from the second harmonic laser, and then it is amplified by the Nd:YVO4 laser crystal pumped by an 808 nm laser diode. Finally, the ultraviolet 355 nm picosecond laser is obtained by combining the 1064 nm fundamental frequency laser with the 532 nm second harmonic laser in the LiB3O5 crystal. The simulation results show that the incident photon ratio of the sum frequency reaction can be changed by amplifying the residual fundamental frequency laser, and the optimum length of the sum-frequency crystal corresponding to the highest conversion efficiency can be shortened. Meanwhile, the absorption and walk-away effect of the sum frequency crystal can be also reduced. The final 355 nm laser output power can be increased more than 40 percent compared with the traditional scheme of early reports. In consequence, the high sum frequency conversion efficiency of the UV 355 nm picosecond laser can be obtained by changing the photo ratio of the incident laser beams through amplifying the fundamental frequency laser.

Optical methods in distance measurement, which are categorized by interferometry and time-of-flight (TOF) detection, have received widespread attention in recent years. However, interferometry cannot provide absolute distance and traditional TOF measurement cannot obtain a high precision measurement result either. The TOF ranging by femtosecond lasers, a novel precise measurement approach, enabling a sub-micrometer precision for long distance absolute ranging, can solve the problems above and has a wide application prospect in aerospace, remote sensing and surface profilometry. Particularly, a dual-comb ranging approach has attracted great attention due to high update rate (~kHz) and a simple system structure (i.e., working with free running mode-locked laser system). However, the quantum limited timing jitter of mode-locked lasers will inevitably introduce uncertainty into TOF estimation due to the equivalent sampling nature of a dual-comb scheme. As a result, the distance measurement precision is significantly degraded. Even though a simple multiple averaging can be used to alleviate this problem, the measurement speed is limited to a very low level, which is unacceptable to many applications. Moreover, multiple averaging fails in the presence of more complex noise sources. Singular spectrum analysis (SSA), known as a non-parametric spectral estimation technique, has been widely used in dynamic systems to distinguish complex patterns in signals without a priori knowledge of the dynamical model. In this paper, for the first time, we apply SSA to extract distance information from a noisy time series generated by a high update rate dual-comb ranging system. Numerical simulation shows that the SSA is a powerful tool for separating distance series into signal and random noise regardless its color. Specifically, we extract a one-dimensional step profile with high precision in the presence of violet noise (density proportional to f2). In experiment, a dual-comb ranging system is built based on two home-built polarization maintaining mode-locked fiber lasers by using carbon nanotube as saturable absorber. Their repetition rates are both about 74 MHz, their difference being about 2 kHz. We measure the distance of a moving target placed at ~0.5 m away from the range finder and use the SSA for signal extraction. The direct measurement precision is 1.9968 m rms at 200 Hz update rate. The SSA successfully separates the quantum noise from the ranging time series, resulting in 0.1522 m rms ranging precision, corresponding to about 13 times ranging precision improvement. This method can be further extended to high dimension, enabling high precision and high speed profilometry for complex surfaces based on femtosecond laser ranging.

The generation of pulse radiation with different frequency based on nonlinear optical frequency conversion technology is an effective method to produce lasers with the wavelength in the visible light or ultraviolet (UV) light range. In recent years, the developments of photonic crystal fiber (PCF) technology and ultra-short pulse technology have brought new solutions to the problems that the system needs great maintenance work, has low frequency conversion rate and much difficulty in popularizing, which the traditional frequency conversion system based on nonlinear crystal is confronting. Research on UV pulse radiation has been consistently attracting much attention of many academics. Particularly, narrowband and broadband UV pulse radiation sources are complementary, each having its own characteristics and scope of applications. The generation of narrowband UV pulse radiation of high sensitivity and high resolution through third harmonic generation (THG) in PCF has already been reported. However, the frequency conversion rate of narrowband UV pulse radiation is relatively low and the tunable ability of the spectrum is limited. These imperfections can be exactly completed by broadband UV pulse radiation. Broadband UV pulse radiation based on THG in PCF can be realized efficiently in PCF. This means that the conversion of UV light increases substantially, and simultaneously, the narrowband UV radiation of any wavelength in a certain range can be acquired more easily and the tunable ability of narrowband UV pulse radiation can be enhanced further. In this paper, the femtosecond pulse with a central wavelength of 1035 nm at a pulse repetition rate of 50 MHz is coupled into a highly nonlinear photonic crystal fiber with an appropriate length. The Raman self-frequency shift soliton produced from the ultra-short input pulse acts as a pump resource of third harmonic, transmitting through fundamental mode in PCF. Phase-matching between the fundamental mode and the high order modes is achieved and the third harmonic transmitted by specific high order modes (such as HE13) at deep UV wavelength is acquired effectively. Besides, the very high order UV mode (HOUVM) transmitting third harmonic with shorter wavelength is stimulated when intentionally inputting the ultra-short pulse into the PCF in the direction of a certain angle deviating from the axis of fiber core. Broadband deep UV (320-360 nm) pulse radiation with a UV light conversion rate of 3.6% can be acquired effectively in nonlinear PCF by stimulating a number of adjacent HOUVMs and achieving phase matching between the modes. Good agreement between theoretical results and experimental results is achieved.

Using multi-core photonic crystal fiber (PCF) has advantages of large-mode-area that can support high beam intensity and disperse heat. However, only when the beam profile in far-field and the focal point of in-phase super mode is Gaussian-shaped, the energy can be more concentrated as compared with other shapes. And this beam profile feature limits the applications of multi-core PCF.With the development of optics, there is a practical solution to improve the beam profile of multi-core PCF in which a Kagome fiber is used. This solution is to couple the in-phase super mode source (obtained from multi-core PCF) into Kagome fiber to achieve the beam combination of multi-core photonic crystal fiber, i. e. the beam profile remains to be Gaussian-shaped at any location in the optical field. The Kagome fibers have a novel hollow structure and thus will show some new properties, such as broad optical transmission bands with relatively low loss, no detectable surface modes, and high confinement of light at the core, and these features are suitable for beam combination.In this paper, a Ti: sapphire femtosecond pulsed fiber oscillator, with its center wavelength of 800 nm and output power of 550 mW, is used to pump a piece of seven-core nonlinear PCF, with an efficiency of 19%. EFL of the coupling lens is 18.40 mm and the NA is 0.15. Then the in-phase super mode source can be obtained from the 15 m multi-core PCF, with a broadband spectrum from 700 to 1050 nm. The beam profile of farfield and the focal point of in-phase super mode is Gaussian-shaped and there is a seven-core-shaped pattern at nearfield and other locations in the optical field. In order to combine the beams of multi-core fiber, the in-phase super mode source is coupled into a piece of Kagome fiber, 10 cm long, by using the coupling lens whose EFL is 13.86 mm. Its coupling efficiency is 71% and the output beam profile remains to be Gaussian-shaped at any locations in the optical field; this means that there is no seven-core-shaped pattern. It also transmits broadband spectrum with low loss. Moreover, this experiment also proves that the solution can be used for different multi-core PCFs and can have a higher coupling efficiency, 80%. Thus a reference can be given for high power applications of multi-core PCF, and inspiration may be given to some other frontier fields in fiber optics.

Terahertz technology has been developed rapidly in the past 30 years. Numerous applications in medicine, biology, agriculture, materials, security, communication and astronomy have been demonstrated. Terahertz sources can be divided into narrowband (monochromatic) source and broadband source according to their spectral characteristics. From a spectral perspective, coherent broadband and narrowband terahertz sources are mutually complementary, each having its own characteristics and scope of applications. Broadband terahertz sources can be used for quick access to the hybrid spectra of rotational and vibrational molecular fingerprints or imaging in a wider spectral range. Narrowband terahertz source with good spectral resolution and sensitivity, is suitable for pump-probe, fine structure resolution of molecular fingerprints and terahertz remote detection and imaging. Therefore, developing the tunable high peak power and narrowband terahertz sources is very important for the applications in the detection and identification of molecular fingerprints. The difference frequency generation is one of the most important techniques for obtaining widely tunable, high power and narrowband terahertz sources. In this review, the recent progress of tunable terahertz sources based on the difference frequency generation in the last five years is reviewed, including the two fields of optical laser-based difference frequency sources and quantum cascade laser-based difference frequency sources. For the former class, the experimental results from reports with different difference frequency sources and several typical nonlinear crystals are classified, and the corresponding experimental techniques and results are introduced. For terahertz wave generation, different optical difference frequency sources by a dual-wavelength laser, double laser, a laser and an optical parametric oscillator (OPO), the signal and idler waves of an OPO, and double OPOs are demonstrated in increasing their tunabilities. Significant progress has been made in the nonlinear crystals used to generate terahertz wave by the difference frequency process, for example, by improving the property of inorganic crystals with ion doping, taking advantage of waveguide and PPLN structures, and especially developing novel nonlinear organic crystals. For the quantum cascade laser-based difference frequency sources, the latest advances in the techniques of difference frequency generation and wavelength tunability are presented. GaAs-based terahertz quantum cascade lasers are powerful semiconductor THz sources but cryogenic cooling is still a necessity. Recently, difference frequency generation was combined with the mid-infrared quantum cascade laser technology, thus becoming a leading room temperature semiconductor source in the terahertz range. To improve the frequency tuning range in the difference frequency terahertz quantum cascade laser, wavelength tuning techniques of the inner cavity and the external cavity have been developed. The difference frequency generation quantum cascade terahertz laser source has been the only technique workable at room temperature for the quantum cascade laser so far, which opens the door for developing the compact and widely tunable room temperature terahertz sources.

Ultrashort pulse laser with a repetition rate of below 10 MHz is suitable for a variety of micromachining applications to avoid plasma shielding effects. Besides, the parabolic pulse possesses clean wings, short pulse duration, and large peak power because only the linear chirp is accumulated during the propagation. Based on these two points, a similariton oscillator with a repetition rate of below 10 MHz is a most perfect seed source of an amplification system for micromachining. In this paper, an amplifier similariton oscillator with dispersion map based on a piece of 10 m Yb-doped large-mode-area single-polarization photonic crystal fiber is demonstrated. The semiconductor saturable absorber mirror is employed in the linear cavity as an end mirror to initiate and maintain the mode-locking operation. An adjustable slit is adopted between the end mirror and grating pair in another arm, as a central wavelength adjuster and the spectral filter to ensure the laser operational wavelength in accordance with the working wavelength of semiconductor saturable absorber mirror and the stability of mode-locking operation. The stable single-pulse mode-locking operation can be achieved by adjusting the intracavity dispersion and the operating wavelength. With the net cavity dispersion of-0.89 ps2, a spectrum with steep and smooth edges is obtained, which means that the laser does not operate in the soliton regime but in the dispersion-mapped amplifier similariton regime. A highest output power of 820 mW is obtained with a pulse duration of 6.2 ps and spectral width of 3.84 nm under a pump power of 12.8 W. The repetition rate is 8.6 MHz, corresponding to a pulse energy of 95 nJ. It is the first time that the similariton with a repetition rate of lower than 10 MHz and a highest pulse energy of 95 nJ from a similariton laser has been achieved, to the best of our knowledge. Numerical simulation results confirm that the self-similar evolution is achieved in the gain fiber, and the parabolic-and gauss-shaped pulse can be emitted at the zero-order reflection of the grating and after the slit, respectively.

A femtosecond laser single-stage nonlinear amplification system composed of Yb-doped large-mode-area single-polarization photonic crystal fibers is demonstrated. Effects of net cavity dispersion and pump power on oscillator output parameters and the evolution dynamics of the amplified pulse after compression are discussed for different seed pulse parameters. Under the experimental conditions in this paper, the longer and less chirped pulses are obtained with a larger negative net intracavity dispersion in the oscillator. When a nearly-transform-limited pulse is chosen as seed pulse nder the condition of oscillator pump power of 4.53 W, the shortest nearly-pedestal-free amplified pulse is achieved under the amplifier pump power of 60 W after the dispersion is compensated by a grating pair, in which the pulse duration is 45.7 fs with an average power of 28 W at a refletition frequency of 42 MHz. When the oscillator pump power is increased to 5.08 W and most nearly-transform-limited pulses under the pump condition are selected as the seed pulses, the maximum average power of 34.5 W with a duration of 53.5 fs is obtained at an amplifier pump power of 70 W.

Mode-locked fiber lasers output ultra-short pulse trains with extremely high temporal stability, showing great potential in systems that require precise timing synchronization, such as pump-probe experiments, high-speed analog-to-digital conversion, large-scale timing distribution and coherent combination. The fiber lasers are usually simpler, less costly, more efficient and more robust to the environment than solid state lasers, making them a better option for real-world applications. With the atto second temporal resolution of the balanced optical cross-correlation (BOC) method, timing jitter of mode-locked fiber lasers has been carefully measured and optimized over the last decade. However, due to the inherently large amplified spontaneous emission noise in the long gain fiber and broad pulse width inside the laser cavity, the quantum-noise-limited timing jitter of mode-locked fiber lasers is still much higher than that of the solid state lasers. In order to further optimize the timing synchronization of mode-locked fiber laser, larger locking bandwidth is required to suppress the low-frequency timing jitter, which contributes significantly to the total amount of residual timing jitter. In this work, tight timing synchronization between two mode-locked Yb-fiber lasers is achieved via a feedback loop built on an intra-cavity electro-optic phase modulator. Both lasers work in the stretched-pulse regime, which has been proven to support the lowest quantum-noise-limited timing jitter of mode-locked fiber laser. The output of the BOC system provides a timing error discriminator of 40 mV/fs, corresponding to 13 as resolution within the integration bandwidth. When the pulse trains from both lasers are successfully synchronized, the residual timing jitter can be measured with the same signal as that used for timing synchronization Based on the residual timing jitter measurement, the intra-cavity dynamics of the laser and the locking parameters of the feedback loop can be further optimized and a tight synchronization with 400 kHz locking bandwidth is finally achieved. When performing the integration from 1 Hz to 10 MHz, the residual timing error is as low as 109 as, corresponding to 77 as averaged timing jitter of each laser. A parallel out-of-loop single-arm cross-correlation measurement is also performed to test the validity of the in-loop results, and both measurements agree with each other.

A model based on propagation-rate equations by considering the multi-transverse mode is constructed to describe the amplifier made from seven-core photonic crystal fibers. The output power of the seven eigenmodes in the amplifier infected by the dopant distribution, coupling coefficient and the pump power is discussed using the split-step Fourier algorithm. Mode selection can be realized by the design of dopant distribution and suitable coupling coefficient without the need of other devices. Mode selection may become more convenient due to this method. Moreover, high pump power can contribute to the improvement of the in-phase supermode. These results are helpful for improving the light quality of the amplifier.

A femtosecond laser source tuned from red to mid-infrared is demonstrated. It is based on intracavity sum frequency generation of a MgO-doped periodically poled LiNbO3 optical parametric oscillator synchronously pumped by mode-locked Yb large-mode-area photonic crystal fiber, which has high average power and high repetition rate. The optical parametric oscillator has a wide spectral tuning range from 1450–2200 nm (for the signal) and 2250–4000 nm (for the idler) while the wavelength of the pump is 1040 nm. In the experiment, the output power of 374 mW at 1502 nm is achieved when the pump power is 2 W and the slope efficiency is 18.7%. In addition, 166 mW idler at 3.4 μm are achieved. By using a β-BaB2O4 for intracavity sum frequency generation, the femtosecond pulse over 610–668 nm is obtained. A 694 mW average output power of sum frequency generation is achieved for 4.1 W pump, representing 16.9% conversion efficiency at 615 nm.

A Kerr-lens mode-locked Ti:sapphire laser operating in a non-soliton regime is demonstrated. Dispersive wave generation is observed as a result of third order dispersion in the vicinity of zero dispersion. The characteristics of the Ti:sapphire laser operating in a positive dispersion regime are presented, where the oscillator directly generates pulses with duration continuously tunable from 0.37 ps to 2.11 ps, and 36 fs pulses are achieved after extracavity compression. The oscillation is numerically simulated with an extended nonlinear Schrodinger equation, and the simulation results are in good agreement with the experimental results.

A nonlinear pre-shaper which optimizes initial pulses for self-similar evolution in a following short fiber amplifier is demonstrated. It consists of a pair of transmission gratings and a segment of single mode fiber, by which pulses are shaped temporally and spectrally before amplification. To confirm the benefit of nonlinear pre-shaping for the self-similar evolution, pulse amplifications with and without the nonlinear pre-shaper are simulated. From comparison, pulses optimized by nonlinear pre-shaper show a shorter pulse duration, less pedestal and broader spectrum after amplification and compensation. With this optimization, the self-similar amplification can be realized in a 2.2-meter Yb3+-doped fiber in a large range of pump power, generating 60 fs transform-limited pulses after compression. This nonlinear pre-shaping method can efficiently shorten the fiber length and release the seed quality required for self-similar amplification. An all-normal dispersion mode-locked fiber laser is employed as the seed of a self-similar amplifier for the first time, thus facilitating an all-fiber system.

To investigate the energy scaling level of large-mode-area photonic crystal fiber-based dissipative soliton mode-locked fiber oscillators under limited pump power, a multipass cell is inserted in the cavity to lower the repetition rate of the system, and thus higher single energy level can be mapped under the same average power level. High energy mode-locked fiber lasers based on two spectral filters with different bandwidths are demonstrated both working in the all-normal dispersion regime at a repetition rate of 15.58 MHz. Employment of filters with FWHMs of 6nm and 12 nm can achieve stable mode-locked pulses with average powers of 3.73 W and 4.9 W, corresponding to single pulse energies as high as 239 nJ and 314 nJ, respectively. The FWHM durations of the dechirped pulses by a transmission grating pair can reach 56 fs and 75 fs, which can generate pulses with peak powers exceeding 3MW in both cases.

High power Bessel pulses directly output from a fiber-based amplifier system are demonstrated. A compact solution based on the inverse micro-axicon (IMAX) on fiber end is proposed for the conventional ultrashort pulse fiber laser system to enable the direct generation of high power Bessel pulses from lasers without any additional exhausting alignments. The IMAX is fabricated on one facet of a ytterbium-doped large mode area fiber by focusing ion beam technique and constitutes an integrated beam shaper in combination with an inherent collimating lens in the fiber laser system. The experimental results accord qualitatively with the simulations. The system can directly generate chirped Bessel pulses with diffraction-free propagation in meter-scaled free space. The highest average power of such a wavepacket can reach 10.1 W, correspongding to 178 nJ, and the pulse duration can be dechirped to 140 fs.

The nonlinear optical properties of semiconductor nanowires are of vital importance in the researches of nano-optics and fabrication of nano-scale optoelectronic components. GaAs is a direct bandgap semiconductor material of wide bandgap, high electron mobility, large χ(2), high laser damage threshold and stable chemical properties, all of which make it a potential nonlinear optical material. In this report, based on the finite element method (FEM), we investigated the optical response and local field enhancement of GaAs nanowires perpendicular to the GaAs substrate surface. Under the radiation of femto-second laser pulses at different wavelengths, efficient second harmonic generation (SHG) signal was acquired from the nanowires. Furthermore, noise-free broadband SHG signal was also detected to be excitated by super-continuous femto-second pulses (1000-1300 nm). The high-efficiency SHG process could be attribated mainly to the local field enhancement effect of the nanowires. Our investigation is the first, as far as we know, demonstrate the SHG properties of GaAs nanowires, and the results suggest that GaAs nanowires are promising in the potential applications in nano-scale optical devices, integrated nanophotonic circuits, from which related nano-optics researches can benefit.

High-precision distance measurement in a long range is critical for many advanced applications, such as satellite formation flying, free space optical communication and large scale machining. A 52 m absolute distance measurement in free space based on time of flight of femtosecond laser is demonstrated. The timing offset between target-reflected and the reference pulses is precisely characterized by balanced optical cross-correlation method. The balanced cross correlation signal is used for the feedback control of the cavity length and tightly locks the distance under test to multiple of pulse separation. As a result, the time of flight of the target-reflected pulse is determined by the repetition rate of the femtosecond laser, which effectively avoids the loss of timing resolution caused by direct access of pulse time-of-flight from photo-detection. In the experiment, a Yb -doped high repetition rate mode-locked fiber laser working at 1.04 μm is used as a femtosecond laser source, and a measurement precision of 12 nm is achieved in an average time of one second.