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.     

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.     

Theory of pulse propagation and four-wave mixing in a quantum dot semiconductor optical amplifier

A theory, combining the relations of pulse traveling into quantum dot (QD) semiconductor optical amplifier (SOA) with the four-wave mixing (FWM) theory in these SOAs, is developed. Carrier density pulsation (CDP), carrier heating (CH), and spectral hole burning (SHB) contributions on FWM efficiency are discussed. Effect of QD ground state and wetting layer are included. An additional parameter appears in the gain integral relation of QD SOAs. An equation formulating pulses in the QD SOAs is introduced. We have found that FWM in QD SOAs is detuning and is pulse width dependent. For short pulses, CH is dominant at high detunings (10–100 GHz) while at higher detunings (>100 GHz) the SHB is the dominant one. Undesired paunch behavior is shown in QD SOAs then, CDP must be reduced.     

Quantum cascade structure for mid-IR four-wave mixing

The design and modeling of a quantum cascade optical amplifier (QCOA) using intra-cavity non-linear interactions to achieve wavelength conversion is proposed. The model is based on the nonlinear equation coupled with Maxwell wave equations for different emission modes. In the proposed structure, four wave mixing (FWM) output exhibits a peak as a function of pump and probe frequency if they are tuned to the energy levels of the QC structure subbands. Results demonstrate that the FWM output signal power significantly depends on how subbands are engineered and interact with optical pulses which propagate in multi layer medium. In addition, we show that by adjusting pump and probe signal frequencies, FWM output power can be tuned.     

Optical absorptions of an exciton in a disc-like quantum dot under an electric field

An exciton in a disc-like quantum dot (QD) with the parabolic confinement, under applied electric field, is studied within the framework of the effective-mass approximation. Both the electric field and the confinement effects on the transition energy and the oscillator strength were investigated. Based on the computed energies and wave functions, the linear, the third-order nonlinear and the total optical absorption coefficients were also calculated. We found that the optical absorption coefficients with considering excitonic effects are stronger than those without considering excitonic effects and the absorption peak will move to the right side induced by the electron-hole interaction, which shows an excitonic effect blue-shift of the resonance in QDs. The applied electric field may affect either the size or the position of absorption peaks of excitons. However, the applied electric field may only affect the size of absorption peaks of an electron-hole pair without considering excitonic effects. It is very important to take excitonic effects into account when we study the optical absorption for disc-like QDs. We may observe the excitonic effect induced by the external electric field.     

Reduction to the Fock state via a degenerate four-wave mixing

A scheme to generate the Fock state via a degenerate four-wave mixing and partial measurement is proposed. A conditional state of the signal mode of a degenerate four-wave mixer will be shown to reduce to the Fock state when the outcome of the measurement on the reference mode satisfies a certain condition. The photon number of the Fock state is distributed when the measurement is repeated many times. Conditioning for the quantum state of the signal mode is carried out by the photon counting measurement on the reference mode whose input state is assumed to be the vacuum. The phase coherence of the conditional signal state is also considered. Furthermore conditioning for the signal mode by means of heterodyne and homodyne detections are briefly considered.     

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.     

The nonlinear optical rectification of a confined exciton in a quantum dot

An exciton in a disc-like quantum dot (QD) with the parabolic confinement, under applied electric field, is studied within the framework of the effective-mass approximation. The nonlinear optical rectification between the ground and the first-excited states has been examined through the computed energies and wave functions in details for the excitons. The results show that the optical rectification susceptibility obtained in a disc-like QD reach the magnitude of 10⁻² m/V, which is 3-4 orders of magnitude higher than in one-dimensional QDs. It is found that the second-order nonlinear optical properties of exciton states in a QD are strongly affected by the confinement strength and the electric field.     

Optical absorptions of an exciton in a quantum ring: Effect of the repulsive core

We study the optical absorptions of an exciton in a quantum ring. The quantum ring is described as a circular quantum dot with a repulsive core. The advantage of our methodology is that one can investigate the influence of the repulsive core by varying two parameters in the confinement potential. The linear, third-order nonlinear and total optical absorption coefficients have been examined with the change of the confinement potential. The results show that the optical absorptions are strongly affected by the repulsive core. Moreover, the repulsive core can influence the oscillation in the resonant peak of the absorption coefficients.     

Impurity and exciton effects on the nonlinear optical properties of a disc-like quantum dot under a magnetic field

A detailed investigation of the nonlinear optical properties of the (D⁺, X) complex in a disc-like quantum dot (QD) with the parabolic confinement, under applied magnetic field, has been carried by using the perturbation method and the compact density-matrix approach. The linear and nonlinear optical absorption coefficients between the ground (L = 0) and the first excited state (L = 1) have been examined based on the computed energies and wave functions. The competition between the confinement and correlation effects on the one hand, and the magnetic field effects on the other hand, is also discussed. The results show that the confinement strength of QDs and the intensity of the illumination have drastic effects on the nonlinear optical properties. In addition, we note that the absorption coefficients of an exciton in QDs depend strongly on the impurity but weakly on the magnetic field. Furthermore, the light and heavy hole excitons should be taken into account when we study the optical properties of an exciton in a disc-like QD.     

Excited state absorptions of an exciton bound to an ionized donor impurity in quantum dots

An investigation of an exciton bound in a parabolic two dimensional quantum dot by a donor impurity has been carried out by using the matrix diagonalization method and the compact density-matrix approach. The linear, third-order nonlinear, total optical absorption coefficients and refractive index changes have been calculated for the s-p, p-d, and d-f transitions. The results show that the parabolic potential has a great effect on the optical absorptions. The calculated results also reveal that as the angular momentum quantum numbers of transitions increase, the optical absorption and refractive index peaks shift towards lower energies and the absorption and refractive index intensities increase.     

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.     

Coherent dynamics in InGaAs quantum dots and quantum dot molecules

We measure the dephasing time of the exciton ground state transition in InGaAs quantum dots (QD) and quantum dot molecules (QDM) using a sensitive four-wave mixing technique. In the QDs we find experimental evidence that the dephasing time is given only by the radiative lifetime at low temperatures. We demonstrate the tunability of the radiatively limited dephasing time from 400 ps up to 2 ns in a series of annealed QDs with increasing energy separation of 69–330 meV from the wetting layer continuum. Furthermore, the distribution of the fine-structure splitting δ₁ and of the biexciton binding energy δ_B is measured. δ₁ decreases from 96 to with increasing annealing temperature, indicating an improving circular symmetry of the in-plane confinement potential. The biexciton binding energy shows only a weak dependence on the confinement energy, which we attribute to a compensation between decreasing confinement and decreasing separation of electron and hole. In the QDM we measured the exciton dephasing as function of interdot barrier thickness in the temperature range from 5 to 60 K. At 5 K dephasing times of several hundred picoseconds are found. Moreover, a systematic dependence of the dephasing dynamics on the barrier thickness is observed, showing how the quantum mechanical coupling in the molecules affects the exciton lifetime and acoustic-phonon interaction.     

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.     

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.     

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.     

Combined effects of hydrostatic pressure and temperature on nonlinear properties of an exciton in a spherical quantum dot under the applied electric field

Within the framework of the effective-mass approximation, we have calculated the combined effects of hydrostatic pressure, temperature and applied electric field on an exciton confined in a typical GaAs/Ga_0.7Al_0.3As quantum dot. Several inputs of the confinement potential, hydrostatic pressure, temperature, and applied electric field have been considered. Our findings suggest that (1) the effect of the confinement strength is dominant over the electric field effect, (2) the oscillator strength is an increasing function of the hydrostatic pressure, (3) the absorption coefficients and energy difference depend strongly on the hydrostatic pressure but weakly on the temperature, (4) the absorption coefficients with considering excitonic effects are stronger than those without considering excitonic effects and the absorption peak will move to the right side induced by the electron-hole interaction, (5) the applied electric field may effect either the size or the position of absorption peaks of excitons.     

Electric field effect on the second-order nonlinear optical properties in semiparabolic quantum wells

Electric field effect on the second-order nonlinear optical properties in semiparabolic quantum wells are studied theoretically. Both the second-harmonic generation susceptibility and nonlinear optical rectification depend dramatically on the direction and the strength of the electric field. Numerical results show that both the second-harmonic generation susceptibility and nonlinear optical rectification are always weakened as the electric field increases where the direction of the electric field is along the growth direction of the quantum wells, which is in contrast to the conventional case. However, the second-harmonic generation susceptibility is weakened, but the nonlinear optical rectification is strengthened as the electric field increases where the direction of the electric field is against the growth direction of the quantum wells. Also it is the blue (or red) shift of the resonance that is induced by increasing of the electric field when the direction of the electric field is along (or against) the growth direction of the quantum wells. Finally, the resonant peak and its corresponding to the resonant energy are also taken into account.     

Intense laser effects on nonlinear optical absorption and optical rectification in single quantum wells under applied electric and magnetic field

In this work the effects of intense laser on the electron-related nonlinear optical absorption and nonlinear optical rectification in GaAs-Ga_1−xAl_xAs quantum wells are studied under, applied electric and magnetic field. The electric field is applied along the growth direction of the quantum well whereas the magnetic field has been considered to be in-plane. The calculations were performed within the density matrix formalism with the use of the effective mass and parabolic band approximations. The intense laser effects are included through the Floquet method, by modifying the confining potential associated to the heterostructure. Results are presented for the nonlinear optical absorption, the nonlinear optical rectification and the resonant peak of these two optical processes. Several configurations of the dimensions of the quantum well, the applied electric and magnetic fields, and the incident intense laser radiation have been considered. The outcome of the calculation suggests that the nonlinear optical absorption and optical rectification are non-monotonic functions of the dimensions of the heterostructure and of the external perturbations considered in this work.