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Abstract We report the numerical and experimental studies of the two-dimensional Brillouin gain spectrum (BGS) distribution deformation induced by the self-phase modulation in the Brillouin optical time domain reflectometry (BOTDR) with a 20.6 km sensing distance. The BGS distribution deformation is investigated by analyzing the evolution of the point spread function along the fiber in the two-dimensional model of the BOTDR. In the simulation and experimental results, the specific deformation degree of the BGS distribution induced by the self-phase modulation is related to the pump pulse profile, pump pulse peak power, BGS demodulation method, and detected scattered light component. By comprehensively analyzing the evolution of the point spread function induced by the self-phase modulation and using the image deconvolution, a typical BOTDR sensor with a 25 ns pump pulse reaches the 20 cm spatial resolution over the 20.6 km sensing fiber.

We demonstrate the generation, spectral broadening and post-compression of second harmonic pulses using a thin beta barium borate (BBO) crystal on a fused-silica substrate as the nonlinear interaction medium. By combining second harmonic generation in the BBO crystal with self-phase modulation in the fused-silica substrate, we efficiently generate millijoule-level broadband violet pulses from a single optical component. The second harmonic spectrum covers a range from long wave ultraviolet (down to 310 nm) to visible (up to 550 nm) with a bandwidth of 65 nm. Subsequently, we compress the second harmonic beam to a duration of 4.8 fs with a pulse energy of 0.64 mJ (5 fs with a pulse energy of 1.05 mJ) using chirped mirrors. The all-solid free-space apparatus is compact, robust and pulse energy scalable, making it highly advantageous for generating intense second harmonic pulses from near-infrared femtosecond lasers in the sub-5 fs regime.

Abstract Supercontinuum white laser with large bandwidth and high pulse energy would offer incredible versatility and opportunities for basic science and high technology applications. Here, we report the generation of high-efficiency 2.8-octave-spanning ultraviolet-visible-infrared (UV-Vis-IR) (with 350-2500 nm 25 dB bandwidth) supercontinuum white laser from a single chirped periodically poled lithium niobate (CPPLN) nonlinear crystal via synergic high-harmonic generation (HHG) and self-phase modulation (SPM). The CPPLN exhibits multiple controllable reciprocal-lattice bands to simultaneously support the quasi-phase matching (QPM) for simultaneous broadband 2nd-10th HHG via cascaded three-wave mixing against a broadband fundamental pump laser. Due to the efficient second-order nonlinearity (2nd-NL) up-conversion and significant 3rd-NL SPM effect both in the pump and HHG laser pulses, 350-2500 nm supercontinuum white laser is eventually obtained with 17 μJ per pulse under pump of 45 μJ per pulse mid-infrared femtosecond laser corresponding to an average high conversion efficiency of 37%. Our work opens up a route towards creating UV-Vis-IR all-spectrum white lasers through engineering the synergic action of HHG and SPM effects in nonlinear crystals for applications in ultrafast spectroscopy, single-shot remote sensing, biological imaging, and so on.

An all-optical format conversion and regeneration scheme about 4-ary amplitude and phase shift keying (4APSK) signals is proposed and numerically simulated based on nonlinear effects in the high nonlinear fiber (HNLF). The input 4APSK signal is firstly converted into a regular quadrature phase shift keying (QPSK) signal by the nonlinear Mach-Zehnder interferometer (MZI) based on the self-phase modulation (SPM). Secondly, a degenerate phase-sensitive amplification (PSA) based on the four-wave mixing (FWM) is utilized to convert the regular-QPSK into two binary phase shift keying (BPSK) signals. The nonlinear MZI configuration is also used to compress the amplitude noise of BPSK. Thirdly, one phase shifter and one variable optical attenuator (VOA) are used to adjust the relative phase and power relationships of the two amplitude-regenerated BPSK signals. The regenerated 4APSK and converted QPSK signals can be generated in one 3-dB optical coupler through coherent addition of the two regenerated BPSK signals. The error-vector-magnitude (EVM) and the bit-error-rate (BER) are calculated and compared to evaluate the scheme performance. The proposed scheme can be applied as an optical regenerator or format convertor at the network gateway to increase the transmission distance or connect optical networks with different modulation formats.

The post-compression technique based on self-phase modulation of high-energy pulses leads to an increase in achievable peak power and intensity. Typically, the pulses considered in experiments have been less than 100 fs in duration. Here, the method is applied to the ELFIE laser system at the LULI facility, for a pulse of 7 J energy and an initial measured duration of 350 fs. A 5-mm-thick fused silica window and a 2 mm cyclic-olefin polymer were used as optical nonlinear materials. The 9 cm diameter beam was spectrally broadened to a bandwidth corresponding to 124 fs Fourier-limited pulse duration, and then it was partly post-compressed to 200 fs. After measuring the spatial spectra of the beam fluence, a uniform gain factor of 4 increase in the fluctuations over the studied range of frequencies is observed, due to small-scale self-focusing.

In traditional passive optical network (PON) neighboring, optical network units (ONUs) cannot communicate directly but through optical line terminals, resulting in propagation delays, security hazards and unnecessary use of upstream and downstream bandwidth. Inter optical network unit communication (IOC) can be a promising solution for these problems. IOC is mostly demonstrated with the help of dedicated or tunable transceivers increasing the cost of the system and making it complex. Transceiver sharing is also demonstrated in the literature but this will be a bandwidth-inefficient technique. In our paper, the simultaneous transmission of IOC signal and upstream signal is demonstrated in a time-division-multiplexed PON using single transmitter and self-phase modulation-based wavelength convertor at each ONU that converts the upstream wavelength of 1310 nm to 1310.6 nm when IOC signal is being transmitted by that ONU; at the same time another ONU can transmit the upstream data at 1310 nm which results in efficient bandwidth utilization with less delays compared to the traditional PON. In our proposed design the IOC signal is reflected back by a Uniform Fiber Bragg Grating and the upstream signal is transmitted through it. This design supports a data rate of 25 Giga bits/sec.

In synthetic diamond plates, the intrapulse-correlated dynamics of self-phase modulation and spontaneous nonresonant Raman scattering by center-zone optical phonons were for the first time directly investigated for tightly focused (focusing numerical aperture NA = 0.25) positively chirped visible-range high-intensity laser pulses with variable durations (0.3–9.5 ps) and energies transmitted through the sample. The observed self-phase modulation broadening and modulation of the transmitted light and Stokes Raman spectra for the (sub)picosecond pulse durations indicate the considerable Raman–Kerr contribution to the nonlinear polarization. The latter appears through plasma emission of the optical phonons, which emerges on the (sub)picosecond timescale and dominates at ≈1 ps. Later, this phonon contribution is eventually suppressed in the material due to picosecond-scale electron-lattice thermalization and the related thermally enhanced symmetrical decay of optical phonons into lower-frequency acoustic ones.

We demonstrate the damage-free delivery of nearly diffraction-limited picosecond laser pulses at 1064 nm with a maximum peak power of 3.5 MW in a 5 m air-filled anti-resonant hollow-core fiber (AR-HCF). In the air-filled AR-HCF, the transmission efficiency of picosecond pulses is degraded due to stimulated Raman scattering for the incident peak power above 3.59 MW. The temporal compression of pulses is also observed in the air-filled AR-HCF, where the self-phase modulation plays a key role in the anomalous dispersion region. By vacuuming the air in the core, a nearly constant coupling efficiency of 77% is achieved through the 5 m AR-HCF free of nonlinear effects, with M2 of the output beam less than 1.17.

Gas-filled hollow-core fibers are a convenient tool for laser pulse compression down to a few-cycle duration. The development of compact, efficient and high quality compression schemes for laser pulses of relatively low μJ-level energies is of particular interest. In this work, temporal pulse compression based on nonlinear spectral broadening in a xenon-filled revolver fiber followed by a chirped mirror system is investigated. A 250 fs pulse at a central wavelength of 1.03 μm is compressed to 13.3 fs when the xenon pressure was tuned to provide zero group velocity dispersion near 1.03 μm. The energies of input and compressed pulses are 3.8 and 2.7 μJ, respectively. The compression quality factor of 1.8 is achieved.

This article studies highly dispersive optical solitons without of self-phase modulation effect. The numerical algorithm implemented in this work is Laplace-Adomian decomposition method. Both bright and dark solitons are addressed. The error measure for the adopted scheme is impressively low.

In this work, we demonstrate a high-power single-frequency nanosecond fiber master oscillator power amplifier (MOPA) at 1 μm with near transform-limited narrow spectral linewidth. The seed laser pulses were shaped to triangle for the purpose of suppressing the linewidth broadening induced by self-phase modulation (SPM). A tapered Yb-doped active fiber was used to enhance the stimulated Brillouin scattering (SBS) threshold. A high peak power of 31.4 kW with a narrow linewidth of 63 MHz, which was near the transform limit of the 8-ns triangle-shaped pulse, was achieved at a pulse repetition frequency of 20 kHz. No evident pulse distortion was observed at high-power levels. The results show that the triangle-shaped pulse is a promising technique for high-power single-frequency nanosecond pulsed fiber lasers with narrow spectral linewidth.

The demand for data transmission is rising expensively for the applications of biomedical sensors data, multimedia technologies, and ultrahigh-definition online video streaming. Such applications require larger bandwidth with minimum latency and seamless service delivery. Radio-over-fiber (RoF), integrated with wavelength division multiplexing (WDM) technology, is being considered one of the promising technologies. However, the integration of optical fiber and wireless communication also generates non-linear effects as and when the number of users increases. That results in the introduction of signal noise, unwanted frequencies, low quality of signals, and increased latency. In this paper, a 16-channel 160 Gbps data rate WDM-based RoF system has been simulated and evaluated for optimum performance at a variable input power level, from 5 to −15 dBm, with the application of dispersion compensation fiber (DCF) and fiber Bragg grating (FBG), with channel spacing of 50 and 100 GHz. The performance of the system is evaluated with the existing WDM-RoF system. The performance metrics parameters chosen for evaluation are bit error rate (BER), quality factor (Q-factor), and eye diagrams and simulated on opti-system simulator. The optimum performance has been observed at a power level of −5 dBm for all these elected evaluation parameters. It has also been observed that, for channel spacing of 100 GHz, the network performed better in comparison with 50 GHz.

We experimentally demonstrate enhanced spectral broadening of femtosecond optical pulses after propagation through silicon-on-insulator (SOI) nanowire waveguides integrated with two-dimensional (2D) graphene oxide (GO) films. Owing to the strong mode overlap between the SOI nanowires and the GO films with a high Kerr nonlinearity, the self-phase modulation (SPM) process in the hybrid waveguides is significantly enhanced, resulting in greatly improved spectral broadening of the femtosecond optical pulses. A solution-based, transfer-free coating method is used to integrate GO films onto the SOI nanowires with precise control of the film thickness. Detailed SPM measurements using femtosecond optical pulses are carried out, achieving a broadening factor of up to ~4.3 for a device with 0.4-mm-long, 2 layers of GO. By fitting the experimental results with the theory, we obtain an improvement in the waveguide nonlinear parameter by a factor of ~3.5 and in the effective nonlinear figure of merit (FOM) by a factor of ~3.8, relative to the uncoated waveguide. Finally, we discuss the influence of GO film length on the spectral broadening and compare the nonlinear optical performance of different integrated waveguides coated with GO films. These results confirm the improved nonlinear optical performance of silicon devices integrated with 2D GO films.

The generation of high-order harmonics in a semi-infinite cell by femtosecond laser pulses is a common practice for reliable coherent and low divergence XUV source beams for applications. Despite the relative simplicity of the experimental method, several phenomena coexist that affect the generated spectral and divergence characteristics of the high harmonic XUV frequency comb. The ionisation degree of the medium and the consequent plasma formation length imposes a spatiotemporal evolution of the fundamental EM field and XUV absorption. Varying the laser pulse chirp and the focusing conditions, as well as the gas density, we measured intense harmonic spectral and divergence variations attributed mainly to self-phase modulations of the laser EM field in the partially ionised medium. Additionally, low-divergence high harmonics are observed for certain laser chirp values attributed to the strong phase matching of only the short electron quantum path. Thus, a tunable, low divergent, and coherent XUV source can be realised for spatiotemporal imaging applications in the nanoscale.

Linear and nonlinear effects often induce a pulse self-frequency shift as it propagates along with an optical medium. Here, we theoretically investigate the transmission dynamics of asymmetric pulses propagating along with an optical medium in the temporal and spectral domains. Due to the asymmetric nonlinear phase-shift effect in the optical medium, the peak wavelength of asymmetric pulses exhibits a redshift or a blueshift in the spectral domain, while it slows down or speeds up in the temporal domain. Our results show that the peak wavelength shift initiated by a temporal or spectral asymmetric pulse depends not only on the pulse intensity, but also on the initial pulse chirp and dispersion of optical medium. We find that the peak wavelength shift of the asymmetric pulse increases with the pulse intensity and the initial pulse chirp, together with the spectrum width. The temporal and frequency shifts of the asymmetric pulses are found to be sensitive to the asymmetry ratio as well. These excellent properties may lead to the realization of a self-frequency shift-based tunable light source by launching asymmetric pulses into an optical medium.

The self-phase modulation and modulation instability of an optical probe electromagnetic field in multiple quantum well systems under electromagnetically induced transparency has been investigated. The probe field experiences large Kerr and quintic nonlinearities that can be controlled by two controlling laser beams. The probe beam experiences self-phase modulation which is suppressed by the quintic nonlinearity. The probe field is modulationally unstable due to the existence of large nonlinearities. The bandwidth of unstable frequencies and growth of the instability could be controlled by the probe beam power, the Rabi frequency and detunings of two control fields. The presence of the higher order nonlinearity and dispersion significantly reduce the instability growth and bandwidth of unstable frequency.

The single-shot reconstruction of an ultrashort pulse from a fiber laser system by the method based on recording and numerical processing of two self-phase modulated spectra after a nonlinear fiber is demonstrated experimentally. The 0.7-ps asymmetrical signal with an energy of ~1 μJ retrieved by this method without time direction ambiguity is in good agreement with independent measurements by second harmonic generation frequency-resolved optical gating (SHG FROG) technique.

A tapered Er-doped fiber amplifier for high peak power pulses amplification has been developed and tested. The core diameter changed from 15.8 µm (mode field diameter (MFD) 14.5 µm) to 93 µm (MFD 40 µm) along 3.7 m maintaining single-mode performance at 1555 nm (according to the S2-method, the part of the power of high-order modes does not exceed 1.5%). The amplification of 0.9 ns pulses with spectral width below 0.04 nm up to a peak power above 200 kW (limited by self-phase modulation) with a slope pump-to-signal conversion efficiency of 15.6% was demonstrated.

A low-complexity and adaptive nonlinearity estimation module is proposed and experimentally demonstrated based on Godard's error and low-pass filter (LPF). The computational complexity of the proposed adaptive estimation module is significantly reduced by avoiding utilizing the polarization demultiplexing, frequency offset compensation, and carrier phase recovery in the process of finding the optimal value γξopt compared with the previous approach based on phase noise variance. The performance of the proposed module is experimentally verified in a 40-Gb/s polarization-division-multiplexing-quadrature-amplitude modulation (PDM-QPSK) coherent optical communication system over 720-km single-mode fiber (SMF). Experimental results show that the computational complexity of the proposed nonlinearity estimation module is only ~7.35% of the previous approach and ~27.8% of that with an LPF inserted.

We investigated the spectral and temporal characteristics of blue-violetfemtosecond optical pulses generated by a passively mode-locked GaInN laser diode ina dispersion-compensated external cavity. The output optical pulses at 400 nm wereanalyzed in detail by intensity auto- and cross-correlation measurements using secondharmonic generation on the surface of a β-BaB2O4 crystal. The obtained results clarifiedwavelength-dependent chirp characteristics of the optical pulses. The analysis suggestedthat a large frequency shift due to saturation in the saturable absorber and gain sectionsplayed an important role in the generation of femtosecond optical pulses.

The bandwidth of ultrafast pulses in the UV is limited by the finite acceptance bandwidth of the nonlinear crystals used for their generation. For fundamental laser pulses it is well established that spectral broadening can be used to overcome intrinsic bandwidth limits. We show that self-phase modulation of UV pulses in bulk materials leads to large spectral broadening and allows for a significant reduction of the pulse duration. We find that for pulse energies in the range of a few μJ, a thin crystal is favorable due to the strong dispersion in the UV and the limitations set by self-focusing. In contrast to spectral broadening in gaseous media, the self-focus has to lie outside the crystal to avoid beam break up. We focus UV pulses into a 1 mm thick CaF2 crystal. For moderately short input pulses, a shortening factor up to 2.4 is achieved: the 120 fs long third harmonic output of a Ti:sapphire amplifier is compressed down to 50 fs FWHM. For a central wavelength of 315 nm, we generate pulses as short as 14.9 fs after compression with an UV pulse shaper. In both cases the resulting beam shape is close to Gaussian and fully usable for spectroscopic experiments. We use the pulses in a collinear 2D-UV experiment and clearly resolve vibronic off-diagonal peaks of the S2 1B2u vibronic progression of pyrene.

In this article, we analytically investigate the spectral broadening by self-phase modulation of strongly chirped optical pulses. The dispersion due to the nonlinear optical process is expressed as functions of a linear and a nonlinear initial chirp. As a result, it is found that the third-order dispersion strongly depends on the initial linear chirp and the nonlinearity for self-phase modulation.

We report on observation of self-guiding of picosecond laser pulses in air that produces large-scale self-phase modulation. The converging picosecond laser beam produced a confined filament over 3 m of propagation with the whitelight spectrum.

We show via a numerical simulation that the temporal coherence function (TCF) can be shaped by the destructive interference of pulses characterized by different amounts of self-phase modulation (SPM) in the spectral domain. We find that pulse spectra destructively interfering with one another can yield a TCF with distinct peaks. Numerical investigation demonstrates that the shape of the TCF is changeable not only by broadening the spectrum but also by overlapping spectra of the pulses that have experienced different amounts of SPM.

We consider the Raman amplification problem for silicon waveguides in the regime in which both the pump and signal pulses are relatively short but wide enough that their duration exceeds the phonon lifetime (about 3 ps in silicon). We use the coupled pump-signal equations for numerical simulations that include all competing nonlinear effects such as self- and cross-phase modulations, two-photon and free-carrier absorptions, and changes in the refractive index induced by the free carriers. However, numerical simulations do not provide much physical insight. For this reason, we also develop an approximate analytic approach for solving the Raman amplification problem. We introduce the concept of an effective Raman gain and show analytically how it depends on the pump bandwidth. As the pump spectrum broadens inside the silicon waveguide, the effective Raman gain is reduced considerably. We obtain an analytical form of the nonlinear phase accumulated during propagation inside a silicon waveguide and use it to calculate the total spectral broadening experienced by a pump pulse. Using this result, we can predict changes in the effective Raman gain as a function of pump pulse energy. A comparison of our predictions with the recent experimental data shows that our model is reasonable and captures the essential physics.

A discontinuous space variant sub-wavelength dielectric grating is designed and fabricated for generating radially polarized light in visible region (λ = 632.8 nm). The design is based on sub-wavelength silicon nitride structures introducing a retardation of π/2 by form birefringence, with space variant orientation of the optical axis. The pattern is divided into concentric ring segments with constant structural parameters, therefore reducing electron-beam writing time significantly. The design avoids the technological challenges encountered in the generation of a continuous space variant grating while maintaining good quality of the resulting polarization mode.

We analytically calculate the transverse energy fluxes that would be respectively induced in high-power Airy beams by the Kerr self-focusing and the Airy profile itself if they were the only active process. Under experimental conditions representative of laser filamentation experiments of high-power ultrashort laser pulses in air and condensed media, the Kerr lens induces transverse energy fluxes much larger than the Airy “prism” at the main peak. As a consequence, the curved plasma channels in Airy beams are not only a plasma spark on a curved focus, but indeed self-guided filaments, and their curved trajectory appears as a perturbation due to the linear Airy propagation regime.