Higher-order Four-wave Mixing Research Articles

Intensity Noise of Semiconductor Lasers Induced by Inter-Mode Beating

Beating between the lasing main mode and the non-lasing side modes is one of the intensity noise sources of single longitudinal mode lasers. Its characteristics were investigated experimentally recent years. This paper presents a theoretical study of mode-beating noises in semiconductor lasers, and intends to explain the experimentally observed phenomena. The effects of coherent population oscillation (CPO) induced by mode beating on gain coefficient and on reflective index are analyzed based on Maxwell-Bloch equation and rate equations. The power ratio of the side mode over its conjugation mode generated by four wave mixing (FWM) is discussed; formulas of amplitude and frequency of mode beating intensity noise are given with relations to pump levels and mode orders. The obtained results are suitable for the edge emitting diode lasers and the external cavity lasers. The line shape of mode beating intensity noises is discussed based on CPO-induced phase noise, giving explanations of the experimentally observed phenomenon of multiple sub-peak spectra. The roles of intensity noise reduction by nonlinear optical absorber (NLA) inserted in the laser cavity are described. More factors related to the mode beating noise are discussed qualitatively, such as spectral hole burning of gain (SHB), the effect of external cavity, and higher order FWM.

Highly Sensitive FBG Strain Sensor With Enhanced Measurement Range Based On Higher Order FWM

To meet the simultaneous requirement of high sensitivity and high measurement range is an uphill task in the development of fiber Bragg grating (FBG) strain sensor. A unique scheme of highly sensitive FBG strain sensor is proposed based on nonlinear four wave mixing (FWM) with a high measuring range. In this paper, both the edges of FBG reflection spectrum are used without increasing the number of sources. The FWM products generated are tuned to the reflection edges of the FBG. The signals reflected from the edges of the FBG are then utilized in the subsequent FWM process to enhance the sensitivity of the system. The proposed scheme can provide a strain measurement range of 2310 με with strain sensitivity of 91.21 dBm/nm.

Ultrahigh-resolution interrogation of a fiber Bragg grating sensor based on higher order four-wave mixing.

The performance of a highly sensitive strain sensor based on nonlinear four-wave mixing (FWM) using a fiber Bragg grating (FBG) is investigated. The power change due to the wavelength shift induced by very small strain over the FBG is significantly magnified by a higher order FWM process. Strain sensitivity of 5.547 dBm/μϵ is achieved and minimum wavelength shift of 2.18×10-6 nm (which corresponds to a strain of 1.80×10-3 μϵ) is detected with uniform FBG, whereas in case of chirped FBG (CFBG) strain sensitivity of 0.3 dBm/μϵ with minimum detectable wavelength shift of 4×10-5 nm (which corresponds to a strain of 0.033 μϵ) is obtained.

Augmentation of sensitivity of FBG strain sensor for biomedical operation.

The performance of a highly sensitive strain sensor based on nonlinear four wave mixing (FWM) using two uniform fiber Bragg gratings (FBGs) is investigated. Strain is measured by the proposed setup with high resolution and precision. It is observed that the wavelength shift induced by very small strain over the FBG is significantly magnified by the higher-order FWM process. The sensitivity is enhanced by a factor of nine based on a wavelength shift of the eighth-order FWM product. Strain sensitivity of 11.23pm/μϵ is achieved against initial strain sensitivity of 1.23pm/μϵ. The proposed scheme can provide a strain measurement range of about 3500μϵ. Application of the proposed setup in the cardiac and respiratory systems is also studied, and the results are found to be reliable and accurate, even if the applied strain on the FBG is of the order of 0.1μϵ.

Two-pump fiber optical parametric amplifiers: Beyond the 6-wave model

Abstract Two-pump (2-P) fiber optical parametric amplifiers (FOPAs) are a versatile class of FOPAs which can exhibit wide and flat gain spectra in arbitrary wavelength regions, when compared with one-pump (1-P) FOPAs. The 4-wave and the 6-wave models are commonly used to simulate 2-P FOPAs by considering four and six interacting waves, respectively. Although the 6-wave model provides more accurate results than the 4-wave model, it does not take into account higher-order four-wave mixing products (HFPs) especially when the FOPA saturates. The main goal of this paper is to accurately model the 2-P FOPA in which HFPs beyond six interacting waves are included. To this end, the nonlinear Schrodinger equation (NLSE) is solved using the split-step Fourier method and the results are compared with those of previous models such as the 4-wave and 6-wave models as well as an existing analytical solution. The results, which are compared with available experimental data, show that for high input signal levels where the FOPA operates in saturation, the 6-wave model fails to provide accurate simulation results and deviates from results obtained by the NLSE. Therefore, NLSE-based modeling, which includes arbitrary interacting waves beyond the 6-wave model is important for applications in the saturation regime such as signal processing, noise suppression and regeneration.

Crosstalk Mitigation in Multichannel Optical Parametric Sampling via Raman Amplification

We propose to use backward Raman amplification to mitigate the crosstalk in multichannel optical parametric sampling. The performances of multichannel sampling based on four-wave mixing (FWM) have been experimentally compared with different Raman pump powers. Optical crosstalk is suppressed by lowering the input signal power so that the depletion of the parametric pump and higher order FWM products are reduced. Meanwhile, Raman amplification compensates the parametric pump power and improves the conversion efficiency, thus maintaining the output idler power. A 12.2- and 13.6-dB reduction of crosstalk-induced frequency components has been achieved in two output channels. We also analyze bandwidth broadening resulting from the self-phase modulation of the pulsed parametric pump for the two cases when it is amplified by an erbium-doped fiber amplifier and by the Raman pump.

Suppression of Inter-channel Higher Order Four Wave Mixing in Four-Mode Phase-Sensitive Parametric Wavelength Multicasting

Phase manipulation of four-mode phase-sensitive (4MPS) process was developed as a means for suppression of high-order four wave mixing (HoFWM) terms in dual-pump driven parametric wavelength multicasting and, consequently, for reduction of inter-channel crosstalk and inter-channel interference. In contrast to the previous studies that focused on power stabilization and conversion efficiency maximization, the investigation in this paper focuses on the evolution of the inter-channel HoFWM tones, whose suppression can be accomplished by arranging the phases of signals in a complementary manner. In addition, broadband 4MPS multicasting with suppressed HoFWM effects over 100-nm bandwidth, reaching up to 12-dB suppression ratio was demonstrated.

Multichannel wavelength multicasting for two QPSK signals based on FWM in SOA

We experimentally demonstrate multichannel wavelength multicasting for two nonreturn-to-zero quadrature phase-shift keying (NRZ-QPSK) channels based on four-wave mixing (FWM) in semiconductor optical amplifier (SOA). Through the interaction with the two pumps in SOA, the input two 25 Gb/s NRZ-QPSK channels are successfully simultaneously multicast to five and two new wavelengths, respectively. All the multicast channels are with a power penalty less than 2.5 dB at a bit error rate (BER) of 10-3. A characterization of the system performance using conversion efficiency and BER as figures-of-merit in terms of pump and signal powers is also presented. The results indicate that the pump and signal powers can be optimized to eliminate the introduced deleterious nonlinear components. The wavelengths of the two NRZ-QPSK channels and the two pumps need to be specified to avoid the crosstalk induced by high-order FWM.

Higher-order four-wave mixing modeling in DWDM networks

In this paper, we derive a theoretical model for the higher-order four-wave mixing (FWM) power in wavelength division multiplexing networks with non-zero dispersion shifted fibers for the first time. We have investigated the higher-order FWM power theoretically and by numerical simulations. Dividing the fiber into a finite number of elements and applying the boundary conditions allow us to derive an expression for the second-order power penalty. At the end of each element, we derive the first-order FWM power for all wavelengths and use these values to calculate the second-order FWM power in the next element. Consequently, for each channel we can compute the total second-order FWM power penalty at the end of the fiber.

Asymmetric gain-saturated spectrum in fiber optical parametric amplifiers

We demonstrate experimentally and numerically an unexpected spectral asymmetry in the saturated-gain spectrum of single-pump fiber optical parametric amplifiers. The interaction between higher-order four-wave mixing products and dispersive waves radiated as an effect of third-order dispersion influences the energy transfer to the signal, depending on its detuning with respect to the pump, and breaks the symmetry of the gain expected from phase-matching considerations in unsaturated amplifiers. The asymmetry feature of the saturated spectrum is shown to particularly depend on the dispersion characteristics of the amplifier and shows local maxima for specific dispersion values.

Investigating the influence of a weak continuous-wave-trigger on picosecond supercontinuum generation

We numerically study the impacts of introducing a minute continuous-wave (CW) trigger on the properties of picosecond supercontinuum (SC) generation. We show that this simple triggering approach enables active control of not only the bandwidth, but more importantly the temporal coherence of SC. Detailed numerical simulations suggest that depending on the wavelength of the CW-trigger the multiple higher-order four-wave mixing (FWM) components generated by the CW-trigger can create either a relatively more stochastic or a more deterministic beating effect on the pump pulse, which has significant implications on how soliton fission and the onset of SC are initiated in the presence of noise. By controlling the CW-trigger wavelengths, the rogue solitons emerged in SC generation can exhibit high-degree of temporal coherence and pulse-to-pulse intensity stability. The present study provides a valuable insight on how the initial soliton fission can be initiated in a more controllable manner such that SC generation with both high temporal coherence and stability can be realized.

Analysis and experiment of all-optical time-interleaved multi-channel regeneration based on higher-order four-wave mixing in a fiber

Simultaneous all-optical multi-channel regeneration based on second-order four-wave mixing (FWM) in a single highly nonlinear fiber (HNLF) is studied. Interchannel crosstalk, especially cross gain saturation and generation of interchannel FWM, is avoided by properly time-interleaved channels. Preliminary experiment of 2 ch × 10 Gbit/s operation shows simultaneous noise reduction of the two channels and good agreement with numerical analysis. Numerical investigation on 2 ch × 40 Gbit/s operation using the same parameters as the experiment shows that the regeneration can improve qualities of both channels. For more number of channels and higher speed of operation, several parameters need to be adjusted to avoid interchannel crosstalks. Time synchronization techniques for the input channels are also discussed.

Nontransparency and optical phase erasure characteristic of four-wave mixing

Four-wave mixing (FWM) is a well-known nonlinear optical phenomenon and has attracted great interest in nonlinear all-optical signal processing owing to its ultrafast and transparent properties. Here we report the experimental observation via spectra on the nontransparency and optical phase erasure characteristic of FWM. The distinctive feature of “optical phase erasure” is a consequence of square relationship between the converted idler and input signal. It is interesting to find that the optical phase information carried by the input signal is erased in the converted idler by exploiting FWM. Such new attribute of FWM enables optical phase information removal and all-optical format conversion from carrier-suppressed return-to-zero (CSRZ) to return-to-zero (RZ). Moreover, similar phenomena are observed in the higher-order FWM. In addition, the nontransparency phenomenon and optical phase erasure characteristic are also demonstrated by theoretical analyses with optical spectra and phase diagrams.

2R Regeneration of Time-Interleaved Multiwavelength Signals Based on Higher Order Four-Wave Mixing in a Fiber

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> All-optical 2R regeneration of two-wavelength time-interleaved signals is demonstrated using higher order four-wave mixing in a fiber. In this regeneration scheme, a single fiber and a pump are shared by the two channels. The results show that interchannel crosstalk can be avoided when pulses in the two channels are time separated by more than <formula formulatype="inline"><tex Notation="TeX">$\sim$</tex> </formula>3 times their pulsewidth. A possible power monitoring to determine suitable time-interleaving condition is also discussed. </para>

A multiwavelength short pulse source based on saturated optical fiber parametric amplification

We describe a 10-GHz multiwavelength pulse source based on high-order four-wave mixing products generated by a saturated optical fiber parametric amplifier. We employ a nonlinear modulation scheme for the pump which plays two roles. First, it enables us to use a high pump power with no phase modulation, and second, it yields narrow (6 ps) pulses with a constant spectral width and the same jitter level (~150 fs) for the signal and three idler wavelengths

Higher-order four-wave mixing and its effect in WDM systems

Higher-order four-wave mixing effects are evaluated in WDM systems. Calculated and measured results show that higher-order FWM crosstalk, though small compared to the first-order FWM crosstalk, could be significant in unequal channel-spacing WDM systems where the first-order FWM is not a problem.

Stimulated Raman scattering from H 2+ ions

The observation of optical signals due to light scattering from H 2 + molecular ions is reported and discussed. By focusing Q-switched 1064 nm Nd : YAG laser light in H 2 at 20 bar, optical frequencies have been generated. They are assigned partly to stimulated Raman scattering from H 2 + and partly from H 2 molecules. The scattered radiation (Stokes-shifted 1064 nm beam) was transformed into visible light via higher-order four-wave mixing processes. The frequencies thus obtained could be observed with the naked eye if the scattered light was dispersed and projected on a white screen. The temperature of the gas in the focal region of the laser beam was estimated to be 1030 ± 300 K.