REVIEW ARTICLE Dispersive wave generation in supercontinuum process inside nonlinear microstructured fibre Samudra Roy1,3, Shyamal K. Bhadra1,* and Govind P. Agrawal2 1Fiber Optics and Photonics Division, Central Glass and Ceramic Research Institute (CSIR), 196 Raja S.C. Mullick Road, Kolkata 700 032, India 2Institute of Optics and Department of Physics and Astronomy, University of Rochester, New York, 14627, USA 3Present address: Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan gating through a nonlinear medium experiences extreme The presence of higher order dispersion leads to the transfer of energy from soliton to dispersive waves spectral broadening. Owing to its broad and continuous spectrum, such extreme spectral broadening is generally (DWs: also called non-solitonic radiation), which play 1,2 a significant role in blue-component generation in the called supercontinuum (SC) . The generation of white supercontinuum (SC) process. The frequency of DWs laser in terms of SC is an important phenomenon having is controlled by the general phase-matching condition great physical implications. It certainly offers novel solu- requiring that DWs propagate with the same phase tions in the field of optical communication, coherent velocity as that of the soliton. In the present study, the tomography, multiplex light sources for nonlinear spectro- generation of DWs in the SC process inside the non- scopy, biomedical lasers, etc.3. The mechanism of SC gene- linear microstructured fibre/photonic crystal fibre is ration is mainly dominated by soliton dynamics when a explored under different operational conditions. The femtosecond pulse is used as a pump, whereas four wave role of third, fourth and other higher order dispersions mixing (FWM) and nonlinear Kerr effect are considered on the generation and control of DWs is described using numerical solution of generalized nonlinear to be the most important processes in SC generation for Schrödinger equation. The study reveals several wider (pico or nanosecond) input pulses. In both the cases important facts such as all positive, even-order disper- higher-order dispersions (HODs) play a significant role in sion terms always generate dual radiation and all odd- modulating and controlling the spectrum. At this point it order dispersion produces single radiation. Even the is pertinent to mention that in recent years photonic crystal numeric sign of the dispersion coefficient modulates fibre (PCF) has come out to be an excellent medium to the non-solitonic radiations dramatically. A more gen- support the phenomenon of SC generation owing to its eral study unfolds that dispersion profile of a specific high nonlinearity and flexible dispersion properties. The fibre can control the generation of DWs; in fact, the phenomenon of soliton dynamics is primarily involved in zero dispersion points turn out to be excellent predic- the SC generation process when the optical pulse is tors of the number of radiation peaks being generated. pumped in an anomalous dispersion regime. The interplay It is also demonstrated that with proper tailoring of dispersion profile of nonlinear medium, it is possible between nonlinearity and dispersion may produce stable to generate dual radiation in the same side of the pulse propagation in terms of optical soliton which does input pulse in frequency domain. Here we have con- not change its shape in time and spectral domain during 4 sidered the case of a highly nonlinear photonic crystal propagation . The increment of input power makes the optical fibre. Further, it is observed that DWs can still stable propagation periodic over distance. This is a feature be generated when the pump frequency falls on the of higher order soliton, where input pulse evolves peri- normal dispersion domain. Finally the validity of the odically both in time and spectral domain4. However, proposed theory is established through experimental under realistic condition the higher order nonlinear and verification. dispersive effects disrupt this stable periodic evolution and split the soliton into its components through the fis- Keywords: Dispersive waves, optical solitons, photonic sion process5. During the fission process, the presence of crystal fibres, supercontinuum generation. higher order dispersions lead to transfer of energy from soliton to narrow band resonance and associate a low 6 SPECTRAL broadening and the generation of new fre- amplitude temporal pedestal . The radiation of dispersive quency components are the intrinsic features of nonlinear waves (DWs) is also known as non-solitonic radiation optics. Because of these novel characteristics of nonlinear (NSR) because generally its wavelength falls on the optics, it is possible to produce an artificial white light normal dispersion domain where optical soliton ceases to with unique spectral properties having high brightness. exist1,2. The frequency of the radiation emitted by the Under such a process an ultra short optical pulse propa- soliton in terms of DWs can readily be obtained from a phase-matching condition involving the linear and *For correspondence. (e-mail: [email protected]) nonlinear phase change of the soliton and associated CURRENT SCIENCE, VOL. 100, NO. 3, 10 FEBRUARY 2011 321 REVIEW ARTICLE continuous wave7. The generation of DWs is physically rounded by a periodic array of air-holes running along the important because of their imperative contribution in propagation distance. The presence of the air-holes in the producing visible light during the SC process. The blue or cladding region eventually reduces the effective refrac- UV components of the SC spectra are in fact produced tive index compared to the core silica and light guidance through DWs. However, a suitable combination of HODs occurs through the principle of total internal reflection. may produce radiation even in the higher wavelength side The air-hole diameter (d) and their relative separation (Λ) compared to input pump wavelength. An extensive study offer additional degrees of freedom in tailoring the dis- reveals that all HOD terms individually play a crucial persion property9–11. A careful and properly designed role in generating DWs and more importantly, the growth arrangement of air-holes may produce a unique disper- of the radiation peaks is critically dependent on relative sion profile which is difficult to attain in conventional values of HODs and their numeric signs. fibres. The dispersion in the standard telecom fibre is Because of the significant impact of DWs in SC anomalous at wavelengths larger than 1.3 μm, whereas generation, it requires a complete study which unfolds the one can tailor the anomalous dispersion of PCF in the physical mechanism involved in resonant radiation in the range 0.6–1.3 μm by suitably modulating d and Λ. Stan- form of DWs. Though considerable amount of work has dard numerical process based on finite element method already been done in describing the phenomenon of NSR, (FEM) is generally used to study the dispersion property there is ample scope to discuss elaborately the entire of PCFs12. Owing to the tight confinement of the optical physical processes. Our objective here is to present a uni- field in the small core region, PCF possesses enormous fied discussion on the various aspects of DW generation nonlinearity which is an additional advantage to excite during the SC process. The present review is based on higher order nonlinear effects. Another important aspect theory and extensive numerical simulations that illustrate of PCF is its endlessly single-mode nature in which characteristics of soliton-mediated resonant radiation propagation of higher order modes is not observed even covering a wide range of experimental parameters. More- at short wavelengths. The reported SC generation in over, we perform experiments with self-made PCFs and experiments primarily occurs through the excitation of the results are analysed with the existing theory and nu- the fundamental mode and for this reason in our numeri- merical simulation. We mainly focus on understanding cal simulation we assume propagation only for the the complex process of DW generation and the role of fundamental mode. However, in a recent study SC char- different HODs on its evolution. The present article is acteristics were also examined for multimode fibres by organized in the following fashion. First we briefly discuss generalizing NLSE in femto-second regime13. The disper- about PCF and its properties. Since PCF is believed to be sion property of PCF is crucial in SC generation because the most effective and dynamic nonlinear waveguide in it determines the extent to which different spectral com- order to produce efficient SC, it is pertinent to include a ponents of an ultrashort pulse propagate at different brief discussion on its nonlinear and dispersion proper- group velocities. The identical group velocity of DWs ties. The fundamental aspects of SC generation are then and red-shifted soliton eventually creates a situation described. The role of soliton dynamics in the femtosec- where blue-shifted radiation is trapped, a phenomenon ond regime and the characteristics of experimentally gene- experimentally observed by Nishizawa and Goto14. rated SC are discussed by introducing the generalized The group velocity dispersion (GVD) coefficient of an nonlinear Schrödinger equation (NLSE). In the derivation MOF is defined as follows: we have used the convenient form of dimensionless NLSE. Finally, we elaborately