Yuzhe Xiao

Polarization filter characters of the gold-coated and the liquid filled photonic crystal fiber based on surface plasmon resonance

The polarization filter characters of a gold-coated and liquid-filled photonic crystal fiber are studied using the finite element method. Results show that the resonance strength and wavelengths are different in two polarized directions. Filling liquid of refractive index n=1.33 (purified water) in holes in longitudinal direction can increase the loss of core mode polarized in the y-direction around the resonance peak. The resonance strength is much stronger in y-polarized direction than in x-polarized direction. The resonance strength can achieve 508dB/cm in y-polarized direction at the communication wavelength of 1311nm in one of our structures. Moreover, the full width half maximum is only 20nm. Such a small number makes such photonic crystal fibers promising candidate to filter devices. A liquid filled PCF of the small hole in the fiber core is designed and we find that filling liquid increases the resonance strength peak by thirty eight percent for the y-polarized resonance point.

Theory of intermodal four-wave mixing with random linear mode coupling in few-mode fibers.

We study intermodal four-wave mixing (FWM) in few-mode fibers in the presence of birefringence fluctuations and random linear mode coupling. Two different intermodal FWM processes are investigated by including all nonlinear contributions to the phase-matching condition and FWM bandwidth. We find that one of the FWM processes has a much larger bandwidth than the other. We include random linear mode coupling among fiber modes using three different models based on an analysis of the impact of random coupling on differences of propagation constants between modes. We find that random coupling always reduces the FWM efficiency relative to its vale in the absence of linear coupling. The reduction factor is relatively small (about 3 dB) when only a few modes are linearly coupled but can become very large (> 40 dB) when all modes couple strongly. In the limit of a coupling length much shorter than the nonlinear length, intermodal FWM efficiency becomes vanishingly small. These results should prove useful in the context of space-division multiplexing with few-mode and multimode fibers.

Spectral and temporal changes of optical pulses propagating through time-varying linear media

We present universal formulas for the spectral and temporal output optical fields from a linear traveling-wave medium whose refractive index changes during its propagation within the medium. These formulas agree with known changes in central wavelength and energy that are associated with adiabatic wavelength conversion (AWC). Moreover, they reveal new changes to the optical pulses that have not been noticed, such as pulse compression and spectral broadening. Most significantly, we find that AWC alters the pulse power, pulse chirp, and pulse delay. All of these effects depend on whether the central wavelength is blueshifted or redshifted, the first sign of asymmetry to be reported for AWC. These findings impact the applications of AWC to optical signal processing in microphotonic and nanophotonic structures as well as in lightwave systems.

Reflection and transmission of electromagnetic waves at a temporal boundary

We consider propagation of an electromagnetic (EM) wave through a dynamic optical medium whose refractive index varies with time. Specifically, we focus on the reflection and transmission of EM waves from a temporal boundary and clarify the two different physical processes that contribute to them. One process is related to impedance mismatch, while the other results from temporal scaling related to a sudden change in the speed of light at the temporal boundary. Our results show that temporal scaling of the electric field must be considered for light propagation in dynamic media. Numerical solutions of Maxwells equations are in full agreement with our theory.

New approach to pulse propagation in nonlinear dispersive optical media

We develop an intuitive approach for studying propagation of optical pulses through nonlinear dispersive media. Our new approach is based on the impulse response of linear systems, but we extend the impulse response function using a self-consistent time-transformation approach so that it can be applied to nonlinear media as well. Numerical calculations based on our new approach show excellent agreement with the generalized nonlinear Schrodinger equation in the specific case of the Kerr nonlinearity in both the normal and anomalous dispersion regimes. An important feature of our approach is that it works directly with the electric field associated with an optical pulse and can be applied to pulses of arbitrary width. Numerical calculations performed using single-cycle optical pulses show that our results agree with those obtained with the finite-difference time-domain technique using considerably more computing resources.

Nonlinear pulse propagation: A time–transformation approach

We present a time-transformation approach for studying the propagation of optical pulses inside a nonlinear medium. Unlike the conventional way of solving for the slowly varying amplitude of an optical pulse, our new approach maps directly the input electric field to the output one, without making the slowly varying envelope approximation. Conceptually, the time-transformation approach shows that the effect of propagation through a nonlinear medium is to change the relative spacing and duration of various temporal slices of the pulse. These temporal changes manifest as self-phase modulation in the spectral domain and self-steepening in the temporal domain. Our approach agrees with the generalized nonlinear Schrödinger equation for 100 fs pulses and the finite-difference time-domain solution of Maxwells equations for two-cycle pulses, while producing results 20 and 50 times faster, respectively.

All-Optical Semiconductor Optical Amplifier-Based Wavelength Converters With Sub-mW Pumping

We experimentally study the wavelength conversion of 10-Gb/s return-to-zero signal using interband four-wave mixing inside a semiconductor optical amplifier with 10-ps gain-recovery time. Power of the converted signal exceeds that of the original signal for wavelength shifts of up to 8 nm. Our technique is energy efficient as the required input pump power is <; 1 mW . We discuss the observed performance of such a wavelength converter in terms of required pump power, conversion efficiency, and optical signal-to-noise ratio of the converted signal. For an 8-nm wavelength shift, the converted data signal exhibits no Q-factor degradation while having 2.7-dB power gain.

Optical pulse propagation in dynamic Fabry–Perot resonators

We present a simple and intuitive model based on the impulse response of linear electrical systems for describing the propagation of optical pulses through a dynamic Fabry–Perot resonator whose refractive index changes with time. Our model shows that the adiabatic wavelength conversion process in resonators results from a scaling of the round-trip time with index changes. For pulses longer than the cavity round-trip time, we find that more energy can be transferred to the new wavelength when the input pulses are slightly detuned from the cavity resonance and the refractive index does not change too rapidly. In fact, the optimum duration of index changes scales with the photon lifetime of the resonator. We describe the evolution of the shape and spectrum of picosecond pulses inside a resonator under a variety of input conditions and with the magnitude and duration of index variations. We also apply our general theory to the case of pulses whose widths are shorter than the round-trip time and derive an analytical expression for the output field under quite general conditions. This analysis reveals a shifting of the spectral comb as well as compression of the temporal pulse train that depends on the both the magnitude and sign of the index change. Our results should find applications in the area of optical signal processing using resonant photonic structures.

Effect of random linear mode coupling on intermodal four-wave mixing in few-mode fibers

We study numerically intermodal four-wave mixing (IM-FWM) in few-mode fibers including both birefringence fluctuations and random linear coupling. We find that linear mode coupling reduces idler power by 3.5 dB for non-degenerate IM-FWM.

Propagation of few-cycle pulses in nonlinear Kerr media: harmonic generation

We apply the recently developed time-transformation technique to optical pulse propagation in nonlinear Kerr media, and to study carrier-wave shocking and generation of odd-order harmonics.