Multiple, polarization diverse, idler wave generation in fibers from competing four-wave mixing processes

We report on a theoretical and experimental characterization of polarization-dependent four-wave mixing processes in highly nonlinear optical fibers. Two or three idler waves at different polarizations are experimentally generated in an optical fiber from the propagation of two wavelength-detuned, orthogonally-polarized pumps and a signal. Each idler wave results from a different four-wave mixing process involving the signal and one or both pumps. Orthogonally-polarized idler waves are demultiplexed in a polarization beam splitter with a cross-polarization suppression of over 17 dB. The parametric process equations for this system are analytically solved and the efficiencies of the competing processes analyzed for the small pump detunings and identical pump powers. This experimental setup can be used in telecommunication systems for producing and selectively rerouting various copies of a data signal.     

Polarization insensitive wavelength conversion based on four-wave mixing for polarization multiplexing signal in high-nonlinear fiber

We have theoretically and experimentally investigated polarization insensitive of all optical wavelength conversion for polarization multiplexing signal based on four-wave mixing (FWM) in nonlinear optical fiber. Optical polarization multiplexing technique can be used to double the transmission bit rate by adding data on each of two orthogonal optical states. At the receiver side, the two orthogonal signals can be obtained by direct detection. The eye diagrams of the original signals have been probed and compared with the converted one in this experiment. The characteristics of the converted signal have been fully studied and a little crosstalk which leads a better corresponding eye diagram has been obtained after polarization demultiplexing.     

All-optical demultiplexing of 4-ASK optical signals with four-wave mixing optical gates

A new all-optical technique to demultiplex quaternary-amplitude-shift keying (4-ASK) signals into two on-off keying (OOK) signals is proposed. We show that such quaternary-to-binary conversion may be performed with two types of optical gates (OGs); a first one that implements an S-shaped optical power transfer function (TF), which is also the characteristic TF of optical pulse reshaping devices, and a second type that implements a U-shaped TF. Furthermore, we describe a heuristic approach to design such OGs by using the fiber four-wave mixing effect in highly non-linear dispersion-shifted fibers. The performance of the technique is evaluated by simulating the demultiplexing of 4-ASK signals with these OGs. Results indicate that the proposed devices are able to provide binary signals with acceptable BERs even after the 4-ASK signals are propagated through a cascade of eight fiber links of 50 km followed by optical amplifiers with a 4.5-dB noise figure.     

Measurement of nonlinear coefficient of a highly nonlinear fiber based on peak four-wave mixing signal generation conditions

We introduce a new measurement method of the nonlinear coefficient (NC) of a highly nonlinear fiber based on a four-wave mixing (FWM) technique. The NC along with the fiber's zero-dispersion wavelength (ZDW) was determined from the precise measurement of the pump power dependent optimum pump frequency for peak FWM signal generation conditions. The measurement errors of the NC and ZDW values determined with this method were less than 4.6% and 0.051 nm, respectively.     

Beat structure in spectrally resolved four-wave mixing under crosslinear polarization in GaAs quantum wells

The polarization dependence of beat structure in spectrally resolved four-wave mixing was investigated on 50 Å GaAs multiple quantum wells. Under crosslinear polarization we observed a beating structure at higher energy region of the main spectral peak due to biexciton–exciton transition. The beat has a period of 0.95 ps and is constructive at delay time T=0 ps, which suggests the corresponding double Feynman diagrams to be of the same type. By shortening the central wavelength of the sub-ps laser, we observed the distinctive peak corresponding to the beat period. Even in GaAs system, which is generally believed to have a small biexcitonic effect, there are two effective 2-exciton states with well-defined energies which are required to describe the third-order optical nonlinearly.     

All-optical continuously tunable delay with a high linear-chirp-rate fiber Bragg grating based on four-wave mixing in a highly-nonlinear photonic crystal fiber

A scheme for hi-fi all-optical continuously tunable delay is proposed. The signal wavelength is converted to a desired idler wavelength and converted back after being delayed by a high linear-chirp-rate (HLCR) fiber Bragg grating (FBG) based on four-wave mixing (FWM) in a highly-nonlinear photonic crystal fiber (HN-PCF). In our experiment, 400 ps (more than 8 full width of half maximum, FWHM) tunable delay is achieved for a 10 GHz clock pulse with relative pulse width broaden ratio (RPWBR) of 2.08%. The power penalty is only 0.3 dB at 10⁻⁹ BER for a 10 Gb/s 2³¹−1 pseudo random bit sequence (PRBS) data.     

Influence of the volume speckle on fiber specklegram sensors based on four-wave mixing in photorefractive materials

In this work, the dependence on the speckle size in the performance of a micro displacement sensor based on fiber specklegrams stored in a photorefractive BSO (Bi₁₂SiO₂₀) crystal is experimentally demonstrated. In our experimental setup, a plastic optical fiber (POF) was used to generate a subjective speckle pattern which was recorded in the crystal by using a four-wave mixing arrangement in transmission geometry. The speckle size was controlled by modifying the diameter of a pupil aperture adjacent to a lens producing the image of the speckle. The signal speckle beam was mixed into the crystal with two counter propagating pump beams to generate a fourth beam which is proportional to the conjugate of the original speckle beam. Real time fringe patterns were obtained at the output of the system by producing micro displacements of the fiber output end. Increases of the phase conjugation reflectivity and the visibility of the fringe patterns were appreciated when the speckle length was increased by decreasing the pupil aperture diameter. This behavior allowed recovering the autocorrelation functions of fringe patterns associated to micro displacements that initially led to decorrelation, and therefore, to improve the dynamic range of the metrological system. Until the best of our knowledge this is the first report about the influence of the speckle size on fiber specklegrams sensors recorded on photorefractive materials by four-wave mixing.     

Reconfigurable all-optical logic gate using four-wave mixing (FWM) in HNLF for NRZ-PolSK signal

We demonstrate a reconfigurable all-optical logic gate for NRZ-PolSK signal based on FWM in a highly nonlinear fiber at 10 Gb/s. Half subtracter, XOR, AB?, āB or XNOR, AND, and NOR logic gates can be implemented simultaneously. The input power for the HNLF is optimized to be as low as about 15.2 dBm and the high Q factors above 8 dB for eye diagrams are achieved. Experimental results show Q factors of AB?, āB, AND, and NOR were higher than those of XOR, and XNOR. Error-free operation is achieved experimentally for 10 Gb/s 2⁷-1 pseudorandom bit sequence (PRBS) data. Power penalties for the logic gate are less than 3 dB. Simulation analysis about the wavelength characteristic for all logic gates is given and it predicts that the reconfigurable logic gate can realize error-free operation when the wavelength separation is less than 5 nm.     

Transmission performance of 10-Gb/s DPSK WDM signals due to phase-error and four-wave mixing in SOAs

We present a complete dynamic model of semiconductor optical amplifiers (SOAs) including the inter-channel four-wave mixing (FWM). The model has been implemented using the time-dependent transfer matrix method (TMM) and applying the discretization scheme in both the spatial and spectral domains. In SOA-based wavelength division multiplexing transmission systems using 10-Gb/s differential phase shift keyed (DPSK) signals, the system performance due to the SOA-induced phase-error and the FWM effect has been analyzed. By the injection of a reservoir channel into SOAs, the transmission performance of non-return-to-zero (NRZ) DPSK signals can be improved through the phase-error reduction. Both the NRZ-DPSK and return-to-zero (RZ) DPSK signals are found to be suffered from the FWM-induced crosstalk. The overall nonlinear tolerance of RZ-DPSK is shown to be better than that of NRZ-DPSK.     

Stimulated Brillouin scattering limited intensity-dependent four-wave mixing between pump and signal in a non-zero dispersion shifted fiber

The intensity-dependent four-wave mixing (FWM) efficiency is derived by the nonlinear Schrodinger equations including the self phase modulation and cross phase modulation between the two Fabry–Perot modes of a pump and a single-wavelength signal. The maximum FWM for mixing the pump with signal in non-zero dispersion shifted fiber is explained as the minimum phase mismatch for FWM due to equal group delay for the pump and signal. It was also found that the experimental measurements for the generated FWM power are limited by the stimulated Brillouin scattering (SBS) threshold. Under the SBS threshold, the experimental results are still coincided well with the theoretical calculations of the FWM generated power ratio to have the difference of 0.12 dB for the input signal power of 12 mW.     

Multiple four-wave mixing in optical fibers: 1.5-3.4-THz femtosecond pulse sources and real-time monitoring of a 20-GHz picosecond source

In this work, we report recent progress on the design of all-fibered ultra-high repetition-rate pulse sources for telecommunication applications around 1550 nm. The sources are based on the non-linear compression of an initial beat-signal through a multiple four-wave mixing process taking place into an optical fiber. We experimentally demonstrate real-time monitoring of a 20 GHz pulse source having an integrated phase noise 0.01 radian by phase locking the initial beat note against a reference RF oscillator. Based on this technique, we also experimentally demonstrate a well-separated high-quality 110 fs pulse source having a repetition rate of 2 THz. Finally, we show that with only 1.4 m of standard single mode fiber, we can achieve a twofold increase of the repetition rate, up to 3.4 THz, through the self-imaging Talbot effect. Experimental results are supported by numerical simulations based on the generalized non-linear Schrödinger equation.     

Polarization insensitive wavelength conversion based on dual-pump four-wave mixing for polarization multiplexing signal in SOA

We have theoretically investigated polarization insensitive all-optical wavelength conversion for polarization multiplexing signal based on dual-pump four-wave mixing (FWM) in a SOA. The simulation result shows that the polarization insensitive converted signal can be separated into two lightwaves without crosstalk when one of the two orthogonal data lightwaves is parallel with one pump and the SOA should be polarization insensitive. Several conditions which affect the conversion efficiency for polarization multiplexing signal are also discussed.     

Analysis of a 2R all-optical regenerator utilizing cascaded four-wave mixing in a highly nonlinear fiber

The properties of an all-optical 2R regenerator based on cascaded four-wave mixing (FWM) in a highly nonlinear fiber (HNLF) are investigated. The regeneration is based on the nonlinear cascaded FWM transfer function and a study of the system's static behavior reveals the operating conditions, under which the transfer function approaches most the ideal, step-like discrimination characteristic function. Numerical simulations for the regenerated temporal satellite wave with different signal and pump powers are investigated, and the optimal transfer function based on different fiber lengths and different injected wavelengths are also demonstrated.     

Pulse propagation in four-wave mixing process with group index difference of signal and idler waves

Four-wave mixing process with a large group index difference of the signal and idler pulses in a nonlinear optical fiber is theoretically investigated when the pump is continuous light. We prove that in the four-wave mixing process, the signal and idler waves would finally propagate in a common group velocity in spite of their different group indices. When the effective phase mismatch in four-wave mixing is not zero, their carrier frequencies shift in different directions. The asymptotic result of the signal and idler shape and carrier frequency shift are obtained. The theoretical prediction is validated by the numerical simulation.     

Room temperature multiwavelength erbium-doped fiber ring laser using a highly nonlinear photonic crystal fiber

A multiwavelength laser source is demonstrated with a high power erbium-doped fiber amplifier as the gain medium. A highly nonlinear photonic crystal fiber (PCF) is inserted in the ring cavity to provide nonlinear gain by four-wave mixing. A Sagnac loop is incorporated in the ring cavity serving as a comb-like multichannel filter. The comparison between fiber ring laser without PCF and with PCF shows that the highly nonlinear PCF can generate a larger number of excited wavelengths and help stabilize the output power.     

Multi-channel 80-GHz RZ pulse train generation based on parametric process in highly-nonlinear fiber

It is experimentally shown that six-channel C + L-band 80-GHz short pulse trains are generated based on parametric process in highly-nonlinear fiber (HNLF). By launching a pulsed pump and three-channel continuous wave (CW) lights into 1-km HNLF, three-channel signals are amplified and three-channel idlers are generated. The waveforms of the generated 80-GHz short pulses are measured by an auto-correlator. The bit-error-rate (BER) of each channel is analyzed numerically. In the back-to-back case, the power penalties of the generated channels are less than 1.5-dB.     

Priority-based parameter optimization strategy for reducing the effects of four-wave mixing on WDM system

In order to meet the ultra high speed and ultra long-haul transmission distance in wavelength division multiplexing (WDM) systems, the nonlinear impairment affecting the overall spectral efficiency and system performance should be minimized. This paper proposes a strategy to mitigate the four-wave mixing (FWM) effect in WDM system. The strategy determines the effect of both single and combined effects of second, third, and fourth optimization priority parameters such as fiber length, input power, dispersion, channel spacing, and effective area on FWM power. A comparison study was made under different types of optical fiber such as single-mode fiber (SMF), dispersion shifted fiber, non-zero dispersion fiber, and non-zero dispersion shifted fiber. In addition, the system performance in term of bit-error-rate was calculated in the case of single priority (impact of effective area) and combined priority (impact of effective area, input power, fiber length and channel spacing). The results show that the FWM effect was reduced based on the transmission parameters order of optimization, i.e., priority selection proposed. Moreover, the results indicated that increasing sequentially the effective area, fiber length; channel spacing and decreasing the input power provide the most significant sequence in suppressing the effects of FWM. This priority sequence brought the suppression ratio to approximately 26.3% in SMF, which suppressed the FWM effects up to −50 dBm. In term of BER; the combined priority introduces improvement in BER of 2.31 × 10⁻²⁵ in comparison with single priority that has value of BER 4 × 10⁻¹⁴. Finally, this work suggests that the proposed priority-based parameter optimization strategy is an ideal solution for optimum performance of WDM system.     

Four-wave mixing self-stability based on photonic crystal fiber and its applications on erbium-doped fiber lasers

The analytic solutions of coupled-mode equations of four-wave mixings (FWMs) are achieved by means of the undepleted approximation and the perturbation method. The self-stability mechanism of the FWM processes is theoretically proved and is applicable to design a new kind of triple-wavelength erbium-doped fiber lasers. The proposed fiber lasers with excellent stability and uniformity are demonstrated by using a flat-near-zero-dispersion high-nonlinear photonic-crystal-fiber. The significant excellence is analyzed in theory and is proved in experiment. Our fiber lasers can stably lase three waves with the power ripple of less than 0.4 dB.     

Demonstration of an all-optical switching operation using an optical fiber grating coupler

An optical fiber grating coupler (FGC) is a fused optical fiber coupler with a tapered region in which refractive index-modulated gratings are written. In the FGC, the light with specific wavelength satisfying the Bragg condition of the grating can be dropped to one output port and other lights are transmitted to another output port when lights with various wavelengths are launched into the input port. The FGC can operate as an all-optical switch by controlling the Bragg wavelength of the grating using a third order nonlinear optical effect caused by a control light that are launched with a signal light. In this paper, an all-optical switching operation due to a third order nonlinear optical effect in an FGC is first demonstrated for a signal light with 1.55 μm-wavelength to be changed from one port of the FGC to another one by the 720 W peak of a control light from a Nd:YAG laser with 1.06 μm-wavelength. The switching efficiency obtained was 7%. It was clarified that a longer pulse length of the control light compared to the grating length is required to obtain a large Bragg wavelength shift for the switching. It was also clarified that the Bragg wavelength shift is caused by a third order nonlinear effect and a photothermal effect. A contribution of the photothermal effect was estimated. We also estimated the switching efficiency for pump power in the FGC switch.     

Simultaneous measurements of non-linear coefficient, zero-dispersion wavelength and chromatic dispersion in dispersion-shifted fibers by four-wave mixing

We report on a new simple technique for the simultaneous measurement of non-linear coefficient, zero-dispersion wavelength, and chromatic dispersion in dispersion-shifted fibers based on partially degenerated four-wave mixing. Both zero-dispersion wavelength and chromatic dispersion of the dispersion-shifted fibers can be measured with high accuracy. The experiment results of two dispersion-shifted fibers will be presented and the technique for obtaining accurate chromatic dispersion and zero-dispersion wavelength will also be discussed.