1.1 Photonic Crystal Fibers
The research of photonic crystal fibers (PCFs) started as early as in the 70’s [1].
However, its impact was not prominent until the 90’s when the technology was able to fabricate the perfect structures of PCFs. The great flexibility in the design of PCFs led to tremendous progress in various domains such as optical frequency metrology, sensor technology, medical science, and telecommunications [2-6].
Photonic crystal fibers [7-9] can be classified into two categories: microstructured fibers (MFs) and photonic bandgap fibers (PBFs). Figure 1.1 shows the MF in which its solid core is surrounded by an array of air holes. Due to its higher refractive index of the core than the cladding, the MF can guide light as the standard fibers by the principle of the total internal reflection.
Fig. 1.1 The scheme of the microstructured fiber. d is the diameter of the air holes and Λ is the pitch, the distance between the two air holes.
The dispersion profile of MFs strongly depends on the air-filling fraction and core size. For example, increasing the air-filling fraction and reducing the size of the core allows for a drastic increase of the waveguide dispersion, thus enabling to shift
the zero-dispersion wavelength of MFs to below 800 nm [10]. The dispersion is then anomalous at visible wavelengths and soliton propagation becomes possible for this range of wavelengths. A shift of the zero-dispersion wavelength to any value from 500 nm to 1500 nm can be obtained in MFs. Furthermore, by choosing the appropriate air-hole size and pitch, it is possible to fabricate MFs that exhibit very low and flat dispersion over a relatively broad wavelength range [11-13].
PBFs are the fibers which guide light in their hollow core. Figure 1.2 shows the scheme of PBFs. In PBFs, the periodic arrangement of the air holes can be seen as the photonic bandgap structure and their hollow core is the defect inside the structure.
The photonic bandgap structure will result in a bandgap which allows only certain range of wavelength exiting in it. Outside this range, PBFs is anti-guiding.
Guiding light in a hollow core holds many promising applications like high power delivery without the risk of fiber damage, gas sensors or extreme low loss guidance in vacuum. Furthermore, they are almost insensitive to bending (even at very small bending radii) and have extreme dispersion properties, such as anomalous dispersion values in the thousands of ps/nm/km regime are easily obtained. Due to a negligible contribution from the core material (air), the total dispersion of PBG fibers is to a high degree dominated by waveguide dispersion.
Fig. 1.2 The scheme of photonic bandgap fibers (PBFs). Light is guided in the air-core of PBFs.
1.2 Supercontinuum Generation
Supercontinuum (SC) generation is formation of broad continuous spectra by propagation of high power pulses through nonlinear media [14]. Provided enough power, SC generation can be observed in a drop of water [15]. However, the nonlinear effects involved in the spectral broadening are highly dependent on the dispersion of the media; and a clever dispersion design can significantly reduce the power required. The widest spectra are obtained when the pump pulses are launched close to the zero-dispersion wavelength of the nonlinear media. Due to the technology which can fabricate the shiftable dispersion profile and small core MFs, MFs become powerful tools to generate the SC and was first demonstrated in 1999 [16]. The zero-dispersion wavelength of MFs can be shifted close to the pumping wavelength and the small core of MFs enhances the nonlinear effects, mechanisms leading to the SC.
To generate the SC with MFs, femtosecond [17][18] and picosecond mode-locked laser systems were generally used as the pumping sources [19]. For femtosecond pumping, it’s easily to get higher peak power of the pumping pulse due to its short pulse duration and therefore to induce strong nonlinear effects. These nonlinear effects include high-order soliton breakup [20][21], self-frequency shift [22] and four-wave mixing [23]. Usually about mini-watts of average pumping power are needed to generate the supercontinuum for a femtosecond mode-locked laser system [18]. However, a femtosecond mode-locked laser system is more expensive and complex to build. A picosecond mode-locked laser system is a better way to choose.
For picosecond pumping, the major nonlinear effects for spectrum broadening are modulation instability and stimulated Raman scattering if it is pumped in the anomalous dispersion region, where the group-velocity dispersion β2 is negative. In
2002, Mickael Seefeldt reported the SC from 700 nm to 1600 nm with an average input power of 5.0 W using passively mode-locked Nd:YVO4 which generated a pulse width of 10 ps. [19] Compared with femtosecond pumping, an average power up to several watts should be needed to generate sufficient supercontinuum for picosecond pumping. It is due to its longer duration of pulse width. Therefore, a higher average power is necessary to get enough pumping peak power.
1.3 Motivation
To enhance the effect of the SC, a simple way is to increase the pumping peak power. In our passively mode-locked Nd:GdVO4 laser system which can generate a pulse width of 15 ps, the peak power of Q-switched mode-locked (QML) state is about 14 times higher than that of CW mode-locked state (CML). We can utilize this characteristic to strengthen the nonlinear optical effects for the SC.
1.4 Organization of this Thesis
In Chapter 2, we will introduce the theory of SC. The content describes several nonlinear effects and the nonlinear Schrödinger equation, a general equation presenting the nonlinear phenomenon. In Chapter 3, we will describe how to simulate the nonlinear Schrödinger equation. Then, we will introduce our experiment, including the pumping laser system, the specification of our MF and the experimental setup in Chapter 4. Chapter 5 is the experiment results and discussion.
We will compare the experiments results with the numerical results in this chapter.
Finally, we will give a conclusion and the future works in Chapter 6. Appendix will show how to simulate the dispersion of the fiber using “Mode solutions”, software
made by Lumerical.