Sech Pulses Research Articles

Simulative demonstration of soliton pulse stability over the nonlinear regime in a birefringent optical fiber

In this paper, the results of numerical analysis are demonstrated for sech pulse (soliton) propagation in a birefringent optical fiber using computer modeling and simulation. Here, the initial pulse is polarized linearly and guided into the fiber at an angle of 45° to its polarization axes. The birefringence-induced time delay of 200 and 440 ps between X and Y polarization components has been reported at a fiber length of 631.72 km (10 soliton periods) by considering linear and nonlinear regimes, respectively. The Kerr nonlinearity, which stabilizes solitons against spreading due to GVD, also stabilizes them against splitting due to birefringence. A similar fact is true for the birefringent walk-off. Above a certain soliton order ( N th), the evolution scenario is qualitatively different and two orthogonally polarized components of the soliton move with a common group velocity despite their different modal indices or polarization mode dispersion (PMD) at a fiber length of 631.72 km (10 soliton periods) and 1264.344 km (20 soliton periods) over a nonlinear regime at θ≠45°. The physical effect responsible for this type of behavior is the cross-phase modulation (XPM) between the two polarization components.

Generation of in-phase pulse train from optical beat signal

We propose and demonstrate generation of an in-phase optical pulse train from an optical beat signal. The proposed method is based on four-wave mixing occurring between the two continuous waves of the beat signal and on spectral filtering to shape the spectrum to be symmetric about the carrier frequency. We perform an experiment to verify the proposed method and obtain a 1.5 ps width in-phase pulse train from a 160 GHz beat signal. Furthermore, we employ a pulse compression scheme to reshape and compress the obtained pulse train, and we show that a 160 GHz repeating, 0.7 ps FWHM, nearly transform-limited, in-phase sech pulse train is successfully generated.

Theoretical study of fast light with short sech pulses in coherent gain media

We investigate theoretically the phenomenon of so-called fast light in an unconventional regime, using pulses sufficiently short that relaxation effects in a gain medium can be ignored completely. We show that previously recognized gain instabilities, including superfluorescence, can be tolerated in achieving a pulse peak advance of more than one full peak width.

High compression of similariton pulses under the influence of higher-order effects

We present numerical and analytical results that confirm that similariton pulses can be compressed by 2 orders of magnitude in a dispersion-decreasing Raman-pumped fiber amplifier yielding pulses as short as 120 fs. Physical conditions have been derived, subject to which, higher-order nonlinearities and dispersion terms do not affect the shape and slope of the linear chirped sech pulse, although they shift the similariton amplitude in time and downshift it in mean frequency. The developed analytical theory is in good agreement with numerical simulations. This predicted similariton regime with an optimized fiber amplifier and input pulse may, find important applications in optical pulse compression.

Exact stationary solutions for the translationally invariant discrete nonlinear Schrödinger equations

From a wide class of translationally invariant discrete nonlinear Schrödinger (DNLS) equations, we extract a two-parameter subclass corresponding to Kerr nonlinearity for which any stationary solution can be derived recurrently from a quadratic equation. This subclass, which incorporates the integrable (Ablowitz–Ladik) lattice as a special case, admits exact stationary solutions that are derived in terms of the Jacobi elliptic functions. Exact moving solutions for the discrete equations are also obtained. In the continuum limit, the constructed stationary solutions reduce to the exact moving solutions to the continuum NLS equation with Kerr nonlinearity. Numerical results are also presented for the special case of localized solutions, including sech (pulse, or bright soliton), tanh (kink, or dark soliton) and 1/tanh (called here inverted kink) profiles. For these solutions, we discuss their linearization spectra and their mobility. Particularly, we demonstrate that discrete dark solitons are dynamically stable for a wide range of lattice spacings, contrary to what is the case for their standard DNLS counterparts. Furthermore, the bright and dark solitons in the non-integrable, translationally invariant lattices can propagate at slow speed without any noticeable radiation.

Proposal for optical U(1) rotations of electron spin trapped in a quantum dot

We present a proposal to optically implement rotations of the electron spin in a quantum dot about the growth direction ($z$ axis). In particular, we make use of the analytic properties of sech pulses in two-level systems to realize spin rotations about the growth direction by an arbitrary angle, for which we give an analytical expression. We propose to use this scheme to experimentally demonstrate this spin rotation. Using realistic system and pulse parameters we find the fidelity of the rotation to be more than 96% for pulses in the picosecond regime, and robust against small errors in pulse parameters. We design a feedback (adaptive) loop to correct for errors originating from unintended dynamics. The rotation is still evident---albeit with a large fidelity loss---in the ensemble case, providing the possibility of demonstration of this optical spin rotation in an ensemble of quantum dots.

Stationary rescaled pulse in dispersion-decreasing fiber for pedestal-free pulse compression

By using the concept of a stationary rescaled pulse (SRP), we analyze an adiabatic soliton compression system based on dispersion-decreasing fiber (DDF). We show that a SRP can exist in a DDF with a linearly decreasing dispersion profile and that the SRP resembles a linearly chirped sech2 pulse. According to the analysis, we show numerically that pedestal-free pulse compression is possible by using the SRP.

Ultra-flat SPM-broadened spectra in a highly nonlinear fiber using parabolic pulses formed in a fiber Bragg grating

We propose a new method for generating flat self-phase modulation (SPM)-broadened spectra based on seeding a highly nonlinear fiber (HNLF) with chirp-free parabolic pulses generated using linear pulse shaping in a superstructured fiber Bragg grating (SSFBG). We show that the use of grating reshaped parabolic pulses allows substantially better performance in terms of the extent of SPM-based spectral broadening and flatness relative to conventional hyperbolic secant (sech) pulses. We demonstrate both numerically and experimentally the generation of SPM-broadened pulses centred at 1542 nm with 92% of the pulse energy remaining within the 29 nm 3 dB spectral bandwidth. Applications in spectra slicing and pulse compression are demonstrated.

Low-threshold, dual-passive mode locking of a large mode area Nd:GdVO4laser

The all solid-state combination of a saturable Bragg mirror for amplitude modulation and a cascaded chi((2)):chi((2)) nonlinearity (phase-mismatched second harmonic crystal) as an axial-mode phase locker for continuous-wave mode locking of large mode area lasers is investigated. The dual-passive mode-locking technique generates extremely stable sub-10ps sech(2) pulses at 76MHz from a ~6W, TEM(00)-mode, diode-pumped, thermal-lens-shaped, Brewster Nd:GdVO(4) laser.

Quantum computing with an inhomogeneously broadened ensemble of ions: Suppression of errors from detuning variations by specially adapted pulses and coherent population trapping

The proposal for quantum computing with rare-earth-metal-ion qubits in inorganic crystals makes use of the inhomogeneous broadening of optical transitions in the ions to associate individual qubits with ions responding to radiation in selected frequency channels. We show that a class of Gaussian composite pulses and complex sech pulses provide accurate qubit $\ensuremath{\pi}$ rotations, which are at the same time channel selective on a 5 MHz frequency scale and tolerant to $\ifmmode\pm\else\textpm\fi{}0.5\mathrm{MHz}$ deviations of the transition frequency of ions within a single channel. Rotations in qubit space of arbitrary angles and phases are produced by sequences of $\ensuremath{\pi}$ pulses between the excited state of the ions and coherent superpositions of the qubit states.

Analytical description of GMAX-induced magnetization

The Gradient-Modulated Adiabatic Excitation (GMAX) method is characterized by the use of adiabatic pulses with main applications on volume localization in spectroscopy and slice selection in MRI. Its use derives from the interesting nodal point magnetization profile induced throughout the sample. Nevertheless, the interpretation on such behavior for the magnetization has been of qualitative purpose only, using the adiabatic condition as a starting point. Here, we present discrete spatial analytic solutions, starting from the solution in terms of the hypergeometric functions for sech and tanh pulses. From these discrete solutions, it is possible to infer analytically the characteristic behavior of transverse magnetization, on the purpose to obtain greater control of the magnetization from parameters of the sequence that carry physical interpretation.

Diode-pumped passively mode-locked Nd:KGd(WO_4)_2 laser with 1-W average output power

Continuous-wave passive mode locking of a diode-pumped Nd:KGd(WO(4))(2) laser is demonstrated. The use of a saturable Bragg reflector as the mode-locking element permits the generation of 6.3-ps pulses, assuming a sech(2) pulse shape. An output power of 1 W was obtained, which corresponds to a slope efficiency of 34.5%.

Ultrashort optical pulse transmission characteristics of vertically coupled microring resonator add/drop filter

The ultrashort optical pulse transmission characteristics of a vertically coupled microring resonator (VCMRR) filter were measured at 1.55 /spl mu/m wavelength, and the transmission capacity per channel was evaluated. The pulsewidth at the output was measured to be 3.4 ps, when 1.2 ps input pulse with a sech pulse shape from a fiber laser was incident on the microring resonator filter with a fullwidth at half-maximum (FWHM) of 0.75 nm (94 GHz). From this result, the maximum transmission capacity of the filter was estimated to be approximately 50 Gb/s. The pulse broadening through the filter was theoretically analyzed, and it was confirmed that the pulse broadening evaluated from the bandwidth of the filter spectrum response were in good agreement with the measured results.

Optical heterodyne detected spectrograms of ultrafast nonresonant electronic responses

The dispersed optical heterodyne detected (OHD) birefringence and dichroism that result from the electronic response of nonresonant materials are described for a number of ultrafast pulse shapes. The OHD spectrograms that correspond to these dispersed instantaneous electronic responses display detuning oscillations along both the interpulse delay and the probe frequency dimensions. The frequency of these oscillations depends only on the detuning of the selected Fourier component of the probe pulse from the carrier frequency and the pulse shapes. This effect is demonstrated for Gaussian, sech2, and one-sided exponential probe pulses. For each of these pulse shapes the OHD spectrograms exhibit a characteristic dependence on detuning frequency. The effects of linear chirp on these OHD spectrograms are also considered. Experimentally observed nonresonant electronic spectrograms are compared with theory. These OHD spectrograms are also compared with the well-known frequency-resolved optical gating traces. Analysis of the OHD spectrograms may provide a more useful approach for the characterization of ultrafast pulses because of the phase-specific, amplitude level origin of these responses.

High-quality sub-100-fs optical pulse generation by fiber-optic soliton compression of gain-switched distributed-feedback laser-diode pulses in conjunction with nonlinear optical fiber loops

We report our investigations of a new and simpler femtosecond fiber-optic soliton compressor for chirp-compensated gain-switched diode-laser pulses and of pedestal suppression by a compound fiber loop mirror (CFLM) and nonlinear-optical loop mirrors (NOLM's), both of which are designed for sub-100-fs pulse generation of high quality. The soliton compressor, composed of a 21.1-m-long steplike dispersion profiled fiber, exhibited 44-fs pulses and a compression ratio of approximately 60. Pedestals of 100-fs soliton pulses were suppressed successfully (>20 dB) by the CFLM and the NOLM's. In particular, 63-fs pedestal-free sech(2) pulses were obtained by NOLM propagation.

Self-mode-locked pulsed monomode laser

We predict the existence of a new pulsed-laser operation regime, when the phases and polarizations of the two coupled cold-cavity eigenstates of a monomode solid-state laser are taken into account in the derivation of the Maxwell-Bloch equations. This monomode pulsed regime is experimentally observed, without any normal mode locking or Q switching occurring inside the cavity. We obtain close agreement between experiments and theory, even in the simple case of a Nd:YAG microchip laser, for which sech(2) pulses at nearly megahertz repetition rates are readily observed.

Operation of a Kerr-Lens Mode-Locked Cr:LiSGaF Laser with a Tight-Focusing Cavity Geometry

A femtosecond Kerr-lens mode-locked Cr:LiSGaF laser based on a compact cavity geometry is demonstrated. With a combination of 488, 476, and 458 nm lines as a pump source, 58 fs pulses centered at 845 nm were generated. The average output power is 30 mW, and time-band product is 0.331, assuming a sech2 pulse shape. Neither acousto-modulator nor physical aperture or slit were used in this cavity.

Soliton mode-locked Nd:YAlO_3 laser at 930 nm

We report on a soliton mode-locked Nd:YAlO3 laser at 930 nm. We used a semiconductor saturable absorber mirror and a Gires–Tournois Interferometer for dispersion compensation to achieve soliton mode locking. The generated pulses were as short as ΔτFWHM = 1.9 ps with a spectral bandwidth of Δλ=0.5 nm. The pulses were almost transform limited assuming a sech2 pulse shape. The averaged output power was 410 mW at an absorbed pump power level of 1.76 W. An investigation of the effect of the third-order dispersion of the Gires–Tournois interferometer on the spectra of the mode-locked laser is presented.

Generation of Transform-Limited Pulse Train in New Scheme of Harmonically Mode-Locked Er-Doped Fiber Ring Lasers

A new scheme of an amplitude modulated harmonically mode-locked Er-doped fiber ring laser is proposed, and the lasing characteristics are experimentally investigated. The transform-limited sech2 pulses at the repetition frequency of 1.64 GHz are stably generated. The pulse width and spectral bandwidth are independent of both the amplitude modulated (AM) modulation signal frequency and the AM modulation depth.

10 GHz modelocked, dispersion-managed and polarisation-maintaining erbium fibre ring laser with variable output coupling

A 10 GHz regeneratively modelocked, dispersion-managed and polarisation-maintaining erbium fibre ring laser has been constructed with a variable outcoupling; it produced very stable and nearly chirp-free 3.2 – 8.1 ps sech2 pulses at 1560 nm. It is experimentally shown that the stable operation region of the ML-EFRL is extended by increasing the laser output coupling.