Photon Round-trip Time Research Articles

Ultrafast Buildup Dynamics of Terahertz Pulse Generation in Mode-Locked Quantum Cascade Lasers

Ultrashort terahertz pulse generation is essential for a range of proven terahertz applications, from time-resolved spectroscopy of fundamental excitations to nondestructive testing and imaging. Recently, it has been shown that semiconductor-based terahertz quantum cascade lasers (QCLs) can be used to generate pulses as short as a few picoseconds through active mode locking. However, further progress for subpicosecond and high peak power pulse generation is hampered by poor knowledge on how the electric field actually forms in these lasers. Here, we theoretically and experimentally show the amplitude- and phase-resolved buildup of pulse generation through active mode locking, from initiation of pulse generation to the nanosecond steady state. The experimental results, using an ultrafast coherent seeding technique to probe the laser from femtosecond to nanosecond time scales, are in full agreement with the theoretical calculations based on a theoretical model using multimode reduced rate equations. In particular, we show that the electric field buildup to achieve short pulse operation is extremely fast, requiring only a few photon round trips, owing to the ultrafast gain dynamics of the lasers. Further, this shows a gain recovery time of the order of a few picoseconds, an order of magnitude smaller than the photon round-trip time, highlighting that terahertz QCLs are categorically class-A lasers. This demonstration marks an important formulism for future progress towards exploring the ultrafast pulse generation buildup dynamics of these complex semiconductor lasers.

The Ice, Cloud, and Land Elevation Satellite – 2 mission: A global geolocated photon product derived from the Advanced Topographic Laser Altimeter System

The Ice, Cloud, and land Elevation Satellite – 2 (ICESat-2) observatory was launched on 15 September 2018 to measure ice sheet and glacier elevation change, sea ice freeboard, and enable the determination of the heights of Earth's forests. ICESat-2's laser altimeter, the Advanced Topographic Laser Altimeter System (ATLAS) uses green (532 nm) laser light and single-photon sensitive detection to measure time of flight and subsequently surface height along each of its six beams. In this paper, we describe the major components of ATLAS, including the transmitter, the receiver and the components of the timing system. We present the major components of the ICESat-2 observatory, including the Global Positioning System, star trackers and inertial measurement unit. The ICESat-2 Level 1B data product (ATL02) provides the precise photon round-trip time of flight, among other data. The ICESat-2 Level 2A data product (ATL03) combines the photon times of flight with the observatory position and attitude to determine the geodetic location (i.e. the latitude, longitude and height) of the ground bounce point of photons detected by ATLAS. The ATL03 data product is used by higher-level (Level 3A) surface-specific data products to determine glacier and ice sheet height, sea ice freeboard, vegetation canopy height, ocean surface topography, and inland water body height.

High peak power cavity dumping semiconductor lasers.

We report on the development of a nanosecond pulsed kW-class optically pumped InGaAs semiconductor laser emitting around 1020 nm, which is suitable for applications such as incoherent laser radar, nonlinear optics, and materials processing. Using an intracavity Pockels cell to cavity-dump VECSELs, we are able to access large pulse energies by storing energy in the optical cavity rather than in the gain medium. We demonstrate peak powers >1 kW and 3 μJ pulses, show the pulse length is equivalent to the photon round-trip time, and show that the wavelength can be tuned within the gain bandwidth of the semiconductor gain.

Delay line length selection in generating fast random numbers with a chaotic laser

The chaotic light signals generated by an external cavity semiconductor laser have been experimentally demonstrated to extract fast random numbers. However, the photon round-trip time in the external cavity can cause the occurrence of the periodicity in random sequences. To overcome it, the exclusive-or operation on corresponding random bits in samples of the chaotic signal and its time-delay signal from a chaotic laser is required. In this scheme, the proper selection of delay length is a key issue. By doing a large number of experiments and theoretically analyzing the interplay between the Runs test and the threshold value of the autocorrelation function, we find when the corresponding delay time of autocorrelation trace with the correlation coefficient of less than 0.007 is considered as the delay time between the chaotic signal and its time-delay signal, streams of random numbers can be generated with verified randomness.

Power fluctuations of a weakly optically-injected semiconductor laser in a period-one state

The frequency spectrum and the power output of a weakly optically-injected semiconductor laser in a period-one state are investigated. It is found that the oscillations in the power output consist of three components each caused by different physical effects, namely the relaxation oscillation frequency, the detuning between master and the slave laser frequency and the photon roundtrip time. For each set of parameters the spatio-temporal dynamics are obtained and the same internal oscillations occur.

Nonadiabatic semiconductor laser rate equations for the large-signal, rapid-modulation regime

The standard multimode rate equation for semiconductor lasers is based on the approximation that modal field shapes (if they change at all) depend on the instantaneous value of the time-dependent dielectric function. This is known as the adiabatic approximation. It will break down if the inverse of the modulation frequency approaches the photon round-trip time in the cavity. In this paper, we derive a criterion for the validity of the adiabatic approximation and find that it also involves the fractional modulation of the dielectric function, not just the photon round-trip time and the modulation frequency. Recognizing that present laser designs are starting to approach the limits of validity as set by our criterion, we study what can be done to get past that limit. We obtain corrections to the equations presently used by rederiving these equations from the time-dependent wave equation without discarding the time derivative of the dielectric function, an approximation made in every other derivation we have encountered. Retaining this time derivative introduces new terms into the usual equations. These terms correctly account for propagation delay-time effects and for nonadiabatic couplings between the modes. Surprisingly, the new terms alter only the source of photons to each mode. The usual rate equations are driven by a spontaneous emission term ${R}_{\ensuremath{\nu}}^{\mathrm{sp}}(t),$ which represents the rate at which photons are emitted spontaneously into the mode \ensuremath{\nu}. In the rate equation derived here, the spontaneous emission term ${R}_{\ensuremath{\nu}}^{\mathrm{sp}}(t)$ is augmented by a term ${\ensuremath{\Xi}}_{\ensuremath{\nu}}(t)$ which counts photons that were earlier emitted spontaneously into other modes \ensuremath{\mu}, accumulated and perhaps amplified there, and are now, because of the breakdown of the adiabatic approximation, leaking into the $\ensuremath{\nu}\mathrm{th}$ mode. Although casting the equations into this form makes sense from a physical point of view, it leads to great computational difficulties in solving the equations because ${\ensuremath{\Xi}}_{\ensuremath{\nu}}(t)$ refers explicitly to the past history of the laser. To overcome this practical problem, we provide an efficient and accurate algorithm for stepping the laser forward in time without having to retain history prior to the start of the present time step. Our method allows the equations to be solved with substantially the same computational effort as is normally expended in solving the conventional rate equations, and, moreover, provides error estimates at each step of the way.

Transient response of wavelength switching in multicavity mode-locked laser diodes

We report the transient response of wavelength switching in multicavity laser diodes. Spatially separated Bragg gratings embedded in a single fiber are used to map optical emission wavelength to photon round-trip time in an external cavity mode-locked laser diode. Transient emission wavelength and mode-locked pulse formation are explored by switching applied radio frequency modulation. Initial conditions are found to dominate transient response. A hot photon cavity has a characteristic rise time corresponding to approximately two photon cavity round trips. A cold photon cavity exhibits significant turn-on delay and rise time that depends on applied radio frequency signal power and is independent of above threshold steady-state current bias.

INSTABILITIES IN THE POWER SPECTRUM OF MODE-LOCKED SEMICONDUCTOR LASERS

Sideband instabilities in the intensity spectrum of synchronously mode-locked external cavity semiconductor lasers are investigated as a function of the cavity length and frequency detuning. A sideband spectrum with distinct narmw lines is observed in the optical power spectrum for modulation frequencies smaller than the inverse photon round trip time and is attributed to fr&quency and phase modulation of the modelocked pulse train. 1.INTRODUCTION: Mode-locking of semiconductor lasers has been widely used for the generation of coherent short light pulses on the picosecond and subpiposecond timescale applying either active, passive or hybrid mode-locking techniques. With purely active mode-locking coherent pulses with 5ps duration have been obtained /I/. Apart from its use as a source for very short light pulses the mode-locked laser may serve as a model system for the investigations on nonlinear dynamics and instabilities. We have performed systematic studies of the power spectrum of an actively modelocked semiconductor laser as a function of the detuning between the modulation frequency f and the inverse photon round trip time f . mod res 2.EXPERIMENTAL: We use an external cavity configuration (cavity length 1.87~1) with an one facet antireflection coated GaAs / (GaA1)As CSP laser (Hitachi HLP1400) in the experiments. The residual reflectivity of the coated facet 4 is smaller than 10 . An intracavity etalon (bandwidth 10nm) is employed for spectral bandwidth con(''present address : Research Institute for Technical Physics of the Hungarian Academy of Sciences. H-1325 Budapest. Hungary Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988296 C2-406 JOURNAL DE PHYSIQUE trol and tuning. The cw threshold in the external cavity configuration is about the same as for the solitary laser (1~~=54.5mA) without antireflection coating. Mode-locking is achieved by modulating the prebiased diode ( I ~ ~ * I ~ ~ ) with the current pulses from a comb generator (HP33002A), which have a duration of 130ps and an amplitude of typically 15V at an impedance of 50 Ohms. The optical output was analyzed by a fast photodiode (risetime loops) and an electrical spectrum analyzer (DC-2GHz). HR Etalon MO ARcoated Laser APD ca.8OMHz 0.5 -1 W HP33002A HP33150A HLPUM) TEK4514 MSGllA Fig.l:Experimental setup. 3.RESULTS: Under optimum mode-locking conditions, fmod=fres=80MHz, the power spectrum consists of a series of equally spaced narrow lines of width 150kHz and signal to noise ratio 50dB at multiples of the modulation frequency fmodt indicating proper mode-locking. The power spectrum shows an unstructured noise band of width 13MHz for positive detuning (fmod-f >O). This broad noise band res is symmetric with respect to the inverse resonator round trip time fres9 independent on detuning. Its height and width are a measure for the amplitude and phase fluctuations in qualitative agreement with the results of mode-locked dye lasers /2/. Opposite, the power spectrum shows a characteristic structure of narrow sidebands (Fig.21, if the laser is detuned a few 10kHz to the negative side. This sideband structure is symmetric with respect to the modulation frequency fmod

A comparative study of intensity pulsations in a double heterostructure AlxGa1?xAs laser with and without an external resonator present

This paper describes the pulsing behaviour of AlxGa1−x As double heterostructure (DH) lasers with and without an external dispersive resonator present. We have investigated only those lasers which show self-sustained oscillations under dc excitation. For the solitary diode we have found pulses possessing a width at half-power points, Δτp, where Δτp=0.9 ns and a repetition frequency,fos, ranging from 176 to 775 MHz depending on injection currentJ. Introducing a correlation time,tc, as a measure of the stability of the pulse height we have obtained 5 <tc < 40 ns. The maximum value oftc occurs in the vicinity of the crossing point offos2 andτc−2, whereτc is the effective carrier lifetime. Output pulsations are accompanied by spectral shifts of the longitudinal diode cavity modes. The frequency halfwidth, ΔνHw, ranging from 30 to 90 GHz is closely related to the maximum pulse power,Pmax. Coupling the laser diode to an external resonator, pulse widths, oscillation frequencies and correlation times have been determined as functions ofJ/Jth (Jth is the threshold injection current), provided the photon roundtrip time is nearly equal toτc and the equivalent reflection factorR* of the external resonator isR* ∼ 0.87. By evaluating the experimental findings pulsing under dc excitation may be described, without a detailed knowledge of the reasons leading thereto, by using the concepts of a nonstationary quality factorQns and time-dependent resonator losses characterized by ΔνHw/δτp. Oscillations become self-sustained forQns=const., i.e. the minimum photon density with which the pulses start to grow has to be time and excitation independent, in this casefos2 is proportional toJ/Jth as well as Δτp to (J/Jth−1)−1/2.

Bistability, regular self-pulsing, and chaos in lasers with external feedback

Steady states and dynamic behavior of the light field in a lasing medium contained in the cavity of a Fabry–Perot (FP) resonator are investigated theoretically. The FP resonator is optically coupled to an external resonator (ER), which reflects light back into the laser within a small frequency interval. It is assumed that the lasing threshold cannot be exceeded without feedback from the ER. The losses of the compound-cavity system depend on the light frequency’s giving rise to dispersive bistable effects. The static hysteresis cycle as well as transients between its branches has been calculated. Moreover, various types of regular and chaotic self-pulsing that are due to the oscillation of several modes of the compound-cavity system have been found, depending on the ratio of longitudinal relaxation time T1 to the photon round-trip time T. Finally, phase modulation and frequency chirping have been determined.

Laser interferometer as a gravitational wave detector

An analysis is made of the effect of a gravitational wave on coherently pumped Michelson and Fabry–Perot optical interferometers. Allowance is made for the complex structure of the response associated with the triplet character of the photon frequency perturbation in the interferometer. As a result, the response of the interferometer depends strongly on the angle of incidence of the gravitational wave not only in respect of intensity but also in terms of its profile. In the long-wavelength limit, these characteristics are only reflected in the angular structure of the phase of the response. For gravitational wave bursts shorter than the photon round trip time between the mirrors, the temporal and angular structure of the response is extremely specific so that the signal can be isolated from nongravitational perturbations. An analysis is made of the case of a Michelson interferometer with multiple reflections and the case of a gravitational optical resonance for a Fabry–Perot interferometer is also studied. Estimates are given of the sensitivity of such an interferometer antenna subject to the condition that the main noise is due to quantum fluctuations of the optical pumping.

Relaxation Oscillations in Stimulated Ruman and Brillouin Scattering

The equations describing the transfer of intensity from a pump beam simultaneously to forward and backward stimulated scattered beams in an infinite medium are shown to lead to pulsations similar to relaxation oscillations in the scattered intensities. The period of the pulsations is simply related to the gain length for the forward-scattered beam, and may be much longer than the ordinary transient time (related to the damping of material excitations) usually associated with stimulated scattering. Similar oscillations occur for backward scattering alone (stimulated Brillouin scattering) if the scattering medium is finite. In this case the period equals the photon round-trip time in the medium if the latter exceeds the backward gain length. Both phenomena should be observable in scattering from gases such as ${\mathrm{N}}_{2}$ and ${\mathrm{H}}_{2}$ at high pressure, and may also play a role in determining the temporal structure of light scattered from the region of a self-focus in liquids.