Ultrashort pulse propagation and nonlinear frequency conversion in superconducting and magnetic photonic crystal C. H. Raymond Ooi • Choo Yong Lee Received: 6 January 2013 / Accepted: 12 March 2013 Ó Springer-Verlag Berlin Heidelberg 2013 Abstract We study the propagation and second harmonic generation of ultrashort pulse in nonlinear photonic crystal using a combination of Fourier transform and transfer matrix method. The focus is on the reflected and transmitted output of fundamental pump pulse and second harmonic pulse in frequency and time domains, the temperature dependence of the reflection and transmission spectra where the supercon- ducting transition frequency is close to the magnetic reso- nance. Interesting features include output pump and second harmonic pulses that can be strongly modulated with the transmitted pulses being delayed by slow light effect. 1 Introduction Photonic crystal structures can control the propagation of electromagnetic wave [1] and play an important role in developing various optical devices [2]. The multiple reflections of electromagnetic wave at the layer interface in one-dimensional photonic crystal lead to forbidden (pho- tonic bandgap) region where electromagnetic field is reflected and strongly damped (evanescent wave) within the structure [3, 4]. Second harmonic generation (SHG) is important for generating higher frequency waves [5]. Pulsed SHG in one -imensional photonic band gap material doped with v ð2Þ medium has been demonstrated [6]. SHG in metal and antiferromagnetic thin film has also been studied [7, 8]. Zhou et al. [9] also investigated SHG from antiferromagnetic film embedded in one-dimensional photonic crystal. It is shown that strong SHG would occur near photonic band edge [10]. In silicon photonic, second- and third-order susceptibilities are used to convert wavelengths in optical communication [11]. In many cases, phased matching is an important factor contributing to SHG enhancement. There are various approaches to enhance SHG in photonic crystal. One method is by using periodically poled photonic crystal [5, 12, 13]. Other methods use defect or cavity quantum electrodynamic effect[14, 15], disorder structure [16], pumping of slow light [17, 18], controlling of pump beam intensity [19] and introduction of Bragg reflector mirrors [20] in which strong localization of fundamental field (FF) enhances coupling of waves in v ð2Þ medium. Normally semiconductor or dielectric materials are used. Superconductor has not been used in nonlinear pho- tonic crystal. The presence of bandgap at low-frequency region and its tunability with temperature make supercon- ductor an attractive material for engineering optothermal devices for pulses in the far infrared (FIR) region. The two- fluid model [21, 22] provides a convenient description for investigation of band structure in superconducting photonic crystal [23]. Recently, optical properties of super- conductor-ferromagnetic bilayer structure [24] have been studied using the two-fluid model. Nonlinear PC introduces strong dispersion for spectral broadening and strong nonlinearity which enables pulse shaping and light-control-light functionality. Recent work shows SHG in periodically poled lithium niobate wave- guide driven by femtosecond laser pulses [25]. Besides, generation of ultrashort pulse in organic crystal has been demonstrated in the range of 10–30 THz [26]. Split ring resonator [27] and thin wire array [28] can be used to yield frequency-dependent magnetic permeability and permit- tivity. The feasibility of SHG in metamaterials has been demonstrated [29, 30]. C. H. R. Ooi (&)  C. Y. Lee Department of Physics, University of Malaya, 50603 Kuala Lumpur, Malaysia e-mail: rooi@um.edu.my 123 Appl. Phys. B DOI 10.1007/s00340-013-5417-2