Equilateral Triangle Resonator Research Articles

Theoretical design and analysis of multichannel plasmonic switch based on triangle resonator combined with silver bar

A multichannel plasmonic switch consisted of four metal–insulator–metal (MIM) waveguides and an equilateral triangle resonator (ETR) with a silver bar is proposed. Calculated by coupled mode theory (CMT) and standing wave theory, structural transmittance characteristics are numerically studied by finite difference time domain (FDTD) method. And the results show that the transmission spectrum of the ETR with a silver bar, coupled with a MIM waveguide, can be adjusted by increasing the height and width of the bar. As for the switch, varying with structural parameters of the bar, the transmission spectra in three ports can be tuned by rotating the bar into different angles. And this multichannel plasmonic switch owes a high on/off contrast ratio (R = 36 dB). The proposed switch has potential application value in the area of telecommunication and all-optical signal procession.

Nanosensing and slow light application based on Fano resonance in waveguide coupled equilateral triangle resonator system

Plasmonic Fano resonance effect is investigated in a novel metal-insulator-metal waveguide structure, which consists of a stub MIM waveguide and a triangle shaped resonator. The transmission properties of the proposed plasmonic waveguide structure are numerically investigated by the two dimensional finite-difference-time -domain (FDTD). The coupling between the stub resonator and the triangle resonator results in a Fano resonance. The transmission characteristics and the slow light effect, sensing performance of the proposed plasmonic structure are studies in detail. By proper design, the sensitivity and the optical delay time of the proposed structure can be up to 800 nm/RIU and 0.053 ps. The above characteristics indicate the proposed plasmonic structure may have application in slow light device, plasmonic filter, all optical switch and nanosensing.

Proposal of a wavelength filter with a cut corner based on Equilateral-Triangle-Resonator

We propose an equilateral triangle resonator filter with an output waveguide and analyzed by the finite-difference time-domain technique. The filter can realize directional output with a high Q mode by means of the mode-field coupled into the output waveguide, which results a reduction in the scattering loss at the vertices. In addition, to the deformed equilateral triangle resonator filter, an optimum parameter with a cut corner of 0.23 μm, which is equal to that of the input waveguide and can be an optimal cut, is found to help increase in finesse, Q factors, extinction ratio and the output intensity on resonance of the drop port normalized with the through port .

Mode Analysis for Equilateral-Triangle-Resonator Microlasers with Metal Confinement Layers

Mode characteristics are analyzed for electrically injected equilateral-triangle-resonator (ETR) semiconductor microlasers, which are laterally confined by insulating barrier SiO2 and electrode metals Ti-Au. For the ETR without metal layers, the totally confined mode field patterns are derived based on the reflection phase shifts, and the Q -factors are calculated from the far-field emission of the analytical near field distribution, which are agreement very well with the numerical results of the finite-difference time-domain (FDTD) simulation. The polarization dependence reflections for light rays incident on semiconductor- SiO2-Ti-Au multi-layer structures are accounted in considering the confinement of TE and TM modes in the ETR with the metal layers. The reflectivity will greatly reduce with a Ti layer between SiO2 and Au for light rays with incident angle less than 30deg especially for the TE mode, even the thickness of the Ti layer is only 10 nm. If the ETR is laterally confined by SiO2 -Au layers without the Ti layer, the Fabry-PEacuterot type modes with an incident angle of zero on one side of the ETR can also have high Q-factor. The FDTD simulation for the ETR confined by metal layers verifies the above analysis based on multi-layer reflections. The output spectra with mode intervals of whispering-gallery modes and Fabry-Perot type modes are observed from different ETR lasers with side length of 10 mum, respectively.

Analysis of mode characteristics for equilateral-polygonal resonators with a center hole

Mode characteristics for equilateral triangles, squares, and hexagonal resonators with a center hole are numerically simulated by the finite-different time domain (FDTD) technique. The center hole does not break the symmetry behavior of the original resonators and can result in modification of the mode field patterns and mode Q factors. In an equilateral triangle resonator the center hole can suppress the symmetry state of degenerate states with the merit of single mode operation. In a square resonator, the Q factor can be enhanced for some modes with a suitable size of the hole. For a hexagonal resonator with a side length of 1 μm and a refractive index of 3.2, the mode Q factors first gradually decrease with the increase of the hole diameter for modes at a wavelength of about 1500 nm, then the modes transform to that of a microdisk with a jump of the mode wavelength as the hole diameter approaches 0.7 μm. Finally, the mode Q factors greatly enhance as the hole diameter reaches about 1 μm. The results indicate that the center hole can greatly modify mode characteristics, especially that of the mode Q factor.

Optical bistability in InP/GaInAsP equilateral-triangle-resonator microlasers

Optical bistability is reported in InP/GaInAsP equilateral-triangle-resonator (ETR) microlasers, which are fabricated by planar technology. For a 30 mum side ETR microlaser with a 2-mum-wide output waveguide connected to one of the vertices of the ETR, hysteresis loops are observed for the output power versus the injection current from 215 to 235 K. The laser output spectra are measured in the upper and lower states of the hysteresis loop, which show strong mode competition among transverse modes. The hysteresis loops are demonstrated by two-mode rate equations with asymmetric cross gain saturation and different output efficiencies.

Equilateral-Triangle and Square Resonator Semiconductor Microlasers

The characteristics of equilateral-triangle resonator (ETR) and square resonator microlasers are reported, which are potential light sources in the photonic integrations. Based on the numerical simulations, we find that high-efficiency directional emission can be achieved for the triangle and square microlasers by directly connecting an output waveguide to the resonators. The electrically injected InP/InGaAsP ETR and square resonator microlasers with a 2-mum-wide output waveguide were fabricated by standard photolithography and inductively coupled plasma etching techniques. Room-temperature continuous-wave (CW) operations were achieved for the ETR microlasers with the side length from 10 to 30 mum and the square resonator microlasers with the side length of 20 mum. The output power versus CW injection current and the laser spectra are presented for an ETR microlaser up to 310 K and a square resonator microlaser to 305 K. The lasing spectra with mode wavelength intervals as that of whispering-gallery-type modes and Fabry-Parot modes are observed for two square lasers, which can lase at low temperature and room temperature, respectively.

GaSb based midinfrared equilateral-triangle-resonator semiconductor lasers

Theoretical calculations of the mode characteristics of an equilateral-triangle resonator (ETR) with a 10μm cavity side length show that the fundamental mode, with longitudinal mode index of 25, has a wavelength of 2.185μm and a longitudinal mode separation of 100nm. This mode has a quality factor (∼2×105) that is much larger than the first (∼5×104) and second (∼3×104) order modes, indicating that single fundamental mode lasing should be accessible over a broad wavelength tuning range. An electrically injected ETR based on this design is fabricated from an InGaAsSb∕AlGaAsSb∕GaSb, graded-index separate-confinement heterostructure, laser diode wafer with a 2.1μm emission wavelength. This device achieved single mode, continuous wave operation at 77K with a threshold current of 0.5mA and a single mode wavelength tuning range of 3.25nm, which is accomplished by varying the injection current from 0.5to6.0mA.

Room-Temperature Continuous-Wave Electrically Injected InP–GaInAsP Equilateral-Triangle-Resonator Lasers

Equilateral-triangle-resonator (ETR) microlasers with an output waveguide connected to one of the vertices of the ETR are suitable to be a light source for photonic integrated circuits. InP-GaInAsP ETR lasers with side length from 10 to 30 mum and the output-waveguide width of 1 or 2 mum are fabricated using standard photolithography and inductively coupled-plasma etching techniques. Continuous-wave electrically injected 1520-nm ETR laser with 20-m sides is realized with the maximum output power 0.17 and 0.067 mW and the threshold current 34 and 43 mA at 290 K and 295 K, respectively.

Equilateral-Triangle-Resonator Injection Lasers With Directional Emission

Equilateral-triangle-resonator (ETR) lasers with an output waveguide jointed at one vertex of the resonator are fabricated on (100) GaInAsP-InP wafers using photolithography and a two-step inductively coupled plasma (ICP) etching technique. Distinct peaks with the mode spacing of longitudinal mode intervals are observed in the luminescence spectra at room temperature. Furthermore, some minor peaks appear in the middle of the main peaks, which can be attributed to the first-order transverse modes as predicted in the theoretical results. CW directional lasing emissions are achieved for ETR lasers with side lengths ranging from 15 to 30 mum up to 200 K. The temperature dependences of the threshold current and lasing wavelength are measured for an ETR laser with the side length of 20 mum from 80 to 200 K. The observed threshold current rapidly increases as temperature increases over 170 K

Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries

The influence of imperfect boundaries on the mode quality factor is investigated for equilateral-triangle-resonator (ETR) semiconductor microlasers by the finite difference time domain technique and the Padé approximation with Baker's algorithm. For 2-D ETR with a refractive index of 3.2 and side length of 5 μm, the confined modes can still have a quality factor of about 1000 as small triangles with side length of 1 μm are cut from the vertices of the ETR. For a deformed 5 μm ETR with round vertices and curve sides, the simulated mode quality factors are comparable to the measured results.

Analysis of Mode Quality Factors for Equilateral Triangle SemiconductorMicrolasers with Rough Sidewalls

The eigenmode characteristics for equilateral triangle resonator (ETR)semiconductor microlasers are analysed by the finite-difference time-domaintechnique and the Padé approximation. The random Gaussian correlationfunction and sinusoidal function are used to model the side roughness of theETR. The numerical results show that the roughness can cause the split ofthe degenerative modes, but the confined modes can still have a high qualityfactor. For the ETR with a 3 µm side length and the sinusoidalfluctuation, we can have a quality factor of 800 for the fundamental modein the wavelength of 1500 nm, as the amplitude of roughness is 75 nm.

Size limit and spontaneous emission factor for equilateral triangle semiconductor microlasers

The size of equilateral triangle resonator (ETR) needed for confining the fundamental mode is investigated by the total reflection condition of mode light rays and the FDTD numerical simulation. The confinement of the TM modes can be explained by the total reflection of mode light rays, and the confinement of the TE modes requires a larger ETR than the TM modes, which may be caused by excess scattering or radiation loss for the TE modes. With the multilayer staircase approximation, it is found that the spontaneous emission factor of the ETR lasers has the same form as that of strip waveguide lasers.

Analysis and numerical simulation of eigenmode characteristics for semiconductor lasers with an equilateral triangle micro-resonator

The eigenmodes confined in the equilateral triangle resonator (ETR) are analyzed by deriving the eigenvalues and the mode field distributions and by the finite difference time domain (FDTD) technique. The analytical results show that the one-period-length for the mode light rays inside the ETR is the perimeter of the ETR, and the number of transverse modes is limited by the condition of total internal reflection. In addition, the sum of the longitudinal mode index and the transverse mode index should be an even number, which limits the number of confined modes again. Based on the FDTD technique and the Pade approximation, we calculate the mode resonant frequencies and the quality factors from the local maximum and the width of the spectral distribution of the intensity. The numerical results of mode frequencies agree very well with the analytical results, and the quality factor of the fundamental mode is usually higher than that of the higher order transverse modes. The results show that the ETR is suitable to realize single-mode operation as semiconductor microcavity lasers.

Analysis of semiconductor microlasers with an equilateral triangle resonator by rate equations

Semiconductor microlasers with an equilateral triangle resonator (ETR) are analyzed by rate equations with the mode lifetimes calculated by the finite-difference time-domain technique and the Pade approximation. A gain spectrum based on the relation of the gain spectrum and the spontaneous emission spectrum is proposed for considering the mode selection in a wide wavelength span. For an ETR microlaser with a side length of about 5 /spl mu/m, we find that single fundamental mode operation at about 1.55 /spl mu/m can be obtained as the side length increases from 4.75 to 5.05 /spl mu/m. The corresponding wavelength tuning range is 93 nm, and the threshold current is about 0.1 to 0.4 mA.

Influence of output waveguide on mode quality factor in semiconductor microlasers with an equilateral triangle resonator

Semiconductor microlasers with an equilateral triangle resonator (ETR) and an output waveguide are proposed and analyzed by the finite-difference time-domain technique and the Padé approximation. The numerical results show that microlasers with an output waveguide still have a high-quality factor (Q factor) and are suitable to realize directional emission. For the ETR with a 0.46-μm-width opening in one of the vertices connected to the output waveguide, we have the Q factor of 1.5×103 and 2.5×102 for the TM fundamental mode at the wavelength of 1.55 μm, as the side length of the ETR is 5 and 3 μm. The simulated intensity distributions are presented for the fundamental mode in the ETR with a side length of 3 μm and an opening of 0.23 μm.