Tailoring Čerenkov second-harmonic generation in bulk nonlinear photonic crystal

We investigate theoretically the ?erenkov-type second-harmonic generation in two-dimensional bulk nonlinear photonic crystal with longitudinal modulation of the χ((2)) nonlinearity. We show that in this scheme the ?erenkov radiation can be achieved simultaneously at multiple directions with comparable intensities. The angles of emission are controllable by the spatial modulation of the nonlinearity. We propose a design of the periodically poled domain pattern, which maximizes the efficiency of the second-harmonic emission.     

Floquet–Bloch solutions in a sawtooth photonic crystal

Band structure of a sawtooth photonic crystal for optical wave propagation along the axis of periodicity is investigated. Floquet–Bloch solutions are found and illustrated for the bandgaps, allowed bands, and bandedges of the crystal. Special attention is given to the cases where Floquet–Bloch solutions become periodic functions.     

Probe spectrum of a four-level atom in a double-band photonic crystal

In this paper, the probe absorption spectrum of an atom in a double-band photonic crystal have been studied. In the modes, we assume that one of the two atomic transitions in a Λ-type atomic system is interacting with free vacuum modes, and another transition is interacting with free vacuum modes, isotropic photonic band gap (PBG) modes and anisotropic PBG modes, separately. The effects of the fine structure of the atomic lower levels on the probe absorption spectrum are investigated in detail in the three cases. The most interesting thing is that the two (four) transparencies at one (two) probe absorption peak(s), caused by the fine structure of the lower levels of an atom, are predicted in the case of isotropic PBG modes.     

Spontaneous emission spectrum of a four-level atom in a double-band photonic crystal

The spontaneous emission spectrum from a four-level atom in a double-band photonic crystal has been investigated.We use the model which assumes three atomic transitions. One of the transitions interacts with the free vacuum modes,and the other two transitions couple to the modes of the isotropic photonic band gap (PBG), the anisotropic PBG and another free vacuum. The effects of the fine structure of the lower levels on the spontaneous emission spectrum of an atom are investigated in detail in the three cases. New features of four (two) transparencies with two (one) spontaneous emission peaks, resulting from the fine structure of the lower levels of an atom, are predicted in the case of isotropic PBG modes.     

Multiple Čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure

We report simultaneous generation of multiple conical second-harmonic waves in a two-dimensional nonlinear photonic structure when illuminated by two overlapping noncollinear fundamental beams. We show that this phenomenon is caused by the nonlinear ?erenkov radiation emitted due to the interaction of photons from each constituent fundamental beam as well as the virtual one propagating along the bisector of the two beams. In addition, by studying the asymmetric geometry of the interaction, we uniquely verify the effects of reciprocal vectors on the ?erenkov-type second-harmonic generation in nonlinear photonic structures.     

Experiment study of wavelength conversion in a dispersion-flattened photonic crystal fiber

Wavelength conversion based on four-wave mixing(FWM)has been demonstrated using a 40-m dispersion flattened highly nonlinear photonic crystal fiber(HNL-PCF).A conversion efficiency of-26 dB for a pump power of 19.5 dBm and a conversion bandwidth of 28 nm have been obtained,which are limited by the continuous wave(CW)laser wavelength range and tunability of optical band pass filters(OBPFs).     

Spontaneous emission spectrum of a three-level atom embedded in photonic crystal

The two models of three-level (one upper level and two lower levels, or two upper levels and one lower level) atom embedded in a double-band photonic crystal are adopted. The atomic transitions from the upper levels to the lower levels are assumed to be coupled by the same reservoir which are respectively the isotropic photonic band gap (PBG) modes, the anisotropic PBG modes and the free vacuum modes. The effects of the fine structure of the atomic ground state levels in the model with one upper level and two lower levels, and the quantum interferences in the model with two upper levels and one lower level on the spontaneous emission spectrum of an atom are investigated in detail. Most interestingly, it is shown that new spontaneous emission lines are produced from the fine splitting of atomic ground state levels in the isotropic PBG case. The quantum interferences induce additional narrow spontaneous lines near the transition from the empty upper level to the lower level.     

Absolute band gaps in two-dimensional graphite photonic crystal

The off-plane propagation of electromagnetic (EM) waves in a two-dimensional (2D) graphite photonic crystal structure was studied using transfer matrix method. Transmission spectra calculations indicate that such a 2D structure has a common band gap from 0.202 to 0.2035 c/a for both H and E polarizations and for all off-plane angles form 0° up to 90°. The presence of such an absolute band gap implies that 2D graphite photonic crystal, which is much easier and more feasible to fabricate, can exhibit some properties of a three-dimensional (3D) photonic crystal.     

Subpicosecond pulse compression in nonlinear photonic crystal waveguides based on the formation of high-order optical solitons

We investigate by numerical simulation the compression of subpicosecond pulses in two-dimensional nonlinear photonic crystal (PC) waveguides. The compression originates from the generation of high-order optical solitons through the interplay of the huge group-velocity dispersion and the enhanced self-phase modulation in nonlinear PC waveguides.Both the formation of Bragg grating solitons and gap solitons can lead to efficient pulse compression. The compression factors under different excitation power densities and the optimum length for subpicosecond pulse compression have been determined. As a compressor, the total length of the nonlinear PC waveguide is only ten micrometres and therefore can be easily incorporated into PC integrated circuits.     

Characteristics of local photonic state density in an infinite two-dimensional photonic crystal

The local density of photonic states （LDPS） of an infinite two-dimensional （2D） photonic crystal （PC） composed of rotated square-pillars in a 2D square lattice is calculated in terms of the plane-wave expansion method in a combination with the point group theory. The calculation results show that the LDPS strongly depends on the spatial positions. The variations of the LDPS as functions of the radial coordinate and frequency exhibit “mountain chain” structures with sharp peaks. The LDPS with large value spans a finite area and falls abruptly down to small value at the position corresponding to the interfaces between two different refractive index materials. The larger/lower LDPS occurs inward the lower/larger dielectric-constant medium. This feature can be well interpreted by the continuity of electricdisplacement vector at the interface. In the frequency range of the pseudo-PBG （photonic band gap）, the LDPS keeps very low value over the whole Wiger-Seitz cell. It indicates that the spontaneous emission in 2D PCs cannot be prohibited completely, but it can be inhibited intensively when the resonate frequency falls into the pseudo-PBG.     

Broadband-cascaded four-wave mixing in a photonic crystal fiber around 1 μm

To our knowledge, efficient generation of broadband four-wave mixing cascades centered at 1 μm and spanning 600 nm is experimentally demonstrated for the first time. This frequency comb is generated from a two-tone seed with a maximum peak power of 25 W in a low-dispersion photonic crystal fiber. It consists of up to 44 new idler waves generated symmetrically around the seed.     

Bound states in the continuum in metal—dielectric photonic crystal with a birefringent defect

By using the difference of the band structure for the TE and TM waves in the metal—dielectric photonic crystals beyond the light cone and the birefringence of the anisotropic crystal, a one-dimensional photonic system is constructed to realize the bound states in the continuum (BICs). In addition to the BICs arising from the polarization incompatibility, the Friedrich—Wintgen BICs are also achieved when the leaking TM wave is eliminated due to the destructive interference of its ordinary and extraordinary wave components in the anisotropic crystal. A modified scheme favorable for practical application is also proposed. This scheme for BICs may help to suppress the radiation loss in the metal—dielectric photonic crystal systems.     

Switching behaviour of nonlinear Mach–Zehnder interferometer based on photonic crystal geometry

Nonlinear Mach–Zehnder interferometer (NMZI) created with photonic crystal waveguides (PCW) and with Kerr-type nonlinearity has been investigated in this paper. The NMZI has been simulated using two-dimensional finite difference time domain (2D-FDTD) method. Input verses output (I /O) characteristics have been obtained for different lengths of the nonlinear arm, nonlinear coefficients of the nonlinear arm, wavelengths of the input beam, sizes of defect rods and NMZI offset. The results obtained are compared with earlier published results of NMZI created with conventional step index waveguides (SIW). It is shown that all useful features of light switching offered by SIW-based NMZIs are also possible with PCW-based NMZIs of extremely small dimensions. Moreover, PCW-based NMZIs offer additional useful feature not available with SIW-based NMZIs.     

Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures

We study experimentally and theoretically the ?erenkov-type second-harmonic generation in a one-dimensional nonlinear photonic crystal. We demonstrate that the power of emitted second-harmonic can be enhanced 270 times by varying the angle of incidence of the fundamental beam such that the reciprocal lattice vector of the crystal can be used to compensate for the phase mismatch in the transverse direction enabling interaction in the nonlinear Bragg diffraction regime.     

Coupling of two defect modes in photonic crystal fibers

The coupling characteristics of two defect modes in photonic crystal fibers are investigated theoretically by the finite-difference time-domain (FDTD) method. The transmission spectrum and eigenmodes of optical wave are found to be very sensitive to the geometrical and physical parameters of the structure, as well as to the relative position of the two defects.     

Influence of group—velocity mismatch on soliton switching in a nonlinear fibre coupler

In this work, the influence of group-velocity mismatch on soliton self-routing pulse switching in a nonlinear fibre coupler is discussed in detail by the use of both variational approach and numerical simulation. The results obtained show that the group-velocity mismatch leads to the relative displacement between the two orthogonal polarization modes, increase of the critical power, and reduction of the elimination-light ratio. For sub-ps pulse, the influence cannot be neglected.     

Numerical analysis of Raman amplification and optical signal-to-noise ratio in a photonic crystal fiber

A numerical design on the triangular photonic crystal fiber (PCF) based backward multi-pump Raman amplifier is presented. It is demonstrated that high flat Raman gain can be reached based on PCF. Influences of different geometric parameters and germanium doping concentrations on the Raman net gain, amplified spontaneous emission (ASE) noise and double Rayleigh backscattering (DRBS) of the signal have been analyzed. For optimizing crystal fiber Raman amplifier (FRA), there is tradeoff between the geometric parameter and germanium doping concentration of triangular PCF. The results show that PCF is an appropriate candidate for high gain Raman amplifiers.     

A ministop band in a single-defect photonic crystal waveguide based on silicon on insulator

This paper reports that a two-dimensional single-defect photonic crystal waveguide in the Г-K direction with triangular lattice on a silicon-on-insulator substrate is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. A ministop band （MSB） is observed by the measurement of transmission characteristics. It results from the coupling between the two modes with the same symmetry, which is analysed from the stimulated band diagram by the effective index and the two-dimensional plane wave expansion methods. The parameter working on the MSB is the ratio of the radius of air holes to the lattice constant, fla. It is obtained that the critical τ/a value determining the occurrence or disappearance of MSB is 0.36. When τ/a is larger than or equal to 0.36, the MSB occurs. However, when τ/a is smaller than 0.36, the MSB disappears.     

Static properties of chiral soliton in a nonlinear σ-field with ρ-meson coupling

The soliton soluton for a lagrangian made of a nonlinear σ-field coupled to a ρ-meson field is studied. The static properties are calculated and compared with experimental values and the results of the Skyrme model.