CW Case Research Articles

Quantum Key Distribution with a Continuous-Wave-Pumped Spontaneous-Parametric-Down-Conversion Heralded Single-Photon Source

Quantum key distribution (QKD) protocols utilize single photons for key exchanging. Heralded single-photon sources (HSPSs) with spontaneous parametric down-conversion (SPDC) is a practical and effective way of producing single photons of high fidelity, bringing extra performance especially at long distances. A pulsed laser is usually used as the pump for HSPS QKD, but it has disadvantages in operational stability and practicality compared to a cw one. On the other hand, a precise model describing the performance of HSPS with a cw pump is still missing. It is inaccurate and unsafe to apply the key rate model of the pulse-pumped HSPS QKD directly to the cw one, and it also overlooks the timing jitter and dead time of the single-photon detectors. In this paper, we study the cw case in detail, including practical imperfections of the experimental instruments. Our model shows that a cw-pumped setup can reach a much longer transmission distance (31 % longer) than the fastest pulsed HSPS QKD system at present, together with other advantages such as higher operational stability and better spectral characteristics.

A new approach to model CW CO2 laser using rate equations

Two popular methods to analyse the operation of CW CO 2 lasers use the temperature model and the rate equation model. Among the two, the latter model directly calculates the population densities in the various vibrational levels connected with the lasing action, and provides a clearer illustration of the processes involved. Rate equation models used earlier grouped a number of vibration levels together, on the basis of normal modes of vibrations of CO 2. However, such grouping has an inherent disadvantage as it requires that these levels be in thermal equilibrium. Here we report a new approach for modelling CW CO 2 lasers wherein the relevant vibration levels are identified and independently treated. They are connected with each other through the processes of excitation, relaxation and radiative transitions. We use the universally accepted rate coefficients to describe these processes. The other distinguishing feature of our model is the methodology adopted for carrying out the calculations. For instance, the CW case being a steady state, all the rate equations are thus equated to zero. In the prior works, researchers derived analytical expressions for the vibration level population densities, that becomes quite a tedious task with increasing number of levels. Grouping of the vibration levels helped in restricting the number of equations and this facilitated the derivation of these analytical expressions. We show that in steady state, these rate equations form a set of linear algebric equations. Instead of deriving analytical expressions, these can be elegantly solved using the matrix method. The population inversion calculated in this manner along with the relaxation rate of the upper laser level determines the output power of the laser. We have applied the model to an experimental CW laser reported in literature. Our resutls match the experimentally reported power.

Continuous-wave, quasi-continuous-wave, gain-switched, and femtosecond burst-mode operation of multi-mode diode-pumped Cr:LiSAF lasers

In this study, we have investigated the power scaling potential of diode-pumped Cr:LiSAF lasers upon pulsed pumping at varying pump pulse widths (5 μs to 10 s) and duty cycles (2%–100%). Compared to continuous-wave (cw) pumping, pulsed pumping allows the laser crystal to cool down while the pump is in the off state, and enables better control of thermal effects and efficient laser operation in the pump active period. Depending on the parameters of the pulsed pump source, the Cr:LiSAF laser operates in cw, quasi-cw, or gain-switched regimes. In cw laser experiments, using a 20 mm long crystal with a relatively low Cr doping of 0.8%, output powers as high as 2.4 W could be obtained at an absorbed pump power of 5.5 W. In quasi-cw operation, laser output powers as high as 3.1 W have been achieved, which represents a 30% improvement compared to the cw case. In gain-switched operation, pulses in the 1.35–5 μs range with peak powers up to 30 W have been observed at kHz repletion rates. Moreover, pulsed pumping has also been investigated in a cavity that is mode locked with a saturable Bragg reflector to investigate the advantage of femtosecond burst-mode operation compared to cw mode locking. In femtosecond burst-mode operation, 250 fs long pulses around 815 nm at a 106 MHz repletion rate with a burst average power of 1.1 W have been acquired. The corresponding pulse energy and peak power of the femtosecond pulses were 10.3 nJ and 36.6 kW, respectively. This represents a twofold improvement in pulse energies compared to cw mode locking. The power levels obtained in this study were limited by the available pump power, and future studies in this direction have the potential to scale the output power of the Cr:LiSAF lasers above the 10 W level.

Bistable action with hybrid plasmonic Bragg-grating resonators

Optical bistability with a hybrid silicon–plasmonic configuration consisting of a nonlinear Bragg-grating resonator side-coupled with a bus waveguide is theoretically investigated. The nonlinear response is studied with a modeling framework combining perturbation theory and temporal coupled-mode theory, fed with three-dimensional finite element method simulations. For the CW case, a general closed-form expression describing the nonlinear response is derived, valid for finite intrinsic quality factors and arbitrary coupling conditions. This generalization is necessary for studying plasmonic resonators which are inherently lossy. The effect of the parameters entering in the expression on the bistability curve is thoroughly investigated and the physical system is accordingly designed so as to exhibit minimum power threshold and an extinction ratio between bistable states exceeding 10 dB. Finally, the temporal dynamics are assessed. The system can toggle between bistable states in approximately 2 ps and is thus suitable for ultrafast memory/switching applications.

Optical bistability with hybrid silicon-plasmonic disk resonators

Optical bistability with a hybrid silicon-plasmonic configuration consisting of a nonlinear traveling-wave (disk) resonator side-coupled with a bus waveguide is theoretically investigated. The nonlinear response is studied with a theoretical framework combining perturbation theory and temporal coupled-mode theory. For the CW case, a general closed-form expression is derived. The effect of the parameters entering in the expression on the bistability curve is thoroughly investigated, and the physical system is accordingly designed so as to exhibit minimum power threshold for bistability and maximum extinction ratio between bistable states. Finally, the temporal dynamics are assessed. The system can toggle between bistable states in approximately 5 ps and is thus suitable for ultrafast memory and switching applications.

Transient quantum coherent response to a partially coherent radiation field

The response of an arbitrary closed quantum system to a partially coherent electric field is investigated, with a focus on the transient coherences in the system. As a model we examine, both perturbatively and numerically, the coherences induced in a three level V system. Both rapid turn-on and pulsed turn-on effects are investigated. The effect of a long and incoherent pulse is also considered, demonstrating that during the pulse the system shows a coherent response which reduces after the pulse is over. Both the pulsed scenario and the thermally broadened CW case approach a mixed state in the long time limit, with rates dictated by the adjacent level spacings and the coherence time of the light, and via a mechanism that is distinctly different from traditional decoherence. These two excitation scenarios are also explored for a minimal "toy" model of the electronic levels in pigment protein complex PC645 by both a collisionally broadened CW laser and by a noisy pulse, where unexpectedly long transient coherence times are observed and explained. The significance of environmentally induced decoherence is noted.

Critical power for self-focusing in the case of ultrashort laser pulses

We attempt to evaluate the applicability of the concept of the critical power for self-focusing, originally developed for intense quasi-continuous-wave (cw) beams, to the case of ultra-intense and ultrashort laser pulses propagating in air. Our results show that, unlike in the cw case, no particular value of peak pulse power can be viewed as a sharp demarcation line between linear and nonlinear propagation regimes. Our analysis further reveals the important role played by chromatic dispersion in the propagation dynamics of the laser pulse.

Beat-note locking in dual-polarization lasers submitted to frequency-shifted optical feedback

We derive a delay-differential equation model that describes continuous-wave (cw) or passively Q-switched (PQS) two-frequency solid-state lasers submitted to frequency-shifted feedback (FSF). The study focuses on the locking of the beat note between the two free-running laser frequencies to a reference external frequency. The locking domain is obtained analytically in the cw regime. The PQS regime is treated by adding a saturable absorber population in the model equations. In this case, numerical simulations permit us to evaluate a locking range that is smaller than in the cw case. We find good agreement between the theoretical predictions and experiments carried out with a cw diode-pumped dual-polarization Nd:YAG laser as well as with previously published experimental results obtained with cw Er:Yb:glass [ Opt. Lett. 32, 1099 (2007)] and PQS Nd:YAG [ Opt. Lett. 33, 2524 (2008)] lasers. Applications of the FSF locking technique include the lidar-radar technique, for which a highly coherent beat note is required.

Composition and Characterization of Femtosecond Optical Lattices Using Double Axicon Holographic Pattern

We demonstrate a method for tailoring the light structure of a femtosecond field using a double-axicon holographic pattern without compensating for additional angular dispersion elements. Tailored light structured on the femtosecond field can be obtained by creating a pair of femtoseond Bessel beams and synthesize them. The spatial property of tailored light structure on femtosecond field investigated and compared to the CW case. We also showed the temporal characteristics of the tailored femtosecond light structure can be expressed by the interference of Bessel beams with different time shift.

TLS와 CW 광원에 따른 트랜스포머 오일 내에서 광섬유 센서의 음압 감지 특성 연구

음압을 감지할 수 있는 Sagnac 간섭계 센서와 온도 및 스트레인을 측정할 수 있는 FBG센서를 결합한 새로운 형태의 하이브리드 광섬유 센서 시스템을 구축하기 위하여 입력 광원인 CW를 TLS로 대체할 필요가 있어 이에 따라 광원의 변화와 맨드릴 재료의 변화에 따른 광섬유 센서의 응답 특성 연구가 필요하게 되었다. 제작된 맨드릴 재료는 PTFE와 PTFE에 카본을 섞어 만든 두 종류로 선택하여 중공 원통형 맨드릴 겉면에 광섬유를 18 m 감아 광섬유 센서로 제작하였다. CW 광원에 대하여 음원의 입력 주파수를 1 kHz~20 kHz까지 바꾸어 가며 트랜스포머 오일이 채워진 유조에서 실험하였다. 또한 FBG와 맨드릴형 광섬유 센서를 결합한 하이브리드형 광섬유 센서 시스템을 구성하고 TLS 광원을 입사광으로 실험하였다. 실험 결과 PTFE 센서의 탐지 크기는 카본 센서 탐지 크기보다 높게 나타났고 맨드릴 재질의 탄성계수 값이 적을수록 커진다는 이론 결과와 잘 일치함을 보였다. CW 광원과 TLS 광원에서 응답한 PTFE 센서의 특성을 주파수별로 상호 비교하여 보면 광원이 CW일 때 보다 TLS일 때 응답 특성이 우수함을 알 수 있었다. 본 연구를 통하여 TLS를 이용한 광섬유 센서는 FBG와의 하이브리드 시스템에 적용 가능하리라 사료된다. To substitute TLS in the hybrid system which is combined with Sagnac interferometer and fiber bragg grating (FBG) it is necessary to investigate how the laser source (TLS and CW) and sensor material variate the response of fiber optic sensor. Two different hollow cylinder type mandrel materials are proposed which are PTFE and PTFE+carbon and 18 m optical fiber is wounded at the mandrel surface. CW laser source experiments had been done in the oil tank which is filled with transformer oil in the 1 kHz~20 kHz frequency range. Also Sagnac interferometer fiber optic sensor is combined with FBG called hybrid system and TLS used as a light source. Based on the experimental results PTFE sensor showed more higher magnitude of detection signal rather than carbon sensor and this result is agreement with the McMahon's theoretical results. Phase variation is inversely proportional to the elastic modulus of the mandrel material. In PTFE fiber sensor, tunable laser source showed more higher performance rather than CW case. Therefore, TLS fiber optic sensor can be applied to the hybrid system which is combined with Sagnac and FBG.

카오스 분석을 통한 용접 품질 정량화

Irregular fluctuation of penetration depth in CW single mode fiber laser welding is analyzed statistically and chaotically. Among various chaos theories, one of the basic concept referred as Lyapunov exponent is applied to the analysis to quantify the irregularity of penetration. Especially, maximal Lyapunov exponent (MLE) is known as the representative value indicating chaotic degree of the system dynamics. MLE calculation method of experimental data is applied to longitudinal spiking defect in fiber laser weld. Laser power modulation is suggested as a remedy then the computed MLE value is compared to CW case. It is shown that the adoption of chaos theory, MLE computation, can be used as a measurement standard to prove the validity of the solutions to prevent the unexpected chaotic behavior of weld through this work.

Optimal Radiated Waveforms From an Arbitrary UWB Antenna

Solutions are presented for the optimal electric field waveforms radiated by an arbitrary ultrawideband (UWB) antenna. Optimization criteria include maximization of the electric field amplitude at a particular time and location, or maximization of energy density over a specified time interval at a particular location. Assuming bandpass signals, constraints are placed on the total radiated energy, the Q of the antenna, and the size of the antenna. The solution is developed using a spherical mode expansion of the fields radiated by an arbitrary antenna enclosed by a spherical mathematical surface, and optimized using variational methods. A closed-form result is obtained for the case of amplitude maximization, while an integral equation must be solved numerically for the case of energy maximization in a time interval. An interesting result from these solutions is that the shapes of the optimal radiated field waveforms are largely independent of the size of the antenna. The solutions also indicate that the antenna characteristics that provide optimum field amplitude or energy in the transient case are identical to those associated with maximum gain in the CW case.

Large Raman gain and nonlinear phase shifts in high-purity As_2Se_3 chalcogenide fibers

Third-order Kerr nonlinearities and Raman gain are studied experimentally in high-purity As2Se3 optical fibers for wavelengths near 1.55 μm. Kerr nonlinear coefficients are measured to be nearly 1000 times higher than those for silica fibers. In pulsed mode, nonlinear phase shifts near 1.2-π rad are measured in fibers only 85 cm long with peak pulse powers near 3 W. However, there are nonlinear losses near 20% for nonlinear phase shifts near π. By use of a cw optical pump, large Raman gains nearly 800 times that of silica were measured. In the cw case there were losses in the form of index gratings formed from standing waves at the exit face of the fiber. Discrete Raman amplifiers and optical regenerators are discussed as possible applications.

Ground-state absorption saturation and thermo-lensing effect as main sources of refractive index non-linear change in Cr 4+:YAG at CW 1.06 μm excitation

Non-linear change of refractive index in Cr 4+:YAG is investigated experimentally by the Z-scan technique (CW case) at wavelength 1.06 μm. Theoretical analysis of the processes resulting in non-linear refraction in Cr 4+:YAG allows one to conclude that the main contributions in non-linear change of the crystal refractive index are the effect of Cr 4+ centers’ population perturbation due to ground-state (GS) absorption saturation and the thermo-lensing effect.

Electron beams formed by photoelectric field emission

Previous measurements of electron emission by cw laser-irradiated tungsten needles have been extended to pulsed laser irradiation using a 7-ns long, doubled Nd : YAG laser at intensities up to 10 11 W/m 2. The results show that the mechanism for emission changes from the tunnelling mechanism observed in the cw case, characterized by exponential voltage dependence, to an ablative mechanism characterized by very weak voltage dependence. The observed emission has a threshold around 10 11 W/m 2, just below the damage threshold for the needles. Using needles with a 1-μm tip radius at voltages up to 50 kV, current densities as high as 10 11 A/m 2 were observed.

Mathematical models for the dynamic response of continuous particulate air monitors

Mathematical models are developed for the dynamic, time-dependent count rate response of fixed-filter (FF), rectangular-window moving filter (RW), and circular-window moving filter (CW) continuous particulate air monitors. These models relate the monitor input, a time-dependent concentration, to the monitor output, its dynamic countrate. The models take the form of a single integral for the FF case, the sum of two double integrals for the RW case, and the sum of three triple integrals for the CW case. The models apply for a single isotope of any half-life, and for sampled concentrations of any time dependence, at any time during a concentration transient. The models are solved for selected concentration behaviors, providing analytical expressions for the prediction of monitor response, and plots comparing these responses of the three monitor types are presented. A numerical simulation of monitor response has also been developed, which starts from first principles, and does not use the analytical solutions. It is shown that this simulation agrees with the analytical solution.

Stochastic model of the deep penetration laser welding of metals

Deep penetration laser welding of metals generates a keyhole surrounded by a molten region which forms the weld on freezing. Mathematical models of the process produce relationships between the process parameters to provide an effective simulation of the process and a guide to optimal operating conditions both for continuous wave (cw) and pulsed systems. It is usual when pursuing such an analysis to assume the existence of a suitably averaged keyhole structure. To assume a steady-state keyhole with suitably averaged properties, however, constitutes a considerable idealization. Actually, the keyhole manifests itself as a writhing, twisting entity. This characteristic arises from many different instabilities that can and do inevitably come into play. They represent the reaction of the material being welded to the laser beam. It is even more necessary to consider such reactions to the laser beam when pulsed lasers or cw lasers with pulsed modulation are considered. The details concerning the characteristics of specific instabilities are not considered here. Instead, a stochastic description of some aspects of the laser welding process is provided when the laser operates in the cw case. The applicability of current mathematical models is thus extended giving increased insight into the nature of the laser welding process.

Laser catalysis with pulses

We present a time-dependent theory of laser catalysis, a process in which a strong light source is used to affect tunneling through a potential barrier by inducing a transient electronic excitation to a bound state. We have performed detailed calculations of pulsed laser catalysis on a one-dimensional Eckart potential as a function of the collision energy and the laser's central frequency. As in the cw case, the barrier transmission coefficients range from 100% tunneling on the blue side to complete suppression of tunneling on the red side of the radiatively broadened line. The point of perfect transmission is explained in the dressed state picture in terms of the equivalence between adiabatic laser catalysis and transmission through a double-barrier potential. The point of complete suppression of tunneling is shown to result from nonadiabatic destructive interference between the nonradiative tunneling and the optically assisted route.

Diffraction of an extremely short optical pulse

We provide a rigorous, closed-form mathematical model of pulsed diffraction in both time and frequency domains and interpret its anomalies. The customary continuous-wave (cw) approximation is corrected for the regime below 3 fs in pulse width, the present state of the art. The time-differentiated aspect of diffraction is linked with old theory and the conservation of energy. Convolution of the pulse with differentiated aperture edges produces traveling waves in the focal plane. Their collision near the focal point corresponds to the cw case. (This is generalized for a Gaussian beam.) Spectral sampling depicts a mode-locked laser of extremely broad spectrum, validating the nonintuitive phenomena. The square-modulus tool is validated for these pulses. Ultrashort pulses are related to data transmission rates above 100 THz. Diffraction anomalies cause confusion and loss of information in the sidelobes. Anomalous diffraction may provide new diagnostics. Diffracted energy (salient sidelobes versus continuum) can measure transform-limited pulse width.

Effect of coupling strength fluctuations on soliton switching in nonlinear couplers

We numerically analyse the effect of coupling strength random fluctuations on both dynamic and static soliton switching in symmetric nonlinear couplers. As in the cw case, the effect is generally found to be strong only near the switching regions. In the dynamical switching regime, the effect appears to increase with the length of the coupler at a rate twice as large for odd multiples of the linear coupling length, π/2, than for even ones. In the static case, the region of bistability shows the greatest change in the effect of random fluctuations, with a maximum at exactly the first bifurcation point. The solitons also appear to be quite stable against the random fluctuations in the sense that no pulse distortion or emission of dispersive radiation was detected.