Cavity Round-trip Time Research Articles

Synchronization Between Kerr Cavity Solitons and Broad Laser Pulse Injection

The synchronization of a soliton frequency comb in a Kerr cavity with pulsed laser injection is studied numerically. The neutral delay differential equation is used to model the light dynamics in the cavity. This model allows for the investigation of both cases where the pulse repetition period is close to the cavity round-trip time and where the repetition period of the injection pulses is close to a rational fraction M/N of the round-trip time. It is demonstrated that solitons can exist in this latter case, provided that the injection pulses are of a higher amplitude, which is directly proportional to the number M. Furthermore, it is shown that the synchronization range of the solitons is also proportional to the number M. The solitons excited by pulses with a period slightly different from the M:N-resonance can be destabilized by the Andronov–Hopf bifurcation, which occurs when the injection level at the soliton position decreases to M times the injection amplitude corresponding to the saddle-node bifurcation in a model equation with uniform injection.

Optical pulse generation with programmable positions in an actively mode-locked optical cavity.

A novel, to our knowledge, approach for generating optical pulses with programmable positions in an actively mode-locked (AML) optical cavity is proposed and experimentally demonstrated. In the AML, active mode locking occurs when the cavity gain exceeds one, and the cavity round trip time equals integer multiples of the repetition period of the electrical driving signal. The generated optical pulses are present at the positions where the optical cavity operates at its maximum transmission points. By periodically controlling the cavity gain with the driving signal, the maximum transmission points can be manipulated using a periodic arbitrary waveform, allowing the positions of the generated optical pulses within one round trip time to be programmed. Thanks to the superposition of the circulating optical field within the optical cavity, the pulse width of the generated pulses can be greatly compressed. In a proof-of-concept experiment, optical pulses with programmable pulse numbers, pulse intervals, and pulse position distributions in one period are generated by programming the driving signals. Optical pulse compression is also successfully verified. Optical pulses with an approximate 34-ps pulse width, ultra-low pulse interval (about 200 ps), and linear positional distribution are achieved.

Controlling the spectral persistence of a random laser

Random lasers represent a relatively undemanding technology for generating laser radiation that displays unique characteristics of interest in sensing and imaging. Furthermore, they combine the classical laser’s nonlinear response with a naturally occurring multimode character and easy fabrication, explaining why they have been recently proposed as ideal elements for complex networks. The typical configuration of a random laser consists of a disordered distribution of scattering centers spatially mixed into the gain medium. When optically pumped, these devices exhibit spectral fluctuations from pulse to pulse or constant spectra, depending on the pumping conditions and sample properties. Here, we show clear experimental evidence of the transition from fluctuating (uncorrelated) to persistent random laser spectra, in devices in which the gain material is spatially separated from the scattering centers. We interpret these two regimes of operation in terms of the number of cavity round trips fitting in the pulse duration. Only if the cavity round-trip time is much smaller than the pulse duration are modes allowed to interact, compete for gain, and build a persisting spectrum. Surprisingly this persistence is achieved if the pumping pulse is long enough for radiation in the cavity to perform some 10 round trips. Coupled-mode theory simulations support the hypothesis. These results suggest an easy yet robust way to control mode stability in random lasers and open the pathway for miniaturized systems, as, for example, signal processing in complex random laser networks.

Theoretical model of passive mode-locking in terahertz quantum cascade lasers with distributed saturable absorbers

Abstract In research and engineering, short laser pulses are fundamental for metrology and communication. The generation of pulses by passive mode-locking is especially desirable due to the compact setup dimensions, without the need for active modulation requiring dedicated external circuitry. However, well-established models do not cover regular self-pulsing in gain media that recover faster than the cavity round trip time. For quantum cascade lasers (QCLs), this marked a significant limitation in their operation, as they exhibit picosecond gain dynamics associated with intersubband transitions. We present a model that gives detailed insights into the pulse dynamics of the first passively mode-locked QCL that was recently demonstrated. The presence of an incoherent saturable absorber, exemplarily realized by multilayer graphene distributed along the cavity, drives the laser into a pulsed state by exhibiting a similarly fast recovery time as the gain medium. This previously unstudied state of laser operation reveals a remarkable response of the gain medium on unevenly distributed intracavity intensity. We show that in presence of strong spatial hole burning in the laser gain medium, the pulse stabilizes itself by suppressing counter-propagating light and getting shortened again at the cavity facets. Finally, we study the robustness of passive mode-locking with respect to the saturable absorber properties and identify strategies for generating even shorter pulses. The obtained results may also have implications for other nanostructured mode-locked laser sources, for example, based on quantum dots.

Nonlinear frequency chirps from a stabilized injected phase-modulated fiber laser loop

A phase-modulated frequency-shifting loop is injected by a single-frequency laser at 1.5 μm. In so-called Talbot conditions, i.e., when the modulation frequency is an integer multiple of the inverse of the cavity round-trip time, the loop generates a frequency comb whose temporal trace consists in a train of pulse doublets whose positions in time depend on the frequency of the injection laser. When the modulation frequency is slightly detuned from the Talbot condition, nonlinear frequency chirps are predicted and observed in the output pulse train. We demonstrate that these nonlinear chirps are not restricted to sinusoidal shapes, and also that the loop can be stabilized by exploiting the intracavity phase modulation.

Bifurcations and spectral pulsations in ultrafast fiber lasers

We employ real-time spectral measurements to investigate the transitions from the stable mode locking to period doubling and long-period pulsations. We highlight the role of self-phase modulation as a general mechanism triggering period-2 bifurcations. We analyze the new frequencies generated during the sequence of bifurcations and report an entrainment where the period of the long oscillation locks to multiples of the cavity roundtrip time.

Phase Nanoscopy with Correlated Frequency Combs.

This study addresses any sensor based on measuring a physical quantity through the phase of a probing beam. This includes sensing of rotation, acceleration, index change, displacement, fields… While most phase measurements are made by detecting an amplitude change in interfering beams, we detect instead a phase change through a relative frequency shift of two correlated frequency combs. This paper explores the limit sensitivity that this method can achieve, when the combs are generated in an Optical Parametric Oscillator (OPO), pumped synchronously by a train of femtosecond pulses separated by half the OPO cavity round-trip time. It is shown that a phase difference as small as 0.4 nanoradians can be resolved between the two pulses circulating in the cavity. This phase difference is one order of magnitude better than the previous record. The root-mean-square deviation of the measured phase over measuring time is close to the standard quantum limit (phase-photon number uncertainty product of 0.66). Innovations that made such improved performances possible include a more stable OPO cavity design; a stabilization system with a novel purely electronic locking of the OPO cavity length relative to that of the pump laser; a shorter pump laser cavity; and a square pulse generator for driving a 0.5 mm pathlength lithium niobate phase modulator. Future data acquisition improvements are suggested that will bring the phase sensitivity exactly to the standard quantum limit, and beyond the quantum limit by squeezing.

Fiber Optical Parametric Oscillator With Wide Tuning Range and Fixed Repetition Rate

We present a widely wavelength-tunable fiber-based optical parametric oscillator (FOPO) with a fixed repetition rate using four-wave mixing in a photonic crystal fiber and an intracavity spectral filter. The FOPO produces nearly transform-limited pulses with a spectral width of 1.1 nm and a pulse duration of 1.0 ps. By changing the wavelength of a pump laser and the passband of the spectral filter, the tuning range between 832 and 922 nm is achieved. Over the entire range, the displacement of a delay stage required to match the cavity round trip time with the period of the pump pulses is as small as 0.8 mm. The present FOPO synchronized with a low-noise picosecond laser will be useful for sensitive and broadband vibrational imaging by stimulated Raman scattering microscopy.

Twin-core fiber sensor integrated in laser cavity

In this work, we report on a twin-core fiber sensor system that provides improved spectral efficiency, allows for multiplexing and gives low level of crosstalk. Pieces of the referred strongly coupled multicore fiber are used as sensors in a laser cavity incorporating a pulsed semiconductor optical amplifier (SOA). Each sensor has its unique cavity length and can be addressed individually by electrically matching the periodic gating of the SOA to the sensor’s cavity roundtrip time. The interrogator acts as a laser and provides a narrow spectrum with high signal-to-noise ratio. Furthermore, it allows distinguishing the response of individual sensors even in the case of overlapping spectra. Potentially, the number of interrogated sensors can be increased significantly, which is an appealing feature for multipoint sensing.

Optoelectronic Oscillator for Arbitrary Microwave Waveform Generation

An optoelectronic oscillator (OEO) for arbitrary microwave waveform generation based on Fourier domain mode-locking (FDML) is proposed. A reconfigurable optical waveform generator (OWG) is implemented via external electro-optical modulation, which serves as the optical source for the proposed OEO. The optical waveform from the OWG can be seen as a series of frequency-scanning optical wavelengths in the frequency domain. At any instant, the number of wavelengths can be from 0 to infinite. By setting the period of the optical waveform or its multiple equal to the cavity round-trip time, an FDML OEO implemented by a frequency-scanning microwave photonic filter (MPF) is realized based on the phase-modulation-to-intensity-modulation conversion using a phase modulator cascaded with a phase-shifted fiber Bragg grating. The scanning characteristics of the MPF changes according to the optical waveform, which can be utilized to generate low-phase-noise arbitrary microwave waveforms using the inherent low-phase-noise merit of an OEO. An experiment is performed. Linearly chirped microwave waveforms and non-linearly chirped microwave waveforms with a scanning bandwidth of 2 GHz, 2-level frequency hopping (FH) microwave waveforms with an FH range of 500 MHz, and 240- and 250-bit binary and quaternary phase-coded microwave waveforms are generated from the OEO. To the best of our knowledge, this is the first time that an OEO is proposed for arbitrary microwave waveform generation.

Generation of ultra-low jitter radio frequency phase pulses by a phase-locked oscillator.

We demonstrate a novel, to the best of our knowledge, method for mode locking of an oscillator, which is based on the injection of a strong sinusoidal signal from an external source into the cavity. The oscillator generates a low phase noise carrier signal with a train of ultra-low jitter, short 2π phase pulses at a repetition period equal to the cavity round-trip time. Both the carrier signal and phase pulses are phase-locked to the external source. We demonstrate the effect in an optoelectronic oscillator that generates a train of short phase pulses at a high carrier frequency with the broadband spectrum of a dense RF frequency comb. The phase pulses can be converted to short, ultra-low jitter intensity RF pulses by beating the oscillator signal with the external source, used for locking.

Delay-differential-equation model for mode-locked lasers based on nonlinear optical and amplifying loop mirrors

Delay differential equation model of a nonlinear optical--nonlinear amplifying loop mirror mode-locked laser is developed that takes into account the finite relaxation rate of the gain medium and asymmetric beam splitting at the entrance of the nonlinear mirror loop. Asymptotic linear stability analysis of the continuous wave solutions performed in the limit of large delay indicates that in a class-B laser flip instability is preceded by the modulational instability and therefore cannot give rise to stable square wave patterns. Numerically it is shown that the model can demonstrate large windows of regular fundamental and harmonic mode-locked regimes with single and multiple pulses per cavity round trip time separated by domains of irregular pulsing.

Control of single and multiple phase solitons in a ring cavity.

Phase solitons are localized structures characterized by phase jumps of 2π or multiples arising in forced ring lasers. Here, we show numerically that they can be created by superimposing to the constant driving field a suitable control beam matched in frequency with a different cavity mode for a time of the order of ten cavity round trip times. If the two beams are separated in frequency by n free spectral ranges of the cavity, a train of solitons like a perfect soliton crystal consisting of n equispaced phase solitons is generated. This may represent a simple way to produce frequency combs with flexible frequency spacing and high power per line.

Fundamental and Harmonic Self Mode-locking in Mid IR Heavily Doped Fiber Lasers

Abstract: Harmonic self mode-locking effects are observed in heavily doped fiber lasers operating near 3 μm. The temporal profiles for the output of an Er-ZBLAN fiber laser operating at ~2.7 μm and an Ho, Pr-ZBLAN fiber laser operating at ~2.87 μm are reported. Stable second harmonic mode-locking is observed in the Er-ZBLAN fiber laser under 970nm pumping for an Er concentration of 50000 ppm, while unstable harmonic mode-locking of order of between 1-1/7 times the round cavity round trip time was observed for the higher concentration of 80000 ppm and for all pump powers. Unstable harmonic mode-locking is observed in the Ho, Pr-ZBLAN fiber laser when pumped at 1064nm, for fiber lengths up to 13m and for all pump powers. The experimental mode-locked pulse train periods are found to be consistent with theoretical analysis. The origin and properties of harmonic self mode-locking in heavily doped ZBLAN fiber lasers operated near 3 μm are discussed. Keywords: Er-ZBLAN fiber laser, Ho, Pr-ZBLAN fiber laser, Self mode-locking, Harmonic self mode-locking. PACS: Fiber lasers, 42.55.Wd, Mode locking, 42.60.Fc.

Numerical study on an optimum Q-switching profile for complete multipeak suppression in an actively Q-switched Ytterbium fibre laser

We propose an optimum Q-switching profile for complete suppression of the multi-peak phenomenon (MPP) without loss of pulse energy in an actively Q-switched ytterbium (Yb)-doped fibre laser. Most of the previously demonstrated approaches to suppress MPP have been based on adjusting of the rise time, and these rely on the assumption that the switching profile of the Q-switch has a trapezoidal temporal shape with a linear leading edge. These approaches leave one fundamental question as to whether or not there exists an optimum leading edge profile other than a simple linear one for complete suppression of MPP without loss of pulse energy. Through comparison among four different leading edge profiles. i.e. linear shape, sinusoidal function shape (increasing slope), sinusoidal function shape (decreasing slope), and composite function shape profiles, the proposed leading edge shape of a sinusoidal function (increasing slope) is shown to be capable of achieving complete suppression of MPP without loss of pulse energy under particular rise time conditions. It is shown that the use of a sinusoidal function (increasing slope) with a rise time of approximately 11 times the cavity round-trip time allows for the complete suppression of MPP without pulse energy loss in an exemplary, Q-switched, Yb-doped fibre Fabry–Perot laser.

Manipulation of temporal localized structures in a vertical external-cavity surface-emitting laser with optical feedback.

We analyze the effect of optical feedback on the dynamics of an external-cavity passively mode-locked surface-emitting laser operating in the regime of temporal localized structures. Depending on the ratio between the cavity round trip time and the feedback delay, we show experimentally that feedback acts as a solution selector that either reinforces or hinders the appearance of one of the multistable harmonic arrangements of pulses. Our theoretical analysis reproduces well the experiment and allows us to evidence asymmetrical resonance tongues due to the parity symmetry-breaking induced by gain depletion.

Numeric Multi-Dimensional (r, z, t) Analysis Method for Compact Yb³⁺:YAG End-Pumped, Passively Q-Switched Lasers

We have applied a new simplified combination of numerical methods for studying the time and three-dimensional space dependence of quasi-three-level Yb <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> :Yttrium Aluminum Garnet (YAG) end-pumped lasers passively Q-switched by a Cr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4+</sup> :YAG saturable absorber. We base our 3-D model on iterative, efficient, time- and space-dependent numerical propagation of the optical field through the laser cavity. The complex-valued laser field is coupled to the Yb <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> :YAG and Cr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4+</sup> :YAG media via complex optical permittivities, which are subsequently altered by gain/loss intensity saturation. The calculation is simplified using the radial symmetry of the system, with the cavity round-trip time as the smallest increment for updating the permittivities. We also include the effects of field diffraction in an intra-cavity air gap. For specified CW spatial pump conditions, self-consistent repetitively pulsed solutions for the laser field in a flat-flat or flat-convex mirror cavity are found with no ad hoc laser mode size or shape assumptions; these solutions are not Gaussian modes. We concentrate on compact lasers with multi-Watt average output power, operating at modest pulse energy (~1.0 mJ), high repetition rate (~5 kHz) and short pulse duration (~1.5 ns). Typical room-temperature pump-to-laser slope power efficiencies exceeding 50% are predicted, depending on laser pump and cavity loss parameters. Model results agree well with recently published experimental data.

Numerical investigation into the impact of Q-switch rise time on the output pulse characteristics in an actively Q-switched ytterbium-doped fiber laser

We report the results of our theoretical investigation into the impact of the Q-switch rise time on three key parameters of the output pulses in an actively Q-switched fiber laser, namely the multipeak phenomenon, pulse energy, and pulse peak power. Our investigation is conducted over a Q-switch time range of up to 12 times the cavity round-trip time (τround). We show that when a longer Q-switch rise time is applied to the cavity, a trade-off exists between multipeak phenomenon suppression and pulse energy maintenance. The results show that the Q-switch rise time (τrise) for the efficient suppression of multipeak phenomenon without loss of pulse energy varies, depending on the cavity parameters. In an exemplary, actively Q-switched fiber laser operating under the condition of a repetition rate of 15 kHz, τrise is estimated to be approximately five times larger than τround.

Triggering of different pulsed regimes in fiber cavity laser by a waveguide electro-optic switch.

A novel practical method for electronic triggering of essentially different pulsed regimes in fiber cavity lasers is introduced. The method relies on electronic control of complementary transmission characteristics of a fiber-coupled LiNbO3 waveguide electro-optic switch (WEOS) which plays the role of the variable output coupler in a fiber cavity. The method was studied using a testbed laser configuration comprised of a semiconductor optical amplifier (SOA) and an all-fiber cavity. Modulation of the WEOS-based output coupling in the fast gain recovery configuration allowed not only high-quality mode locking and harmonic mode-locking at certain pulse repetition rates determined by the cavity round trip time, but it also allowed nanosecond pulsed output of the same quality to be yielded by cavity dumping at widely and continuously tunable repetition rate (ranging from kHz to MHz). Thus, WEOS-based electronically variable output coupling allows uniquely high flexibility for lasing regimes and characteristics within a single all-fiber cavity configuration.

Temporal ghost imaging with random fiber lasers.

Ghost imaging in the time domain has opened up new possibilities to retrieve ultrafast waveforms. A pre-requisite to ghost imaging in the time domain is a light source with random temporal intensity fluctuations that are fully uncorrelated over the duration of the temporal waveform being imaged. Here, we show that random fiber lasers are excellent candidates for ghost imaging in the time domain. We study the temporal correlations of the intensity fluctuations of a random fiber laser in different operating regimes and compare its performance in temporal ghost imaging configurations with that of a conventional multi-mode cavity-based fiber laser. Our results demonstrate that random fiber lasers can achieve superior performance for ghost imaging as compared to cavity-based fiber lasers where strong correlations at the cavity round-trip time can yield artefacts for waveforms of long duration.