Cavity Round-trip Time Research Articles

Brillouin fibre laser enhanced by Raman amplification

A multiple-wavelength Brillouin fibre laser is demonstrated, with channel spacings of ∼10.5 GHz, using Raman amplification in dispersion-shifted optical fibre. More than 20 frequency lines with ∼2 kHz linewidths are obtained using a 14.5 km length of fibre and a 1.3 MHz linewidth Brillouin pump. Gain depletion due to amplified spontaneous emission limits the total number of cascaded Brillouin lines. At high Raman pump powers, the laser produces a pulse train at the repetition rate corresponding to the cavity round-trip time.

Hilbert phase analysis of the dynamics of a semiconductor laser with optical feedback.

The nonlinear dynamics of a semiconductor laser with an optical feedback is studied using Hilbert phase analysis, which reveals interesting facets of the nonlinear dynamical behavior, including the formation and interaction of external cavity modes with increasing external feedback. Here we report measurements on two illustrative cases with very different dynamics; the laser is first biased just near threshold, and then far above threshold. We observe 2pi phase jumps at intervals that are multiples of the external cavity round-trip time, indicating the interaction and transfer of energy between external cavity modes.

Numerical Simulation of a lightwave synthesized frequency sweeper incorporating an optical SSB Modulator composed of four optical phase Modulators

We describe the numerical analysis of a lightwave synthesized frequency sweeper (LSFS) that uses an optical single-sideband (SSB) modulator composed of four optical phase modulators. The SSB modulator realizes a large frequency shift in the LSFS. This means that we can reduce the number of pulse circulations in the LSFS cavity to cover a given frequency sweep range. We propose a frequency-domain analysis method for the LSFS, in which a general optical modulator is expressed by using a matrix that includes optical phase terms. We employ this method to simulate the LSFS for several different phaseand group-velocity dispersion values in the lightpaths in the LSFS cavity. The results indicate that we can realize a linear frequency sweep by adjusting the phase change of the modulation signal during the cavity round-trip time.

High repetition-rate femtosecond optical parametric oscillator based on LiB 3O 5

We demonstrate on a synchronously pumped femtosecond LiB 3O 5 (LBO) optical parametric oscillator (OPO) at telecom wavelengths (1.3–1.6 μm) with a high harmonic repetition rate, which is not determined by the cavity roundtrip time of the OPO, but rather the cavity roundtrip time difference between the OPO and its pump source. This method paves the way for exploiting a femtosecond OPO working at telecom wavelengths with a repetition rate up to 10 GHz, or higher, when the pump laser used has a relatively low repetition rate.

Interpulse period doubling in a self-mode-locked Ti:sapphire laser

Femtosecond pulses with the interpulse periods that are twice the cavity round-trip time accompanied by two decentered TEM00 beam spots have been obtained with a self-mode-locked Ti:sapphire laser. By use of two photodiodes to measure the beam spots separately, I found that the pulses occurred at alternate spots on successive round trips. The observation can be explained by the presence of a double-pass cavity mode that reproduces itself after two return transits in an effective confocal resonator along an off-axis path rather than by total mode locking.

Pulse-train formation in a gain-switched polymer laser resulting from spatial gain inhomogeneity

We present an experimental study of the dynamics of a polymer laser upon excitation with an ultrashort pump pulse. The laser is unusual in the sense that the cavity length is such that the cavity round-trip time is intermediate between the duration of the pump pulse and the spontaneous-emission time of the gain medium. The cavity is only partly filled with gain medium. The unusual time scales, in combination with the spatial gain distribution, result in the emission of a neat and regular train of short pulses. Its generation can be viewed as a special case of gain switching. A one-dimensional rate-equation model that takes the nonuniformity of the gain explicitly into account is presented. The model describes both the evolution of the inversion, which is also measured experimentally, and the dynamics of the output in great detail, and yields excellent agreement with the experimental results. A heuristic description of the arisal of the pulse train in terms of amplified spontaneous emission and gain depletion is given.

Precise operation-frequency control of monolithic mode-locked laser diodes for high-speed optical communication and all-optical signal processing

We describe a method for pulse-repetition-frequency tuning of mode-locked laser diodes (MLLDs) monolithically integrated with a distributed Bragg reflector (DBR). The pulse-repetition frequency, i.e., the cavity-roundtrip time, is tuned through loss-induced change in the effective length of the DBR. The frequency-tuning range as large as the chip-to-chip frequency deviation caused by cavity-length fabrication variation of 10 μm has been confirmed experimentally, and the MLLDs operate at SDH (synchronous digital hierarchy) frequencies of 9.953, 19.906 and 39.813 GHz. Synchronization with an external system-clock through the hybrid mode-locking operation reduces the timing jitter of the optical pulses to less than 0.3 ps. As an optical pulse source for optical communication, error-free 20-Gbps transmission over 3000 km has been demonstrated, confirming that the MLLD properties satisfy the requirements for use in real systems. The novel application of MLLDs to all-optical clock extraction, one of the essential functions required in all-optical signal processing, has been demonstrated at the 40-GHz SDH frequency.

FM lasing phenomena in external cavity lasers

Numerical simulations of frequency modulated external cavity class-B lasers have been performed and a wide range of dynamic and spectral phenomena observed. It is shown that FM, pulsed or coherence collapse like behaviour can be obtained depending on the relative magnitudes of the mirror reflectivities and cavity round-trip times.

High-repetition-rate optical pulse generation using a rational harmonic mode-locked fiber laser

Rational harmonic mode locking takes place in an actively mode-locked fiber laser when the modulation frequency f/sub m/=(n+1/p)f/sub c/, where n and p are both integers and f/sub c/ is the inverse of the cavity round-trip time, the 22nd order of rational harmonic mode locking has been observed when f/sub m//spl ap/1 GHz. An optical pulse train with a repetition rate of 40 GHz has been obtained using a modulation frequency f/sub m/=10 GHz. The theory of rational harmonic mode locking has also been developed. The stability of the mode-locked pulses is improved considerably when a semiconductor optical amplifier is incorporated into the fiber laser cavity. The supermode noise in the RF spectrum of a mode-locked laser is removed for a certain range of current in the semiconductor optical amplifier.

Observation of dark-pulse formation in gain-clamped semiconductor optical amplifiers by cross-gain modulation

We have measured the ultrafast simultaneous cross-gain and laser mode dynamics in a gain-clamped semiconductor amplifier perturbed by an intense detuned 150 fs pump pulse. Besides relaxation oscillations, we demonstrate the instantaneous formation of a dark pulse in the laser mode that repeats itself with a period given by the cavity round-trip time. The dark pulse sequence subsequently decays into two-mode beating and is shown to weakly cross modulate the amplifier gain. To describe dark-pulse formation a time- and spatially dependent model based on rate equations is necessary. The experimental results are in reasonable agreement with numerical simulations.

Theory of transient spontaneous emission by an atom in a planar microcavity

We study the transient regime of spontaneous emission by an atom excited in a planar high-Q microcavity. The variation of the spatial distribution of the radiation outside the cavity is determined as a function of the increasing number of internal reflections for transition dipole moments parallel and perpendicular to the mirrors and for mirror separations equal to $\ensuremath{\lambda}/2$ and $\ensuremath{\lambda}/4.$ Particular attention is given to the parallel dipole in the $\ensuremath{\lambda}/2$ cavity, where the number of reflections is closely proportional to the elapsed time. It is shown that the transient regime extends over times of the order of the cavity decay time, in contrast to the effectively one-dimensional cavities previously studied, where the steady state is achieved after the cavity round-trip time. The field distribution inside the cavity tends to a steady-state form whose dimension parallel to the mirrors is of the order of the transverse coherence length. Despite this transverse localization of the field excitation, it is shown that the conditions for the achievement of strong atom-field coupling and the observation of Rabi oscillations cannot be met in the planar microcavity.

Dynamics and polarization properties of a self-modulated laser with an intracavity quarter-wave plate

The dynamics and polarization properties of self-modulated lasers with a quarter-wave plate were numerically studied using vectorial equations. At a certain pump rate, a stable laser can operate in a self-modulation state since the insertion of a quarter-wave plate in the cavity produces a quadrature between both of the electric field components. The oscillation period is twice the cavity round-trip time and the laser field is in a swaying linear polarization state. The polarization direction rotates by 90° after one cavity round-trip and, along both directions at 45° and 135° to the fast axis of the quarter-wave plate, an antiphase behavior is clearly demonstrated.

Nonlinear dynamics of a solid-state laser with injection

We analyze the dynamics of a solid-state laser driven by an injected sinusoidal field. For this type of laser, the cavity round-trip time is much shorter than its fluorescence time, yielding a dimensionless ratio of time scales $\ensuremath{\sigma}\ensuremath{\ll}1.$ Analytical criteria are derived for the existence, stability, and bifurcations of phase-locked states. We find three distinct unlocking mechanisms. First, if the dimensionless detuning \ensuremath{\Delta} and injection strength $k$ are small in the sense that $k=O(\ensuremath{\Delta})\ensuremath{\ll}{\ensuremath{\sigma}}^{1/2},$ unlocking occurs by a saddle-node infinite-period bifurcation. This is the classic unlocking mechanism governed by the Adler equation: after unlocking occurs, the phases of the drive and the laser drift apart monotonically. The second mechanism occurs if the detuning and the drive strength are large: $k=O(\ensuremath{\Delta})\ensuremath{\gg}{\ensuremath{\sigma}}^{1/2}.$ In this regime, unlocking is caused instead by a supercritical Hopf bifurcation, leading first to phase trapping and only then to phase drift as the drive is decreased. The third and most interesting mechanism occurs in the distinguished intermediate regime $k,$ $\ensuremath{\Delta}=O({\ensuremath{\sigma}}^{1/2}).$ Here the system exhibits complicated, but nonchaotic, behavior. Furthermore, as the drive decreases below the unlocking threshold, numerical simulations predict a self-similar sequence of bifurcations, the details of which are not yet understood.

Laser polarization self-modulation effects

Weakly vectorial lasers with intracavity wave retardation plates can exhibit a rich variety of unusual dynamic polarization characteristics. For example, the output of an external-cavity semiconductor laser with an intracavity quarter-wave plate shows polarization self-modulations alternating between TE and TM modes at a fundamental frequency corresponding to twice the cavity round-trip time and at odd harmonics of this fundamental frequency. Higher-order harmonics greater than the 30th harmonic at frequencies above 5 GHz have been observed, which is much higher than the relaxation-oscillation frequency of the laser. As the pumping level is increased, the period-doubling route to chaos and hysteresis behaviour associated with higher harmonic bifurcations and multiple stable states has also been observed. These experimental results as well as preliminary numerical simulation results are summarized on the basis of a fairly simple model. Apart from possible applications, these results raise interesting questions about the fundamental polarization and nonlinear dynamic characteristics of such lasers. Some of these general issues are discussed.

Demonstration of a frequency-modulated, pulsed optical parametric oscillator

We demonstrate that injection seeding a pulsed optical parametric oscillator with frequency modulated cw light with a modulation period equal to the cavity round-trip time produces pulses that have the same modulated character as the seed. A sensitivity of 10−3 was demonstrated for these pulses in frequency-modulated absorption measurements.

Cavity ring-down spectroscopy with Fourier-transform-limited light pulses

We have investigated the implications of using a pulsed, nearly Fourier-transform-limited, single-mode light source for cavity ring-down spectroscopy (CRDS) in the mid-infrared spectral range. We show that in the case where the coherence time and duration of the light pulse exceeds the cavity roundtrip time, mode beating generates oscillations in the ring-down waveform. When the period of the oscillations is comparable to the ring-down time, it becomes difficult to obtain meaningful decay constants. This situation can be avoided by careful choice of cavity geometry and mode matching conditions together with suitable electronic filtering.

Cladding-pumped passive harmonically mode-locked fiber laser

A passive harmonically mode-locked fiber laser cladding pumped by a broad-area diode-laser array is described. Harmonic mode locking is obtained in a frequency range from 33.3 to 128.6 MHz, where the higher frequency limit is imposed because of insufficient available pump power. The maximum pulse jitter in one cavity roundtrip time is between 300 and 50 ps in the whole frequency range, and the sidebands in the frequency domain are suppressed by as much as 50 dB. 600-fs bandwidth-limited pulses with pulse energies of as much as 20 pJ are obtained, giving rise to an average output power as great as 2.5 mW.

Simulation of passively mode locked lasers, using natural boundary conditions: multi pulse evolution and ordering

We present a method for simulating a passively mode locked laser. By selecting the simulation time step as the cavity round trip time, we achieved a proper tracking of the temporal evolution of the individual cavity modes of the laser. Employing the split step Fourier algorithm using this natural modes base, an efficient simulation method was obtained, while retaining at each propagation step the direct physical relations between the calculated phase terms in the time and frequency domains to the actual optical field and individual cavity modes, respectively. Using this method, we tracked the formation of multiple pulses in a passively mode locked fiber laser cavity, and explored the effect of delayed optical feedback as a means for pulse ordering in fiber lasers.

In situ small-signal gain of solid-state lasers determined from relaxation oscillation frequency measurements

We present a simple, in situ technique to calculate the small-signal gain of typical solid-state continuous-wave lasers, such as Nd:YAG and Nd:YLF lasers, by measuring the frequency of the relaxation oscillation noise peak. The laser's small-signal gain can be directly calculated from the frequency of the relaxation oscillation with knowledge of the upper-state lifetime, the cavity round-trip time, and total losses, which are typically well-known values. When the laser is pumped many times above threshold the losses do not need to be known accurately. This technique is compared with the traditional method of changing output couplers to establish its accuracy.

Semiconductor laser cavity dispersion measurement based on interferometric crosscorrelation of amplified spontaneous emission

The Fourier transform of the interferometric crosscorrelation of amplified spontaneous emission (ASE) is proposed as a general-purpose method for measuring cavity dispersion. The electric field correlation of the ASE from a cavity shows subfringes displaced from the ordinary interferogram by the cavity round-trip time. The cavity transfer function is derived from the subfringe using the Fourier transform. This method is demonstrated on semiconductor devices. It provides a very quick way to measure round-trip group delay dispersion as well as gain across a device’s whole gain band.