Electrostrictive contribution to the intensity-dependent refractive index of optical fibers

Performance of digital servos in an optical frequency transfer network

We demonstrate the use of three kinds of flexible digital servos for the stabilization of the optical fiber link, the interferometer temperature, and the polarization of the transmitted light at the remote site, respectively. The main fiber noise cancellation digital servo provides a large phase detection range (∼2¹⁰π radians), automatic relock function, and low cycle-slip rate over a 62 km field-deployed fiber link achieved by utilizing a feedback optical actuator of an acousto-optic modulator fed by a voltage-controlled oscillator. The temperature control and polarization control digital servos enable that the temperature of the interferometer can be stabilized at a stability of 0.01 K and the data uptime is enhanced from 85.5% to 99.9% by implementing the polarization controller. The results demonstrate that the performance of the three digital servos is sufficient for high-precision optical frequency transfer applications and indicates comparable performance to existing analog optical frequency control systems. The full digital controlled optical frequency transfer method demonstrated here provides guidance for the development of a low-cost, low-complexity, and high-reliability optical frequency transfer system.

Robust optical frequency dissemination with a dual-polarization coherent receiver

Frequency dissemination over optical fiber links relies on measuring the phase of fiber-delivered lasers. Phase is extracted from optical beatnotes and the detection fails in case of beatnotes fading due to polarization changes, which strongly limit the reliability and robustness of the dissemination chain. We propose a new method that overcomes this issue, based on a dual-polarization coherent receiver and a dedicated signal processing that we developed on a field programmable gated array. Our method allowed analysis of polarization-induced phase noise from a theoretical and experimental point of view and endless tracking of the optical phase. This removes a major obstacle in the use of optical links for those physics experiments where long measurement times and high reliability are required.

All-fiber cavity dumping

Cavity dumping of an all-fiber laser system is demonstrated. The active element is a pulse-picker with nanosecond rise time consisting of a microstructured fiber with electrically driven internal electrodes. The device is used for intracavity polarization rotation and dumping through a polarization splitter. The optical flux is removed from the cavity within one roundtrip and most of the amplified spontaneous emission, spiking and relaxation oscillation that follow during the gain recovery phase of the laser are blocked from the output signal.

Optoacoustic solitons in Bragg gratings

Optical gap solitons, which exist due to a balance of nonlinearity and dispersion due to a Bragg grating, can couple to acoustic waves through electrostriction. This gives rise to a new species of "gap-acoustic" solitons (GASs), for which we find exact analytic solutions. The GAS consists of an optical pulse similar to the optical gap soliton, dressed by an accompanying phonon pulse. Close to the speed of sound, the phonon component is large. In subsonic (supersonic) solitons, the phonon pulse is a positive (negative) density variation. Coupling to the acoustic field damps the solitons' oscillatory instability, and gives rise to a distinct instability for supersonic solitons, which may make the GAS decelerate and change direction, ultimately making the soliton subsonic.

Direct measurement of frequency and polarization dependences of cross-phase modulation in fibers from high-resolution optical spectra

We present the results of an experiment for frequency and polarization dependence characterization of non-linear cross-phase-modulation (XPM) effects in optical fibers. The measurement technique is based on the direct analysis of high-resolution optical spectra of a signal wave that is phase modulated by an intensity-modulated pump wave. Measurement results provide experimental confirmation of the scalar character, over the whole resonant frequency range, of the electrostrictive contribution to the nonlinear refractive index. Also, the results confirm experimentally the relation describing the polarization dependence of the Kerr contribution to XPM in non-polarization-maintaining fibers.

Optical spatial solitons in soft matter

We predict that spatial self-trapping of light can occur in soft matter encompassing a wide class of new materials such as colloids, foams, gels, fractal aggregates, etc. We develop a general nonlocal theory that allows one to relate the properties of the trapped state of Maxwell equations to the measurable static structure factor of the specific material. We give numerical evidence for stable trapping in fractal aggregates and suggest also the possibility of soliton spectroscopy of soft matter.

Coherence effect on the measurement of optical fiber nonlinear coefficient

We investigated a source coherence effect on the measurement of the optical fiber nonlinear coefficient by use of dual optical frequencies. We produced coherent and incoherent dual optical frequencies with a self-heterodyne Mach-Zehnder interferometer with and without a delay line, respectively. Our measurement results included both an electrostrictive and a Kerr nonlinear coefficient because of the low modulation frequency. Comparing the coherent case with an incoherent case, we obtained a nonlinear coefficient that was more than 3% higher in the coherent case.

Electrostrictive response in single-mode ring-index-profile fibers

We have theoretically investigated, for what is to our knowledge the first time, the electrostrictive response in a single-mode ring-core fiber. We found that the electrostrictive response function differs strongly from those of standard fibers with a Gaussian light-intensity profile.

Measurement of the nonlinear optical response of optical fiber materials by use of spectrally resolved two-beam coupling

We present measurements of the femtosecond nonlinear response of fiber waveguide materials, obtained with spectrally resolved two-beam coupling. This simple but sensitive technique provides all the parameters that characterize the third-order nonlinear optical response, including the dynamics. Measurements are made with nanojoule-energy pulses from a mode-locked Ti:sapphire laser and a few millimeters of waveguide preform, without the need for drawing fiber.

Mode-profile dependence of the electrostrictive response in fibers

The transverse optical intensity profile in fibers affects the efficiency of acoustic mode excitation by the optical field and the subsequent response of the field to the excited acoustic modes. The magnitude of the electrostrictive nonlinear coefficient for a square-top intensity profile will exceed that of a Gaussian profile by a fact of 2. For current fiber designs the range of values for n(2str) at zero frequency is expected to vary from 0.43 to 0.71x10(-16)cm(2)W(-1) based on mode profile alone. The relative contribution of electrostriction to the total nonlinear response (electrostrictive+Kerr) in fibers increases proportionately as the mode profile flattens.

Electrostrictive cross-phase modulation of periodic pulse trains in optical fibers

Electrostriction-induced cross-phase modulation between subsequent bits of a nonreturn-to-zero pulse train in optical fibers leads to nonlinear frequency shifts of opposite sign for the 1's and the 0's. Direct experimental measurements of the electrostrictive and Kerr-induced nonlinear phase shift across the bit profiles agree well with the theoretical modeling.

Continuous-wave measurement of the fiber nonlinear refractive index

We propose a technique for measuring the nonlinear refractive index of fiber based on transmission-coefficient measurements in a fiber Sagnac interferometer. In contrast with traditional methods, the proposed method uses a single optical source operating in cw mode and direct intensity measurement, enabling one to avoid the errors caused by fiber dispersion and uncertainty of spectral peak difference measurements that occur with pulse-based methods. The nonlinear refractive index in 20-mol. % GeO(2) fiber was measured to be (3.1 +/- 0.2) x 10(-16) cm(2) W(-1) at 1064 nm.

Direct measurement of electrostriction in optical fibers

The electrostriction contribution to the nonlinear refractive index in optical fiber was theoretically calculated and measured. Nonlinearity was induced directly by insertion of the optical fiber into an intense external electric field. With this technique both the Kerr and the electrostrictive contributions to the intensity dependence of the nonlinear refractive index in a step-index fiber were measured. Good agreement between calculated and measured values was observed. These results should confirm and explain the differences observed in measurement of n(2) at different bit rates.

Measurement of the frequency response of the electrostrictive nonlinearity in optical fibers

The electrostrictive contribution to the nonlinear refractive index is investigated by use of frequency-dependent cross-phase modulation with a weak unpolarized cw probe wave and a harmonically modulated pump copropagating in optical fibers. Self-delayed homodyne detection is used to measure the amplitude of the sidebands imposed upon the probe wave as a function of pump intensity for pump modulation frequencies from 10 MHz to 1 GHz. The ratio of the electrostrictive nonlinear coefficient to the cross-phase-modulation Kerr coefficient for unpolarized light is measured to be 1.58:1 for a standard step-index single-mode fiber and 0.41:1 for dispersion-shifted fibers, indicating a larger electrostrictive response in silica fibers than previously expected.

Observation of a Raman-induced interpulse phase migration in the propagation of an ultrahigh-bit-rate coherent soliton train

Coherent soliton packets generated in a passively mode-locked fiber laser are transmitted through 23km of dispersion-decreasing fiber. We observe a shift of the phase difference between solitons that is due to intrapulse Raman scattering. We attribute the stability in propagation of these trains to a trade-off between minimizing soliton-soliton interactions by reduction of the pulse width and minimizing this Raman-induced phase migration, which can force the solitons into a deleterious attractive phase relationship. We are thus able to demonstrate the propagation of 177-Gbit/s soliton packets over a distance of 123 soliton periods.