Pump Depletion Research Articles

Effect of laser beam filamentation on coexisting stimulated Raman and Brillouin scattering

This paper presents the study of stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) when both of these processes are coexisting and pump laser beam initial power is more than filamentation threshold. On account of the ponderomotive nonlinearity, the pump laser beam gets filamented, and both the scattering processes (SRS and SBS) get affected. Simultaneous presence of SRS and SBS (five wave interaction case) also affect the pump filamentation process due to pump depletion. Both the scattering processes (SRS and SBS) are enhanced due to filamentation of laser beam. Results are also compared with the three wave interaction case (either SRS or SBS) with and without filamentation.

PPLN-based OOK and DQPSK optical grooming by amplitude and phase-signal multiplexing through pump depletion

We propose and characterize a simple, integrable, and wavelength-preserving scheme able to groom a 40Gbps (D)QPSK signal with a 20Gbps OOK one into a 20Gbaud (60Gbps) 8-APSK signal. The proposed all-optical scheme is based on the second-order nonlinear signal-depletion effect in a single periodically poled lithium niobate (PPLN) waveguide. Performance of the device, characterized by means of BER measurements, attests error-free operation and a power penalty below 4.1dB.

Noise sources and competition between stimulated Brillouin and Raman scattering: A one-dimensional steady-state approach

A 1D steady-state model is developed to deal with stimulated scattering processes. The volume and boundary noise sources for scattered light are discussed in detail. Our results indicate that the boundary noise sources may play a significant role in estimating the reflectivity of stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS). With the capability of our model to deal with broadband scattered light, we find that pump depletion could be the main reason to the anti-correlation between SBS and SRS versus electron density observed in experiments. A simple method is proposed to phenomenologically include the effect of nonlinear saturation mechanisms in our model and reasonable results are obtained.

Coupled-Mode Theory for Cherenkov-Type Guided-Wave Terahertz Generation Via Cascaded Difference Frequency Generation

A scheme for monochromatic terahertz (THz) generation via cascading enhanced Cherenkov-type difference frequency generation (DFG) in a sandwich-like waveguide is proposed. The novel scheme has the potential to overcome the quantum-defect limit and to provide an efficient output coupling. This process is elucidated by developing a coupled-mode theory and taking into account the pump depletion, waveguide mode properties, and THz output coupling. The effect of cascading enhancement is analyzed by comparing with non-cascaded DFG situation. It is predicted that THz power can be boosted by nearly 8-fold with a 400 MW/cm2 pump in a 40-mm-long Si-LiNbO3-Si waveguide.

Study of Raman amplification in DPP-BOTDA sensing employing Simplex coding for sub-meter scale spatial resolution over long fiber distances

The impact of Raman amplification and Simplex coding is studied in combination with differential pulse-width pair Brillouin optical time-domain analysis (DPP-BOTDA) to achieve sub-meter spatial resolution over very long sensing distances. An optimization of the power levels for the Raman pumps, Brillouin pump and signal has been carried out through numerical simulations, maximizing the signal levels and avoiding at the same time nonlinear effects and pump depletion. A reduction of acoustic-wave-induced distortions in the Brillouin gain spectrum down to negligible levels has also been achieved by numerical optimization of the pulse width and duty cycle of return-to-zero Simplex coding, providing significant signal-to-noise ratio enhancement. Strain–temperature sensing over 93 km standard SMF is achieved with a strain/temperature accuracy of 34µε/1.7 °C, and 50 cm spatial resolution throughout the fiber length.

Effect of pump depletion on second harmonic generation in multiple quasi-phase-matching gratings

Second harmonic generation (SHG) from the aperiodic optical superlattice (AOS) in considering the pump depletion is investigated. It is found the domain configuration designed in undepleted pump approximation (UPA) can also be used to achieve multiple wavelength SHGs with high enough conversion efficiency for an exact solution. The applicable scope of UPA was estimated by a relative tolerance based on the related SHG conversion efficiency calculated in UPA and an exact solution. Results reveal that the relative tolerance is solely determined by the conversion efficiency, and unrelated to the sample configuration, pump intensity, incidental wavelength and nonlinear media. A model to evaluate an exact solution is proposed, and it is suggested that the SHG conversion efficiency can be easily assessed by the developed model. These results can be used to provide direct guidance for practical application, and can also make the estimation of practical samples more convenient.

Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime

Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime.

Stimulated Raman scattering of light in optical silica fiber under subnanosecond pumping

Stimulated Raman scattering (SRS) of light in a single-mode optical silica fiber under excitation by a subnanosecond laser pulse with a wavelength of 532 nm is studied. The dependence of the SRS power and its spectrum on the laser pumping power is investigated. It is shown that, at relatively low pumping powers, SRS is well described by an exponential function predicted by the model, neglecting pumping depletion. At powers causing deviations from this dependence, the SRS band, whose value depends on the pumping power, is additionally broadened. Features of the broadening are similar to that of a laser line in an optical fiber. Intense anti-Stokes scattering on vibrational modes over-populated because of the SRS process is also observed.

Capteur Brillouin réparti à fibre optique à haute résolution et longue portée

Brillouin-based distributed optical fiber sensors have been the subject of intense research in recent years because they offer a unique solution for continuous, real-time monitoring in civil engineering and petroleum industry. These sensors provide strain or temperature measurements with meter spatial resolution over several tens of kilometers. In this work we demonstrate two new Brillouin fiber sensors with enhanced performances based on advanced modulation formats from high-speed lightwave communications systems. We first report a Brillouin distributed sensor with enhanced centimeter resolution using a digital phase-shift keying technique. The second one uses a quadrature phase-shift keying modulator as a single-sideband modulator to balance the pump depletion and the fiber loss by the Brillouin gain. Combined with a specially-designed in-line bidirectional Erbium-doped fiber amplifier, we demonstrate that this technique allows for the achievement of long-range distributed sensing over 100 km.

Pulse shaping during Raman-seed amplification for short laser pulses

Raman-seed pulse amplification in a one-dimensional backscattering geometry is investigated with the help of numerical simulations and analytical estimates. The significant dependence of the initial amplification on the pulse form is revisited on the basis of a three-wave interaction as well as a kinetic Vlasov model. It is shown how the short duration of the input seed pulse influences its subsequent behavior, depending on plasma density and pump strength. The evolution during a "start-up period," which has been observed earlier, can be explained analytically. In the nonlinear (pump depletion) regime, the pulse generated in the start-up period will be further amplified and may evolve into a self-similar π-pulse solution. The Vlasov code predicts algebraic growth in time of the seed amplitude, similar to the findings based on self-similar solutions of the three-wave-interaction model. An initially very narrow pulse is shown to grow more slowly than an initially broad one.

Complete pump depletion by autoresonant second harmonic generation in a nonuniform medium

In this paper, we develop for the first time to our knowledge an analytical theory of second harmonic generation (SHG) in a generic nonuniform χ(2) medium. It is shown that by varying the properties of the medium gradually enough, the system can enter an autoresonant state in which the phases of the fundamental pump and of the generated second harmonic wave are locked. The effect of autoresonance allows efficient transfer of energy between the waves and, due to the continuous phase-locking in the system, all the energy of the pump could be converted to the second harmonic. Simple closed-form expressions for the waves amplitudes as a function of the longitudinal coordinate are derived, and an explicit criterion for the stability of the autoresonant state is obtained. Our analytical theory is compared to the numerical solution of the coupled mode equations, which are found to be in excellent agreement with each other. The analytical closed-form expressions that we derive could be very useful for practical design of SHG devices with increased performances, such as highly efficient, wideband frequency converters.

All-optical NAND/NOT/AND/OR logic gates based on combined Brillouin gain and loss in an optical fiber

A combined Brillouin gain and loss process has been proposed in a polarization maintaining optical fiber to realize all-optical NAND/NOT/AND/OR logic gates in the frequency domain. A model describing the interaction of a Stokes, anti-Stokes, and continuous wave and two acoustic waves inside a fiber, ranging in length from 350-2300 m, was used to theoretically model the gates. Through the optimization of the pump depletion and gain saturation in the combined gain and loss process, switching contrasts of 20%-83% have been simulated for different configurations.

Impact of input profile, absorption coefficients, and chirp on modulational instability of femtosecond pulses in silicon waveguides under fourth-order dispersion

We report the modulational instability (MI) analysis in silicon-on-insulator waveguides under fourth-order dispersion. The two-photon absorption (TPA) generates four symmetric optimum frequencies in the MI gain spectrum. The free-carrier absorption is found to enhance the value of the central MI gain. The chirp amplifies the intensity of the main pulse train peaks, leading to input profile independence. It shifts the occurrence of these peaks at short propagation distances. The absorption coefficients counteract the chirp, creating a pump dependence, and the high values of TPA destroy drastically the spontaneous breakup mechanism, leading to pump depletion.

Vector analysis of depleted stimulated Brillouin scattering amplification in standard single-mode fibers with nonzero birefringence

Numerical and experimental investigations of stimulated Brillouin scattering signal amplification in standard single-mode fibers under pump depletion show that while gains are reduced, the same orthogonal input states of polarization that provide maximum and minimum gain in the undepleted case practically continue to do so in the depleted regime. Using a scaled Brillouin gain coefficient, the power distribution of these max/min polarizations along the fiber can be deduced from a scalar formulation.

Generation of mid-IR and visible radiation from four-wave amplification of ultrashort laser pulses in transparent dielectrics

We analyze and simulate the generation of mid-IR radiation from the propagation of bichromatic laser pulses in transparent, centrosymmetric dielectrics. The process relies on using the beatwave associated with the bichromatic pulse to seed four-wave parametric amplification in the mid-IR. We derive propagation equations describing the evolution of the pump waves and scattered waves including the effects of third-order nonlinearity, dispersion, and finite laser spot size. An expression for the growth rate of the scattered waves due to four-wave mixing is derived in the limit of negligible pump depletion and is characterized for various transparent dielectric materials. For fused silica, it is found that a bichromatic pump with wavelengths near 1 μm can generate forward-directed radiation near 3 μm. Fully explicit particle-in-cell modeling shows exponential growth and high conversion efficiency to mid-IR and visible radiation when the beat-wave-generated frequency comb is tuned to overlap the gain band of the four-wave amplification process.

Long-range parametric amplification of THz wave with absorption loss exceeding parametric gain

Optical parametric mixing is a popular scheme to generate an idler wave at THz frequencies, although the THz wave is often absorbing in the nonlinear optical material. It is widely suggested that the useful material length for co-directional parametric mixing with strong THz-wave absorption is comparable to the THz-wave absorption length in the material. Here we show that, even in the limit of the absorption loss exceeding parametric gain, the THz idler wave can grows monotonically from optical parametric amplification over a much longer distance in a nonlinear optical material until pump depletion. The coherent production of the non-absorbing signal wave can assist the growth of the highly absorbing idler wave. We also show that, for the case of an equal input pump and signal in difference frequency generation, the quick saturation of the THz idler wave predicted from a much simplified and yet popular plane-wave model fails when fast diffraction of the THz wave from the co-propagating optical mixing waves is considered.

Nondegenerate three-wave mixing with the Josephson ring modulator

The Josephson ring modulator (JRM) is a device, based on Josephson tunnel junctions, capable of performing non-degenerate mixing in the microwave regime without losses. The generic scattering matrix of the device is calculated by solving coupled quantum Langevin equations. Its form shows that the device can achieve quantum-limited noise performance both as an amplifier and a mixer. Fundamental limitations on simultaneous optimization of performance metrics like gain, bandwidth and dynamic range (including the effect of pump depletion) are discussed. We also present three possible integrations of the JRM as the active medium in a different electromagnetic environment. The resulting circuits, named Josephson parametric converters (JPC), are discussed in detail, and experimental data on their dynamic range are found to be in good agreement with theoretical predictions. We also discuss future prospects and requisite optimization of JPC as a preamplifier for qubit readout applications.

Distributed Brillouin Fiber Sensor With Enhanced Sensitivity Based on Anti-Stokes Single-Sideband Suppressed-Carrier Modulation

We demonstrate an alternative technique to reduce pump depletion and to improve sensitivity in the long-range Brillouin optical time-domain analysis (BOTDA) sensor. Our BOTDA system uses an anti-Stokes single-sideband suppressed-carrier modulation technique that balances the pump depletion due to fiber loss. With this technique, we show both numerically and experimentally a great improvement compared to the dual sideband standard technique.

Impact of dispersion slope on performance of fibre‐optic‐parametric‐amplifier‐based all‐optical amplitude limiter

The high-speed amplitude limiting performance of a saturated fibre-optic parametric amplifier is numerically studied. It is shown that walk-off between the pump and signal pulses caused by a large dispersion slope makes the saturation behaviour less efficient and induces interaction between neighbouring signal pulses mediated by temporally-broadened pump depletion, both of which degrade the limiter performance.

Theoretical and experimental investigation of an 82-km-long distributed Brillouin fiber sensor based on double sideband modulated probe wave

An 82-km sensing range Brillouin optical time-domain analysis distributed fiber sensor without systematic measurement error is proposed and first experimentally validated, in which the probe wave with two sidebands generates a dual gain-loss Brillouin interaction, giving rise to the remarkable suppressed pump depletion in long sensing range and a relatively narrow Brillouin gain spectrum. Both theoretical analysis and experimental results demonstrate that this technique is capable of accurate long-distance sensing. To the best of our knowledge, it is the simplest technique and does not require extra time for long-distance sensing (>50 km).