Effective transmittance of Fabry–Perot cavity under non-parallel beam incidence

The Fabry–Perot(FP) resonant cavity is widely used in laser and spectroscopic measurements due to its unique interference transfer function(ITF). In the ideal case of parallel incident light, the ITF of the FP resonant cavity can be expressed by the Airy function. However, in reality, it is difficult to achieve perfect parallelism with collimated beams. In this article, a theoretical model is established for non-parallel light incidence, which assumes that the non-parallel incident light is a cone-shaped beam, and the cone angle is used to quantify the non-parallelism of the beam. The transmittance function of the FP resonant cavity under non-parallel light incidence is derived. The accuracy of the model is experimentally verified. Based on this model, the effects of divergence angle, tilt angle and FP cavity parameters(reflectivity, cavity length)on the ITF are studied. The reasons for the decrease in peak value, broadening and asymmetry of the interference peak under non-parallel light incidence are explained. It is suggested that a fine balance between the interference peak and the collimation effect of the incident light should be considered in the design and application of FP resonant cavities, especially for tilted applications such as angle-scanned spectroscopy. The research results of this article have certain significance for the design and application of FP resonant cavities.

Non-volatile dynamically switchable color display via chalcogenide stepwise cavity resonators

High-resolution multi-color printing relies upon pixelated optical nanostructures,which is crucial to promote color display by producing nonbleaching colors,yet requires simplicity in fabrication and dynamic switching.Antimony trisulfide(Sb_(2)S_(3))is a newly rising chalcogenide material that possesses prompt and significant transition of its optical characteristics in the visible region between amorphous and crystalline phases,which holds the key to color-varying devices.Herein,we proposed a dynamically switchable color printing method using Sb_(2)S_(3)-based stepwise pixelated Fabry-Pérot(FP)cavities with various cavity lengths.The device was fabricated by employing a direct laser patterning that is a less timeconsuming,more approachable,and low-cost technique.As switching the state of Sb_(2)S_(3) between amorphous and crystalline,the multi-color of stepwise pixelated FP cavities can be actively changed.The color variation is due to the profound change in the refractive index of Sb_(2)S_(3) over the visible spectrum during its phase transition.Moreover,we directly fabricated sub-50 nm nano-grating on ultrathin Sb_(2)S_(3) laminate via microsphere 800-nm femtosecond laser irradiation in far field.The minimum feature size can be further decreased down to~45 nm(λ/17)by varying the thickness of Sb_(2)S_(3) film.Ultrafast switchable Sb_(2)S_(3) photonic devices can take one step toward the next generation of inkless erasable papers or displays and enable information encryption,camouflaging surfaces,anticounterfeiting,etc.Importantly,our work explores the prospects of rapid and rewritable fabrication of periodic structures with nano-scale resolution and can serve as a guideline for further development of chalcogenide-based photonics components.

Analysis of iris-loaded resonance cavity in miniaturized maser

The size reduction of atomic clocks is a long-standing research issue.Many atomic clocks such as passive hydrogen masers(PHMs)and compact rubidium masers(CRMs)use iris-loaded resonance cavities(IRCs)as their microwave cavities because they can dramatically reduce the radical sizes of the atomic clocks.In this paper,the electromagnetic characteristic of the IRC is investigated by a theoretical model based on electromagnetic field theory.The formulas to calculate the resonance frequency,quality factor,and magnetic energy filling factor are presented.The relationship between the IRC structure and its electromagnetic characteristic is clarified.The theoretical calculation results accord well with the electromagnetic software simulations and experimental results.The results in this paper should be helpful in understanding the physical mechanism of the IRC and designing the atomic clocks.

Enhanced surface plasmon interference lithography from cavity resonance in the grating slits

Surface plasmon interference lithography based on grating diffraction has been studied both theoretically and ex- perimentally in recent years. In this paper, we demonstrate that the cavity resonance in the grating slits can improve the subwavelength interference, not only the intensity but also the uniformity of the pattern. Both the typical lithography structure which merely consists of periodic metallic gratings and the modified structure equipped with a reflection layer are studied. The finite element method has been performed to study the interference pattern. Numerical simulations show that the property of the interference pattern is the optimum when cavity resonance happens. This enhancement can be applied to all the lithography structures which are based on the grating diffraction.

Application of the body of revolution finite-element method in a re-entrant cavity for fast and accurate dielectric parameter measurements

In dielectrometry,traditional analytical and numerical algorithms are difficultly employed in complex resonant cavities.For a special kind of structure(a rotating resonant cavity),the body of revolution finite-element method(BOR-FEM)is employed to calculate the resonant parameters and dielectric parameters.In this paper,several typical resonant structures are selected for analysis and verification.Compared with the resonance parameter values in the literature and the simulation results of commercial software,the error of the BOR-FEM calculation is less than 0.9%and a single solution time is less than 1 s.Reentrant coaxial resonant cavities loaded with dielectric materials are analyzed using this method and compared with simulation results,showing good agreement.Finally,in this paper,the established BOR-FEM method is successfully applied with a machined cavity for the accurate measurement of the complex dielectric constant of dielectric materials.The test specimens were machined from polytetrafluoroethylene,fused silica and Al_(2)O_(3),and the test results showed good agreement with the literature reference values.

Teleportation of two-atom entangled state in resonant cavity quantum electrodynamics

An alternative scheme is presented for teleportation of a two-atom entangled state in cavity quantum electrodynamics （QED）. It is based on the resonant atom-cavity field interaction. In the scheme, only one cavity is involved, and the number of the atoms needed to be detected is decreased compared with the previous scheme. Since the resonant atom-cavity field interaction greatly reduces the interaction time, the decoherence effect can be effectively suppressed during the teleportation process. The experimental feasibility of the scheme is discussed. The scheme can easily be generalized to the teleportation of N-atom Greeninger-Horne-Zeilinger （GHZ） entangled states. The number of atoms needed to be detected does not increase as the number of the atoms in the GHZ state increases.

High-performance Refractive Index Sensor Based on Photonic Crystal Single Mode Resonant Micro-cavity

An effective refractive index sensor built with square lattice photonic crystal is proposed,which can be applicable to photonic integrated circuits.Two photonic crystal waveguides rather than conventional ridge waveguides are used as entrance/exit waveguides to the micro-cavity.Three layers of photonic lattice are set between the photonic crystal waveguides and the micro-cavity to achieve both a high transmission and a high sensitivity.The plane wave method is utilized to calculate the disperse curves and the finite difference time domain scheme is employed to simulate the light propagation.At the resonant wavelength of about 1500 nm,the resonant wavelength shifts up by 0.7 nm for each increment of Δn=0.001.A transmission of more than 0.75 is observed.Although the position disorder of the photonic crystal doesn't affect the sensitivity of the sensor, the transmission reduces rapidly as the disorder increases.

Complete eigenmode analysis of a ladder-type multiple-gap resonant cavity

A theoretical model is developed for calculating the eigenmodes of the multi-gap resonant cavity. The structure of concern is a kind of ladder-type circuit, offering the advantages of easy fabrication, high characteristic impedance （R/Q）, and thermal capacity in the millimeter wave to THz regime. The eigenfunction expansion method is used to establish the field expressions for the gaps and the coupling region. Then, the match conditions at the interface are employed, which leads to a group of complicate boundary equations in the form of an infinite series. To facilitate the mathematical treatments and perform a highly efficient calculation, these boundary equations are transformed into the algebraic forms through the matrix representations. Finally, the concise dispersion equation is obtained. The roots of the dispersion equation include both the axial modes in the gaps, which include the fundamental and the high-order modes, and the cavity modes in the coupling region. Extensive numerical results are presented and the behaviors of the multi-gap resonant cavity are examined.

Resonant cavity-enhanced quantum dot field-effect transistor as a single-photon detector

A resonant cavity-enhanced （RCE） quantum dot （QD） field-effect transistor （RCEQDFET） is designed for single- photon detection in this paper. Adding distributed Bragg reflection （DBR） mirrors to the single-photon detector （SPD）, we improve the light absorption efficiency of the SPD. The effects of the reflectivity of the mirrors, the thickness and light absorption coefficient of the absorbing layer on the detector＇s light absorption efficiency are investigated, and the resonant cavity is determined by using the air/semiconductor interface as the mirror on the top. Through analyzing the relationship between the refractive index of AlxGal_xAs and A1 component, we choose A1As/Alo.15Gao.85As as the material of the mirror on the bottom. The pairs of A1As/Alo.15Gao.85As film are further determined to be 21 by calculating the reflectivity of the mirror. The detector is fabricated from semiconductor heterostructures grown by molecular beam epitaxy. The reflection spectrum, photoluminescence （PL） spectrum, photocurrent response, and channel current of the detector are tested and the results show that the RCEQDFET-SPD designed in this paper has better performances in photonic response and wavelength selection.

Mode separation of resonant cavity by electromagnetic simulation

Presents the investigation of characteristics of mode separation in typical magnetron cavity for the great importance of precise prediction of mode separation used in the theoretical study and engineering design of magnetrons, and the comparative theoretical predication and simulation analysis made using field theory and computer simulation based on commercial EDA tools, Ansoft High Frequency Structure Simulator(HFSS)and POISSON SUPERFISH.

Different optical properties in different periodic slot cavity geometrical morphologies

In this paper,optical properties of two-dimensional periodic annular slot cavity arrays in hexagonal close-packing on a silica substrate are theoretically characterized by finite difference time domain（FDTD） simulation method.By simulating reflectance spectra,electric field distribution,and charge distribution,we confirm that multiple cylindrical surface plasmon resonances can be excited in annular inclined slot cavities by linearly polarized light,in which the four reflectance dips are attributed to Fabry–Perot cavity resonances in the coaxial cavity.A coaxial waveguide mode TE11 will exist in these annular cavities,and the wavelengths of these reflectance dips are effectively tailored by changing the geometrical pattern of slot cavity and the dielectric materials filled in the cavities.These resonant wavelengths are localized in annular cavities with large electric field enhancement and dissipate gradually due to metal loss.The formation of an absorption peak can be explained from the aspect of phase matching conditions.We observed that the proposed structure can be tuned over the broad spectral range of 600–4000 nm by changing the outer and inner radii of the annular gaps,gap surface topography.Meanwhile,different lengths of the cavity may cause the shift of resonance dips.Also,we study the field enhancement at different vertical locations of the slit.In addition,dielectric materials filling in the annular gaps will result in a shift of the resonance wavelengths,which make the annular cavities good candidates for refractive index sensors.The refractive index sensitivity of annular cavities can also be tuned by the geometry size and the media around the cavity.Annular cavities with novel applications can be implied as surface enhanced Raman spectra substrates,refractive index sensors,nano-lasers,and optical trappers.

Topological resonators based on hexagonal-star valley photonic crystals

In valley photonic crystals, topological edge states can be gained by breaking the spatial inversion symmetry without breaking time-reversal symmetry or creating pseudo-spin structures, making highly unidirectional light transmission easy to achieve. This paper presents a novel physical model of a hexagonal-star valley photonic crystal. Simulations based on the finite element method(FEM) are performed to investigate the propagation of TM polarized mode and its application to ring resonators. The results show that such a topologically triangular ring resonator exhibits an optimum quality factor Q of about 1.25×104, and Q has a maximum value for both frequency and the cavity length L. Our findings are expected to have significant implications for developing topological lasers and wavelength division multiplexers.

Measurement of the Dielectric Properties of Volcanic Scoria and Basalt at 9370 MHz

Dielectric data for volcanic scoria and basalt on the earth at microwave frequency are extremely sparse, and also crucial for volcanic terrains imaging, and development. In consideration of their similarity to lunar regolith (soils and rocks) in chemical and mineral composition, the dielectric data is significative for passive and active microwave remote sensing on the Moon. This study provides the data about the dielectric properties of three kinds of scoria and two kinds of basalt in China. The method put forward in this paper is also applicable for measuring the dielectric properties of dry rocks and other granular ground materials with low complex dielectric constants. Firstly, the authors measured the e' and tanδ values of strip specimens prepared from the mixture of scoria or basalt powder and polythene with the resonant cavity perturbation method at 9370 MHz. Secondly, from the ε' and tanδ values of the mixture, the ε' s and tanδ s values of solid scoria and basalt were calculated using Lichtenecker's mixture formulae. Finally, the effective complex dielectric constants, ε' e and tanδ e , of scoria at different bulk densities were calculated. The results have shown that the ε' s and tanδ s values of all solid basaltic materials measured (both solid basaltic scoria or basalt) are approximately 7 and 0.05, respectively. With increasing bulk density of scoria, the ε' c and tanδ e values of scoria increase significantly.

Characteristic findings of malignant melanoma in the sinonasal cavity on magnetic resonance imaging

Background Malignant sinonasal melanoma （MSM） is a rare tumor with a perplexing signal intensity due to variable histopathologic components. This study was undertaken to delineate its MR imaging features. Methods MR imaging findings of 10 patients （6 women and 4 men, mean age 61.3 years old） with pathologically confirmed MSM were retrospectively reviewed. The location, size, signal intensity, enhancement, and internal imaging characteristics of all tumors were evaluated. Signal intensity and degree of enhancement was graded in comparison with the gray matter and adjacent muscle uptake, respectively. Results There were 8 tumors that were pathologically confirmed to contain melanin. Compared to gray matter of the brain, 7 of them demonstrated hyperintensity on T1WI and 6 （6/7） showed hypointensity on T2Wl. There was multiple linear, dark-signal intensity on T2Wl within the mass in 9 of the 10 patients＇ tumors. Evaluated with gadolinium-enhanced imaging, all 10 patients showed moderate enhancement within the areas that were isointense in the lesion on pregadolinium TlWl. Moreover, some parts which displayed hyperintensity on TlWl within the tumors of 7 patients showed mild enhancement that was similar to muscle on a time-intensity curve （TIC）. Conclusions MSM shows characteristic MR signal intensity （hyperintensity on TlWl and the linear, low-signal intensity on T2Wl）, which may provide valuable information for clinical diagnosis. Together with conventional MRI, TIC may be useful for indicating pleomorphic patterns of MSM.

Nonperturbative solutions to cylindrical resonant cavities with dissipative medium and imperfectly conducting walls

Cylindrical waveguides without end surfaces can serve as two-dimensional resonant cavities. In such cavities the electromagnetic oscillations corresponding to an eigenfrequency can always be taken as TM or TE modes even when the walls have a finite conductivity and the medium is absorptive. This paper obtains analytic solutions to the field equations when the cylinder has a circular cross section. Some nonperturbative conclusions are drawn from the eigenvalue equation. Approximate analytic results for the resonant frequencies are obtained when the absorption of the medium is small and the walls are good conductors. Stability of the eigen modes is discussed. Similar results for the coaxial line are presented.

A new model for film bulk acoustic wave resonators

Based on cavity resonance and sandwich composite plate （3D） theoretical model for frequency dispersion characterization theory, this paper presents a universal three-dimensional and displacement profile shapes of the film bulk acoustic resonator （FBARs）. This model provides results of FBAR excited thickness-extensional and flexure modes, and the result of frequency dispersion is proposed in which the thicknesses and impedance of the electrodes and the piezoelectric material are taken into consideration; its further simplification shows good agreement with the modified Butterworth-Van-Dyke （MBVD） model. The displacement profile reflects the vibration stress distribution of electrode shapes and the lateral resonance effect, which depends on the axis ratio of the electrode shapes a/b. The results are consistent with the 3D finite element method modeling and laser interferometry measurement in general.

Flat-top and low-dispersion optical interleavers based on nested prism pair structure

A novel flat-top and low-dispersion optical interleaver using ring cavities （RCs） in a Mach-Zehnder interferometer （MZI） is proposed. It is composed of eight mirrors and two nested prism pairs. Each prism and the two mirrors behave as a RC. Phase shift of RC is a periodic function of the frequency of the input light which acts as a phase dispersive mirror. The two phase shifts needed to achieve a flat-top spectral passband are provided by Fresnel reflectivities at the prism-air interface of the two RCs. The optimum interface reflectivities for flat passband, high isolation and low dispersion can be obtained only by choosing an appropriate material for the prism in each RC. The proposed interleaver in a 25 GHz channel spacing application exhibits a 0.5 dB passband greater than 24 GHz （96% of the spacing）, a 30 dB stopband greater than 21.2 GHz （84.8% of the spacing）, a channel isolation higher than 32 dB and chromatic dispersion ±50 ps/nm within the range of center-frequency ：t：2 GHz ITU passband.

Analysis and Numerical Modeling of a 20 W Microwave Electrothermal Thruster

The microwave electrothermal thruster （MET） is an electric propulsion device that uses an electromagnetic resonant cavity within which free-floating plasma is ignited and sustained in a propellant gas.The thrust is generated when the heated propellant gas is exhausted out of a gas-dynamic nozzle.For an empty cavity without any perturbing regions—e.g.,dielectric regions or antenna regions—it is fairly straightforward to accurately calculate the cavity＇s resonant frequency and describe the electric field intensity distribution within the cavity.However,actual METs do contain perturbing regions,which means that analytical solutions are no longer possible to fully characterize the device.Hence,the numerical methods to simulate the electric field intensity and distribution within the resonant cavity were employed.The simulation results are that with the cap height increasing,the resonant frequency and electric field strength decrease,also increasing the permittivity of dielectric material causes decreasing the resonant frequency and electric field strength.A decrease in resonant frequency and maximum electric field strength,and an increase in resonant bandwidth,were observed with increasing antenna depth.Rounding an antenna of a given depth equals decreasing the depth.

Improvement on the magneto-optical Kerr effect of cobalt film with a quadrilayer structure

The magneto-optical Kerr effect of the HfO2/Co/HfO2/A1 multilayer structure is investigated in this work, and an ob- vious cavity enhancement of the Kerr response for the HfO2 semiconductor is found both theoretically and experimentally. Surprisingly, a maximum value of about -3 of the polar Kerr rotation for s-polarized incident light is observed in our experiment. We propose that this improvement on the Kerr effect can be attributed to the multiple reflection and optical interference in the cavity, which can also be proved by simulation using the finite element method.

Single Mode DR Filters for Wireless Base Stations

This paper presents state-of-the-art high Q single-mode dielectric resonator （DR） cavity filters for PCS wireless base stations. DR cavity filters shrink the cavity size significantly more than waveguide cavity filters and offer about twice higher Q than coaxial resonators. Thus, they have important applications in wireless base stations operating below 2.5 GHz. Dual-mode and triple-mode DR cavity filters have existed for a while; however, single-mode DR cavity filters are predominant because they are cheaper to manufacture. This paper summarizes the main characteristics of TE01 mode DR cavities, including mode chart and field distribution, and compares cavity Q with waveguide and combline （coaxial） cavities. Dielectric combline and TM010 mode DR cavities are analyzed and compared to TE01 mode DR cavities. General filter design techniques are discussed, and several design examples are given to show how filter technology has developed.