Intermodal Cross-phase Modulation Research Articles

Spatially multiplexed picosecond pulse-train generations through simultaneous intra-modal four wave mixing and inter-modal cross-phase modulation

We report on the experimental generation of spatially multiplexed picosecond 40 GHz pulse trains at telecommunication wavelengths by simultaneous intra-modal multiple four wave mixing and inter-modal cross-phase modulation in km-long bi-modal and 6-LP-mode graded-index few-mode fibers. More precisely, an initial beat-signal injected into the fundamental mode is first nonlinearly compressed into well-separated pulses by means of an intra-modal multiple four-wave mixing process, while several group-velocity matched continuous-wave probe signals are injected into higher-order modes in such a way to develop similar pulsed profile thanks to an inter-modal cross-phase modulation interaction. Specifically, by simultaneously exciting three higher-order modes (LP11, LP02 and LP31) of a 6-LP-mode fiber along group-velocity matched wavelengths with the fundamental mode, four spatially multiplexed 40 GHz picosecond pulse-trains are generated at selective wavelengths with negligible cross-talks between all the modes.

Modulation instability induced by intermodal cross-phase modulation in step-index multimode fiber.

Based on linear stability analysis, we theoretically investigate the onset condition and gain spectrum of intermodal cross-phase modulation-induced noise-seeded modulation instability taking place in the normal dispersion regime of step-index multimode fiber, specially designed to support four modes (LP01, LP11, LP21, LP02) at 1064nm. For the case of total power being distributed equally in certain bimodal combinations, the peak sideband frequency scales as the square root of total power, and peak gain increases linearly with total power. For the case of total power being distributed unequally, there exists an optimal power ratio to obtain peak gain, which does not depend on total power significantly. When the mode group velocity mismatch is considered, the range and peak values of gain spectra are notably increased.

Inline measurement of modal phase differences for the characterization of intermodal cross-phase modulation

We present an inline measurement technique for the phase difference between two transverse fiber modes. This technique proves to be well suited for direct measurement of an all-optically changed phase difference between two transverse modes of picosecond probe pulses, induced via intermodal cross-phase modulation by co-propagating picosecond control pulses. We achieved unprecedented agreement with the corresponding analytical description for time-independent changes of the phase difference as well as for time-dependent changes on an intra-pulse timescale. The simple and accurate predictability combined with the ability to measure modal phase differences inline poses a key step towards full all-optical control over transverse modes in fibers. This may lead the way to a variety of novel functionalities for all-fiber applications, like a spatial degree of freedom in fiber-sensing technology by using transverse fiber modes or all-optical spatial and temporal pulse shaping inside a fiber.

Intermodal cross-phase modulation enabling all-optical temporal and spatial shaping in few-mode fibers

We present a concept using intermodal cross-phase modulation to enable all-optical temporal, spatial, and spatio-temporal pulse shaping inside a few-mode fiber. The pulse shaping is achieved by all-optically tuning a fiber-based, inline Mach–Zehnder interferometer, which uses two transverse modes of the fiber as interferometer pathways and long-period gratings for mode coupling. We explore the shaping capabilities of such a two-mode Mach–Zehnder interferometer and compare simulations based on the multimode generalized nonlinear Schrodinger equation to a simplified model based on the analytical description of intermodal cross-phase modulation. Such an approximated description reduces computation times from hours to less than a minute and proves to be valid for most scenarios, enabling fast and easy prediction of the shaping functionality in such devices.

Low-power broadband all-optical switching via intermodal cross-phase modulation in integrated optical waveguides.

We demonstrate the potential of all-optical switches in integrated waveguides based on intermodal cross-phase modulation between transverse modes. For this purpose, the differential phase between two transverse modes of a probe beam was altered by cross-phase modulation with a control beam propagating only in the fundamental mode. A switching behavior was accomplished by spatially filtering the resulting multimode interference of the probe modes, which changed depending on the control beam power. All-optical switching with a contrast of 82% at 1280nm over a frequency range of 4.4THz at 1.6nJ was achieved, representing an improvement of the product of necessary power and waveguide length by a factor of nearly 2000 compared to similar experiments in graded-index fibers. Additionally, we show that the center wavelength of the switch can be tailored by changing the cross-sectional geometry of the waveguide or the involved probe modes.

Ultrafast, all-optical control of modal phases in a few-mode fiber for all-optical switching.

The phase differences between the transverse modes of an optical fiber can be altered all-optically by intermodal cross-phase modulation. In this Letter, we experimentally demonstrate this effect with ultrashort laser pulses. An ultrashort probe pulse, guided in both modes of a two-mode fiber, is co-propagating and temporally overlapping with an ultrashort control pulse, guided in the fundamental mode only and centered at a separate wavelength. The use of ultrashort pulses allows for a notable phase shift at a 33-fold reduced control pulse energy and a 173-fold reduced fiber length, compared to previous experiments. A total phase shift of 0.285π between the two probe modes was achieved at a 9 nJ control pulse energy in a 19 cm long two-mode graded-index fiber. Additionally, the capability of this scheme to switch ultrashort pulses in an all-optical manner was investigated. A modulation depth of 50% was achieved, limited by temporal nonlinear effects.

Experimental Observation of Inter-Modal Cross-Phase Modulation in Few-Mode Fibers

We experimentally demonstrate a broadband nonlinear interaction between a data-modulated pump and an unmodulated probe occupying different spatial modes of a few-mode fiber. This nonlinear interaction is attributed to inter-modal cross-phase modulation (IM-XPM) and found to be maximum when signal and probe have similar group velocities. This can correspond to a few THz of wavelength separation between waves. The magnitude of the measured IM-XPM is found to be comparable to the measured intra-modal XPM with similar nonlinear coefficients. A comparison to a semi-analytical model of XPM shows good agreement with the measurements.