Search

Replica symmetry breaking (RSB) has been widely recognized as a statistical analysis approach to understand the disorder and nonlinear interactions in complex systems ranging from atoms to the cosmic scale. However, it is challenging to analyze the nonlinear optical characteristics of random laser (RL) in disordered gain medium via RSB due to the lack of a general RSB-based statistical analysis framework. In this work, we report the tunable RSB in polymer fiber RL, where the effects of temperature and different structures on RSB are investigated experimentally and theoretically. It experimentally proves that RSB in RL is not robust, and disorder and temperature are responsible for tunable RSB in RL, which contributes to the improvement of the statistical analysis framework for investigating the optical principles of RL using RSB. And the finding of the tunable RSB allows to investigate the dynamical differences for various RL systems, which broadens the directions for the use of spin-glass theory to explore the physical mechanism of RL.

In waveguided nematic liquid crystal random lasers (NLCRLs), we realize polarized random laser (RL) emission and discover that the waveguide effect reduces the transmission loss of the RL whose polarization is parallel to the liquid crystal molecules (LCMs). Compared with the traditional liquid crystal random lasers, the waveguide NLCRLs can achieve the regulation of RLs strength, polarization, and wavelength in the same structure. The electric field can drive the rotation of LCMs to control the RL polarization and intensity. The drop of horizontal polarization laser and the increase of vertical polarization laser prove the role of the waveguide effect. In addition, the disorder of the waveguided NLCRLs is highly sensitive to temperature, which makes it easy to control the wavelength and intensity of the RL. As the temperature rises, the waveguide effect is weakened, resulting in a weakening of the restriction along liquid crystal (LC) cell normal direction. The reduced laser intensity verifies the role of the waveguide effect.

There are many kinds of materials or methods used to make optical microcavities, and they have many different geometric structures. And electrospinning technique has become a very convenient and easy one to prepare polymer fiber. Based on this situation, PM597-doped polymer solution was prepared into high-performance fibers with different diameters by electrospinning technology in our work. In order to better study the temperature sensing of polymer fiber whispering gallery mode, we have placed it on two different substrates with gold and aluminum. A 532 nm pulsed laser beam was used to excite a single fiber in the radial direction, then the whispering gallery mode (WGM) laser was observed and the distribution of WGM was determined by theoretical calculations. The threshold of samples on aluminum substrate is 0.4 μJ. In addition, it is found that the samples on aluminum substrate performed better in temperature sensing, and the value is 0.13 nm/°C. As a result, WGM polymer fiber microcavities on aluminum substrate made by electrospinning technology have very broad development prospects in biosensing, optical pump lasers and other applications.

We have demonstrated the realization of a coherent vesicle random lasing (VRL) from the dye doped azobenzene polymer vesicles self-assembled in the tetrahydrofuran-water system, which contains a double-walled structure: a hydrophilic and hydrophobic part. The effect of the dye and azobenzene polymer concentration on the threshold of random laser has been researched. The threshold of random laser decreases with an increase in the concentration of the pyrromethene 597 (PM597) laser and azobenzene polymer. Moreover, the scattering of small size group vesicles is attributed to providing a loop to boost the coherent random laser through the Fourier transform analysis. Due to the vesicles having the similar structure with the cell, the generation of coherent random lasers from vesicles expand random lasers to the biomedicine filed.

We propose and demonstrate a sensitive vector twist sensor based on a small period long period fiber grating (SP-LPFG) fabricated with a femtosecond (fs) laser. The fabricated SP-LPFG is compact in size (2.8 mm) and shows strong polarization dependent peaks in its transmission spectrum due to the vectorial behavior of high-order cladding modes. Twist sensing is realized by monitoring the polarization dependent peaks, since the polarization of input light changes with fiber twist. The proposed sensor can be interrogated by the peak intensity and wavelength, with high twist sensitivity that reaches 0.257 dB/deg and 0.115 nm/deg, respectively.

A type of Christiansen filter that takes the form of a smooth cylindrical lens of even symmetry is proposed. By varying the shape of the lens, the filter can be made to realize many common filtering responses, including the polynomial function response, the Gaussian function response, and the sinc function response. A systematic design technique based on inverse scattering is established, and a desired, prescribed response can be tailored by properly shaping the lens of the filter. Three prototypical Christiansen filters, namely, a second-order all-real-roots filter, a second-order sinc filter, and a Gaussian filter, are synthesized using the proposed method. A prescribed response at 545 nm with a FWHM of 2 nm is achieved systematically by all of the three Christiansen filters.

Conventionally, the behavior of light transmission in optical devices is based on total internal reflection or photonic bandgaps. The Dirac mode is regarded as another guiding mechanism that relies on the zero-density of radiation states around the Dirac point to avoid power leakage and thus achieves field confinement. Unlike conventional light guiding mechanisms, the Dirac mode features a unique algebraic decay profile around the Dirac frequency. In this study, the Dirac mode in the Kagome lattice of photonic crystals (PCs) at a Dirac frequency that is beyond any complete photonic bandgaps is observed, and its features are verified using finite difference time domain analyses. The results indicate that the Dirac mode in the triangular, honeycomb, and two-compound lattices of PCs also occurs in the Kagome lattice and has an extremely high quality factor of 1 . 03 × 1 0 6 . Furthermore, analyses of the Dirac mode serve as a convenient method to control the all-range Dirac frequency by modifying the structural parameters accordingly, thus extending the applications of the Dirac mode in modern integrated optical devices.

Light trapping at the Dirac point in 2D plasma photonic crystal has been obtained. The new localized mode, Dirac mode, is attributable to neither photonic bandgap nor total internal reflection. It exhibits a unique algebraic profile and possesses a high-Q factor resonator of about 1 0 5 . The Dirac point could be modulated by tuning the filling factor, plasma frequency and plasma cyclotron frequency, respectively. When a magnetic field parallel to the wave vector is applied, Dirac modes for right circularly polarized and left circularly polarized waves could be obtained at different frequencies, and the Q factor could be tuned. This property will add more controllability and flexibility to the design and modulation of novel photonic devices. It is also valuable for the possibilities of Dirac modes in photonic crystal containing other kinds of metamaterials.

We have demonstrated a low threshold and tunable flexible random laser (RL) in dye-doped poly ethylene glycol diacrylate (PEG-DA) hydrogel, which was prepared by crosslinking polymerization using PEG-DA monomer and photoinitiator. The random lasering is attributed to the light scattering from the porous structure of hydrogels, and the wavelength of random lasing can be tuned by ~3.2 nm in the temperature range from 30 °C to 70 °C. Under the continuous increasing and decreasing temperature cycle, the random lasing tunable phenomenon can still be observed, which proves that this flexible material can be used as a new temperature sensor. In addition, we also explored the application of flexible laser in phototherapy. Considering the good elasticity and transparency of hydrogels, this thermo-responsive property will be of great significance to the biomedical applications of flexible material.

Optical waveguides and cavities are important components among modern optical devices. Traditional optical cavities rely on total internal reflection or photonic bandgaps to achieve field confinement. Recently, a new type of trapped mode, the Dirac mode, has been reported to occur in triangular or honeycomb lattice photonic crystal. This novel localized mode is attribute to neither of the traditional light-guiding mechanisms and owns different characteristics. Here we report the discovery of the Dirac mode in honeycomb-like photonic crystal lattice. The Dirac mode occurs at a Dirac frequency, which is beyond the complete photonic bandgaps. It has a different algebraic-decay feature. Our discovery extends applicability of the Dirac mode in designing for optical devices.

Electrospinning is a very simple method of preparing polymer solutions into high performance fibers. In this work, PM597-doped polymer fibers with different diameters have been fabricated by electrospinning technology. Whispering gallery mode (WGM) lasing emission was observed when a 532 nm pulse laser beam radially excited the single electrospun polymer fiber (EPF) created by this method. The distribution of WGMs is also quantitatively confirmed through theoretical calculation. Additionally, the number of WGM laser peaks decrease as the diameter of the EPF decreases. Single longitudinal mode laser emission can be obtained when the EPF diameter decreases to 8.8m. It has also been found that the WGM laser from the single EPF has relatively low thresholds and good lifetime compared to droplet lasers or other fiber lasers. Moreover, EPF networks have unique research prospects in photonic devices, optical pump lasers and biosensing due to their very large surface to volume ratio.

Electrically responsive photonic crystals represent one of the most promising intelligent material candidates for technological applications in optoelectronics. In this research, dye-doped polymer-stabilized cholesteric liquid crystals (PSCLCs) with negative dielectric anisotropy were fabricated, and mirrorless lasing with an electrically tunable wavelength was successfully achieved. Unlike conventional liquid-crystal lasers, the proposed laser aided in tuning the emission wavelength through controlling the reflection bandwidth based on gradient pitch distribution. The principal advantage of the electrically controlled dye-doped PSCLC laser is that the electric field is applied parallel to the helical axis, which changes the pitch gradient instead of rotating the helix axis, thus keeping the heliconical structure intact during lasing. The broad tuning range (∼110 nm) of PSCLC lasers, coupled with their stable emission performance, continuous tunability, and easy fabrication, leads to its numerous potential applications in intelligent optoelectronic devices, such as sensing, medicine, and display.

Ba0.6Sr0.4TiO3 (BST) thin films were deposited on Pt/Ti/SiO2/Si substrates by a RF-magnetron sputtering. The film crystallinity was influenced by the in situ heat treatment. The surface images, dielectric and ferroelectric properties of the thin films were investigated. The BST thin films deposited at 400°C were crystallized after heat treatment over 500°C for 20 minutes. The high dielectric constant of 320 and dielectric tunability of 30% was achieved in the BST thin films while the dielectric loss was less than 0.05 by adjusting the annealing temperature. And the thin films exhibited strong ferroelectric property when the film thickness was over 90 nm.

A novel photonic crystals (PhC) based on 8-shaped scatters with two-dimensional (2-D) square-lattice is presented. By employing the MIT photonic bands (MPB), the relationship between the structural parameters of the PhC and the properties of photonic band gaps (PBG) are investigated. The calculation results of 8-shaped scatters with 2-D square-lattice demonstrate that the reduction of scatters’ symmetry can produce larger number of PBG and broaden the width of PBG only for TM mode, and reversely for TE mode. The peculiarity would meet the distinguish employment of different mode. By optimizing the structural parameters, the maximum absolute PBG 0.1028( ωa /2 πc ) at R = 0.3, ɛ r = 11.56, θ = 45° is obtained and six absolute PBGs is got at R = 0.3, θ = 115°, ɛ r ∈ [32.3, 33.5].

A reconfigurable photonic fractional Fourier transformer is proposed to realize broadband frequency measurement and large-scale chirp rate characterization of microwave signals with a high resolution. This scheme is based on three parallel frequency-shifting loops (FSLs) with co-prime free spectral range (FSR). Tunable high-resolution fractional Fourier transform is achieved through simply changing the frequency shift in each FSL with a small FSR, and large unambiguous frequency and chirp rate measurement range are guaranteed by the proposed recovery algorithm. In the numerical verification, non-aliasing frequency measurement range up to 14.7404 GHz and unambiguous chirp rate characterization range from -4.35 × 105 to 4.35 × 105 GHz/ μ s are obtained by using three FSLs with FSRs of 17.13 MHz, 17.21 MHz and 17.39 MHz, where the frequency resolution and the chirp rate resolution are 139.12 kHz and 0.3356 GHz/ms, respectively. Through properly setting the FSR in each FSL, the frequency and chirp rate measurement range can be further improved, which can find application in electronic warfare to achieve microwave signal recognition.

Brillouin gain spectra (BGS) in an As2Se3 photonic crystal fiber (PCF) are investigated numerically. The profiles of the BGS are simulated by calculating the characteristics of different-order optical and acoustic waves in the PCFs with different core diameters. For the small-core PCF, there are two peaks in BGS, but there is only one peak for the large-core PCF. We also reveal that in the small-core PCF, the difference of Brillouin frequency shift between the LP01 and LP11 modes is obvious, while it is not obvious in the large-core PCF. The Brillouin threshold increases with the core diameter increasing.

Optical cavities and waveguides are essential building blocks of many modern optical devices. They rely upon photonic bandgaps, or total internal reflections, to achieve field confinement. Here a new phenomenon is reported of wave localization that is attributable to neither of the above light guiding mechanisms. It is found that what is known as the Dirac point within a photonic band structure can play the role of a photonic bandgap with the establishment of field confinement. The new localized mode occurs at a Dirac frequency that is beyond any complete photonic bandgap, and exhibits a unique algebraic profile. The features of this new wave localization will add new capabilities and more flexibility to the design techniques of novel photonic components and photonic chip architectures.

In this work, the modified particle swarm optimization is used as an optimization tool to determine the set of wavelengths and power levels of pumps that delivers a flat gain spectrum for Raman fiber amplifiers. The average power analysis technique is used as a numerical method to solve the coupled Raman amplifier equations. By combining the modified particle swarm optimization and average power analysis technique an efficient algorithm for the design of flat-gain-spectrum broadband Raman fiber amplifiers is constructed. Application of this algorithm to the design of flat-gain-spectrum broadband Raman fiber amplifiers shows that the design efficiency of the new method is improved by 1–2 orders of magnitude compared with similar implementations previously reported in the literature. A 4-backward-pump gain-flattened Raman amplifier with bandwidth of 100-nm and maximum gain ripple of

A novel operation mode for development of sensitive and renewable polymeric membrane polyion-sensitive electrodes has been explored in this paper. In contrast to the traditional polyion sensors which are conditioned with highly discriminated ions, the proposed polycation-sensitive membrane electrode with dinonylnaphthalene sulfonate as the ion-exchanger is conditioned with the primary ion (protamine), and activated with the discriminated ion (Na+) before measurement. Using this protocol, the membrane with protamine in the membrane bulk but with discriminated ions rich at the membrane outer surface can be prepared. The protamine inside the membrane efficiently suppresses the fluxes of protamine from the sample-membrane interface into the membrane bulk, thus decreasing the detection limit toward protamine by one order of magnitude. With the reproducible protamine fluxes obtained by the conditioning and activation steps, the protamine-sensitive electrode could be reused without significant signal deterioration. Titrimetric analysis of heparin with this novel technique has been demonstrated. The proposed polyion sensing platform offers much promise in the detection of polyions as well as in other polyion-involved bioanalyses.

In this work, a novel metaheuristic named artificial fish school algorithm is introduced into the optimization of pump parameters for the design of gain flattened Raman fiber amplifiers for the first time. Artificial fish school algorithm emulates three simple social behaviors of a fish in a school, namely, preying, swarming and following, to optimize a target function. In this algorithm the pump wavelengths and power levels are mapped respectively to the state of a fish in a school, and the gain of a Raman fiber amplifier is mapped to the concentration of a food source for the fish school to search. Application of this algorithm to the design of a C-band gain flattened Raman fiber amplifier leads to an optimized amplifier that produces a flat gain spectrum with 0.63 dB in band ripple for given conditions. This result demonstrates that the artificial fish school algorithm is efficient for the optimization of pump parameters of gain flattened Raman fiber amplifiers.

We propose a directional coupler design based on coupled cavity waveguide in photonic crystals. The plane wave expansion is used to give the dispersion of the coupled cavity waveguides and two parallel such waveguides. The couple length is got from the dispersion curves. Based on the research of the dispersion, we present a directional coupler and the transmission property is given. This structure is potentially important for highly efficient directional coupler in integrate optical circuit.

The transmission properties of one-dimensional (1D) photonic crystals containing two kinds of single-negative (ENG and MNG) material are investigated theoretically. A type of photonic gap with zero effective phases (zero- φ eff ) and the effects of absorption on the properties of the zero- φ eff gap were shown. Specifically, it is demonstrated that strong absorption creates photon states inside the gap and this makes the band gap to be of zero width.

In this paper, semiconductor laser beam collimation lenses system has been optimum simulated and designed. The new design methods for aspheric cylinder lenses collimation system have been discussed in detail and the system parameters are calculated and optimized by using a geometrical ray optics approximation. The optical system has been further simulated by software MATLAB, and the simulation results showed that the emergence angle can be collimated effectively, and the output beam can be expanded to a circular spot in centimeter level beam radius.

The plane wave expansion (PWE) method was used to get the three-dimensional band diagram and equifrequency surface (EFS). From the EFS the maximum flatness half width (MFHW) and its position were got. The relation between MFHW and filling fraction P f , dielectric ratio e b / e a were given in order to get the optimal structure we employ in this paper. Then the maximum super collimation was given by beam propagation method (BPM).

The transmission properties of a one-dimensional (1D) photonic crystal containing two kinds of single-negative (permittivity or permeability negative) material with an inserted array of defects (RHM and LHM) were presented by the transfer matrix method (TMM). The dependence of the defect modes on the structure parameters was discussed by using the TMM. In contrast to the Bragg gaps, the properties (the central frequency and width of the gap) of zero effective phase ( zero − φ eff ) and zero - n ¯ gap are invariant with a change in scale length and insensitive to the incident angles. The property of the periodic defect modes in the SNG host periodic structure was studied. It illustrates that the defect modes properties changed more by insert periodic defect than by single-media defect. The defect modes are sensitive to the parameters of the defect layers and the incident angle.

An initial value determination method with a contraction factor for the counter-pumped Raman coupled equations is proposed. This method is used in conjunction with initial guess correction mechanism of Newton's method to construct a new efficient shooting algorithm for the solution of counter-pumped Raman coupled equations. The particle'swarm optimization is used to find the optimal wavelengths and powers for the pumps. By combining the new shooting algorithm and particle swarm optimization a powerful approach to the design of gain spectra for Raman fiber amplifiers is developed. Using this approach a counter-pumped broadband Raman fiber amplifier in C + L-band is designed and optimized. An average on–off gain of 9.3 dB for a bandwidth of 95 nm is obtained using only 4 pumps, with an in-band ripple level of ± 0.7 dB.

Within the Maxwell framework and using the transfer-matrix method, we have determined an exact expression that governs the photonic band structure and the density of states (the group velocity) of one-dimensional superlattices composed of three alternate layers (quasi-sandwiching periodic structure) characterized by three different refractive indexes. We begin by giving the band gap of the quasi-sandwiching period structure. Owing to the advantage of the quasi-sandwiching periodic structure, we develop a specific formula that gives the N-period mode density in terms of the complex transmission coefficient of a unit cell. The specific example of a quarter-wave stack is analyzed.

A theory is developed for the self-phase compensated optical waveguide isolator recently reported in the literature. The operation principle of such device is explained in terms of synchronization of phase and power conversion. The effect of balancing phase mismatches of the two convertors on achieving a proper percentage of mode conversion is revealed. The way to make use of the phase mismatches of different sections to accommodate the different requirements in phase relationship for the reciprocal and nonreciprocal mode convertors is discussed. The theory is extended to the case where phase compensator is used. It is demonstrated that the introduction of phase compensator separates the adjustment of phase from the adjustment of power for the mode convertors so that relaxes fabrication tolerances of such devices. An isolator consists of three phase mismatched waveguide sections is designed and simulated. The simulation results confirm the self-phase compensation theory.

Transmission properties of one-dimensional photonic crystal with two nonlinear defects were investigated based on the nonlinear transfer matrix method. From the inspection of the optical bistabilities around different defect modes, it was found that the threshold of bistability for the bonding mode is always lower than that for the anti-bonding mode. When intensity of the incident wave increases bistability could happen at any wavelength larger than the resonance wavelength of the linear anti-bonding mode in the gap. The threshold of bistability increases initially with the wavelength, then decreases sharply in reaching the resonance wavelength of the linear bonding mode. The coupling behavior of the two defects was also discussed, and it was found that the threshold of bistability increases with the distance between the two defects. A flat spectrum similar to that formed in the photonic crystal molecules was obtained under certain incident intensity.

A novel optical waveguide isolator based on self-phase compensated TE–TM mode conversion was proposed. In this work, the troublesome phase-match condition for the TE–TM mode conversion is eliminated without degradation on the performances. An isolator based on this mechanism is designed and simulated. An insertion loss of −0.1 dB and an isolation of −25 dB was obtained. The tolerance of fabrication and bandwidth of the isolator was also discussed.

A full three-dimensional vector finite-difference beam propagation method is developed and tested. In this scheme, a delicate way to discretize the coupled equations is incorporated. The resulting matrix for the difference equation then has a tri-diagonal structure, which makes the program robust and, computationally, efficient. The transparent boundary condition is also improved so that any exponential growth at a boundary is suppressed. The method is applied to the simulation of magneto-optical devices and the design of a waveguide-based optical switch, with −25 dB isolation, is presented.

In this paper, the multimode waveguide lengths and the output port locations of a SOI (silicon on insulator) material-based 1×4 MMI (multimode interference) optical splitter are optimized by means of FD-BPM (finite difference — beam propagation method). An improved 1×4 MMI optical splitter is designed. Compared with an usual optical splitter, a smaller loss 0. 12dB and a better output port power uniformity 0.11dB are achieved for the optical signal transmission.

An organocatalytic Michael-cyclization cascade of aldehydes with 4-oxa-α,β-unsaturated carboxylic acids has been developed, giving functionalized γ-lactols with high yields and enantioselectivities. The products could be easily transformed into complex trisubstituted γ-lactones and γ-lactams.

The non-degenerate solitons due to three-wave mixing in a quadratic medium are analyzed. A new stability criterion for these solitons is found and verified numerically. The influence of the non-paraxial terms on the instability threshold is also discussed.

With study for switching characteristics and output coupling ratio of fiber nonlinear directional couplers (NLDC), we found that the influence elements on the switching characteristics and output coupling ratio had gain of core 1 and 2, nonlinear coefficient of those, the input power and width of input soliton. We also found numerically that switching efficiencies were improved by controlling gain of core 1, different output coupling ratio would be obtained by controlling gain of core 1 or 2. And we can change the gain by changing pump power of the optical fiber amplifiers. From this, we also made fiber coupler which output coupling ratio was changeable.

Solitons, localized at the interface between a linear magneto-optic half-space and a nonlinear optical medium, are investigated with the aid of an approximate model validated by direct numerical simulations. The interface is located in a planar waveguide, and is characterized not only by the magneto-optic properties but also by a linear refractive index discontinuity. The analysis is based upon a global envelope equation and uses waveguide and magneto-optic parameters that are averaged over the whole waveguide structure. A variational analysis shows that, even though surface solitons can be localized in deeply stable stationary states, they can also be generated in parts of the parameter space that facilitate movement between stable and unstable regions. This leads to suggestions for isolator and multi-switch operation.

In this work, a new metaheuristic called ant colony optimization (ACO) is introduced into the design of flat-gain-spectrum Raman fiber amplifiers (RFAs) for the first time. In this novel design method, the pump powers and pump wavelengths are optimized by ACO to obtain a flat gain spectrum with a prespecified maximum gain ripple under the given parameters of RFAs. The simulations show that the proposed method is efficient and stable. Finally, a C-band RFA with a gain ripple of 0.32 dB is designed to demonstrate the technique in detail.

Using numerical simulations, we investigated the transmission properties for coupled cavity waveguides form in two-dimensional photonic dielectric rods in air with square lattice. The dispersion for the coupled cavity waveguides with different radius of the defects is given. The optimum design waveguide should be perfect transmission for pulse though with a quasi-flat dispersion band. Based on the coupled cavity waveguides, a 3 dB power splitter is designed. Our results may have an important role in the design of efficient power splitters in a photonic circuit.

A novel optical waveguide isolator constructed from mode convertors with unsuppressed phase mismatch is proposed. The troublesome requirement of phase matching for transverse electric (TE)-transverse magnetic (TM) mode conversion is eliminated without degradation on the performances. It is found that a kind of self-phase compensation phenomenon occurs during TE-TM mode conversion that facilitates the operation of the isolator. An isolator based on this mechanism is designed and simulated. An isolation of -24.4 dB is obtained.

The transmission properties of one-dimensional photonic crystals containing double-negative and single-negative materials are studied theoretically. A special kind of photonic band gap is found in this structure. This gap is invariant with scaling and insensitive to thickness fluctuation. But when changing the ratio of the thickness of two media, the width of the gap could be enlarged. The defect modes are analyzed by inducing a linear defect layer in the structure. It is found that the number of defect modes will increase when the thickness of the defect layer becomes larger.

We have demonstrated the realization of a plasmonic random polymer fiber laser (RPFL) based on gold nanoparticles (NPs) doped one-dimensional disordered gain polymer optical fiber (POF). In this work, the plasmonic RPFL is fabricated by directly drawing from a laser dye and gold NPs system codoped POF. The random lasing can be obtained from the waveguide-plasmon-scattering in the POF system. Meanwhile, the dye doped fiber in the presence gold NPs has high photostability.

We have reported the realization of a plasmonic random fiber laser based on the localized surface plasmonic resonance of gold nanoparticles (NPs) in the liquid core optical fiber. The liquid core material contains a dispersive solution of gold NPs and laser dye pyrromethene 597 in toluene. It was experimentally proved that the fluorescence quenching of the dye is restrained in the optical fiber, which is considered one of the main sources of loss in the traditional laser system. Meanwhile, the random lasing can be more easily obtained in the random laser system with more overlap between the plasmonic resonance of the gold NPs and the photoluminescence spectrum of the dye molecules.

In this work, the self-collimating phenomenon in two-dimensional rhombic-lattice photonic crystals is discussed in detail. The equi-frequency contours of a rhombic-lattice rod-type photonic crystal structure are calculated with the plane wave expansion method for different lattice angles and rod radii. A broad range of flat and open equi-frequency contours is found. A rhombic-lattice photonic crystal made of 301???21 silicon rods (n?=?3.5) in air is presented as an illustration to demonstrate the broadband all-angle self-collimation. The bandwidth for all-angle self-collimation is verified to be 17.42% of the central frequency by simulations based on the finite-difference time-domain method. The all-angle self-collimation is found to be polarization-independent and the frequency for simultaneous TM and TE all-angle self-collimation is identified and verified by finite-difference time-domain simulations.