Generation of a train of ultrashort pulses through the propagation of periodic wave in photonic crystal fibres

Atuba, Sunday

Abstract

This thesis presents a study of nonlinear optical phenomena of ultrashort pulse dynamics in photonic crystal fibre (PCF), using analytical and numerical analyses. For complete description of this process, we consider the technique of pulse compression using PCF to generate trains of ultrashort pulses (USP). First, we start by presenting an overview on optical fibre theory and also discuss the highly nonlinear fibre with emphasis on PCF. The various techniques whereby pulse compression and high repetition rate sources can be achieved were also considered. The significance and characteristics of nonlinear optical effects like modulational instability and optical wave breaking are reported. Some insights on optical solitons are also shown, as this concept governs the idea behind pulse compression in PCF.
Until recently, the approach to realising USPs have been the usual trend of single-pulse compression. With the daily rise of internet traffic and applications, the need for different ways and means for increasing the bandwidth has attracted greater attention.
It is a known fact that the repetition rate of an optical pulse does have a direct impact on the bit rate of the communication systems, which in turn is related to the bandwidth.
Hence, several attempts have been made to use a train of USPs obtained from a continuous wave (CW) source. This is quite often referred to as multisoliton pulse compression.
As a direct result of this data rate rise, the source requirements on the quality of pulse and repetition rate have become very stringent, and the eventual limits of conventional laser sources, e.g., mode-locked fibre lasers, are fast being approached. The development of an alternative approach, which is based on the beating of a dual-frequency signal and subsequent compression in a nonlinear fibre with exponential decreasing dispersion, has been achieved. Using this scheme, higher frequencies (> 200 GHz) can be obtained. Therefore, in this work, we propose a high-repetition rate source based on the beating of a dual-frequency signal and a subsequent compression of pulse train using adiabatic compression in a dispersion-decreasing PCF having a periodic wave profile. This profile is described in the form of Jacobian elliptic functions (JEF). The uniqueness of this approach is that we can propagate a train of compressed pulses continuously in the PCF. This cannot be realised if a pulse of hyperbolic secant profile solutions are co-propagated together. Hence, the repetition rate of these pulses is determined by the frequency separation of the two initial continuous wave (CW) signals, and one can realise a very large beat frequency, even 1 THz.
For the first compression technique investigated, we consider a nonlinear Schrödinger wave equation (NLSE) having only an exponentially varying dispersion and nonlinearity parameters, together with a constant gain throughout its longitudinal distance. We obtained exact solutions by employing an analytical approach. This approach involves transforming the NLSE by using the Hirota bilinear transformation (HBT) method and substituting theta functions as dependent parameters into the equations to obtain a set of exact periodic wave solutions in the form of JEF of sn, cn, and dn types. We design a PCF whose air hole size and pitch vary exponentially as a result of tapering. The pulse compression studies for 1550 nm using adiabatic pulse compression with our designed tapered PCF whose dispersion and nonlinearity vary along the propagation direction. Compression factors of over 10,000 can be realised using this technique when 0.8 ps pulses were compressed to generate 75 as by passing them through a 100 m long PCF. We demonstrate numerically the formation of a 1.25 THz train of 75-as pulses by coupling two CWs from two laser diodes. The pulses have negligible pedestal. For purposes of speed, simplicity, and completeness, a program code that generates these chirped periodic waves was developed. We further observed that many other exact solutions could be obtained for our NLSE when we exponentially vary the dispersion and nonlinearity along the negative and positive regimes while maintaining a constant gain. With this, we were able to observe not only the pulse compression phenomenon but also the spectral compression phenomenon. For these new exponentially varying cases, we designed PCF to study the various pulse train dynamics. In order to verify and also match the exact solution results obtained via the HBT approach, we solved the NLSE using the self-similar analysis technique (SSA). This SSA technique was then used to find exact periodic wave solutions to the NLSE whose dispersion, nonlinearity, and gain vary along the propagation distance. This general case is referred to as an inhomogeneous NLSE. Furthermore, to investigate compression of a single pulse in the PCF, we made use of the Lagrangian variational technique in a tapered photonic crystal fibre having periodic wave ansatz of dn- and cn-waves. The results obtained using this method show a good agreement along the fibre length for the pulse parameter and also exhibit a high compression factor.
All the results reported in this thesis on pulse compression using PCF show that our designed PCF is quite efficient and robust for generating trains of ultrashort pulses.

• Thesis Type: Thesis
• Deposit Date: Jul 7, 2025
• Public URL: https://uwe-repository.worktribe.com/output/14681558
• Award Date: Nov 24, 2017