Transmission of a Gaussian beam after incidenting nonnormally on a Fabry–Perot etalon: a nonresonant case

Under the nonresonant case where the carrier frequency of a Gaussian beam deviates from the resonant frequency of a Fabry–Perot etalon, the transmission of a Gaussian beam after incidenting nonnormally on a Fabry–Perot etalon has been investigated. The results show that under the nonresonant case, variations of the peak intensity, the position of the peak intensity and the spot size of the transmitted beam with the input angle behave differently and even with a reversed tendency compared with those obtained under the resonant case.     

Influence of a Fabry–Perot etalon on a chirped optical pulse

Taking into consideration the fact that the output from a Fabry–Perot etalon is formed on the basis of the interference of the multi-reflected beams of the input pulse that enters the etalon, an analytical expression of the output pulse intensity has been derived for an input chirped Gaussian pulse passing through an etalon. Using the expression, the temporal width and the peak power of the output pulse is investigated. Results show that for a given etalon, the chirp factor and the width of the input pulse have intense effects on the width and the peak of the output pulse.     

Transmitting intensity distribution after a Gaussian beam incidenting nonnormally on a wedged Fabry-Perot cavity

After deriving the expression of the intensity of the transmitted beam for a Gaussian beam nonnormally passing through a wedged Fabry-Perot cavity, the influence of the wedged angle in Fabry-Perot cavity mirrors alignment at a different tilted angle on the transmission of a Gaussian beam has been investigated theoretically. Numerical simulations show that the incidental angle and the wedged angle in Fabry-Perot cavity mirrors alignment have an important effect on the intensity distribution, the peak intensity, and the position of the peak intensity of the transmitted beam.     

Stabilized fiber-optic extrinsic Fabry–Perot sensor system for acoustic emission measurement

A fiber-optic Fabry–Perot (F–P) acoustic emission (AE) sensor system based on an improved double wavelength stabilization technique is described. Without stabilization, the sensor system drifts out of quadrature due to the presence of low-frequency dynamic strains. The stabilization is achieved by using a dense wavelength division multiplexer (DWDM) to generate two quadrature phase-shifted output signals. An optimum model of double wavelength stabilization is established. The filtering wavelengths of DWDM are calculated using an optimization design method. The performance of the developed sensor system was verified by two preliminary tests. One was a test on the stabilization of operating point of fiber-optic F–P sensor, and other was the detection of simulated AE signals generated by the impact and pencil lead breaking. The test results demonstrate that simulated AE signals are successfully detected using this stabilized sensor system, which solves the fade-out problem.     

External electro-optic sampling utilizing a poled polymer asymmetric Fabry–Perot cavity as an electro-optical probe tip

External electro-optic sampling utilizing a poled polymer asymmetry Fabry–Perot cavity as electro-optic probe tip has been demonstrated. Electro-optical polymer spin coated on the high-reflectivity mirror (HRM) was corona poled. Thus, an asymmetric F–P cavity was formed based on the different reflectivity of the polymer and HRM and it converted the phase modulation that originates from electro-optic effect of the poled polymer to amplitude modulation, so only one laser beam is needed in this system. The principle of the sampling was analyzed by multiple reflection and index ellipsoid methods. A 1.2 GHz microwave signal propagating on coplanar waveguide transmission line was sampled, and the voltage sensitivity about was obtained.     

Sapphire hard X‐ray Fabry–Perot resonators for synchrotron experiments

Hard X‐ray Fabry–Perot resonators (FPRs) made from sapphire crystals were constructed and characterized. The FPRs consisted of two crystal plates, part of a monolithic crystal structure of Al₂O₃, acting as a pair of mirrors, for the backward reflection (0 0 0 30) of hard X‐rays at 14.3147 keV. The dimensional accuracy during manufacturing and the defect density in the crystal in relation to the resonance efficiency of sapphire FPRs were analyzed from a theoretical standpoint based on X‐ray cavity resonance and measurements using scanning electron microscopic and X‐ray topographic techniques for crystal defects. Well defined resonance spectra of sapphire FPRs were successfully obtained, and were comparable with the theoretical predictions.     

Photon recycling in Fabry–Perot micro-cavities based on Si3N4 waveguides

We present a numerical analysis and preliminary experimental results on one-dimensional Fabry–Perot micro-cavities in Si₃N₄waveguides. The Fabry–Perot micro-cavities are formed by two distributed Bragg reflectors separated by a straight portion of a waveguide. The Bragg reflectors are composed of a few air slits produced within the Si₃N₄ waveguides. In order to increase the quality factor of the micro-cavities, we have minimized, with a multiparametric optimization tool, the insertion loss of the reflectors by varying the length of their first pairs (those facing the cavity). To explain the simulation results, the coupling of the fundamental waveguide mode with radiative modes in the Fabry–Perot micro-cavities is needed. This effect is described as a recycling of radiative modes in the waveguide. To support the modelling, preliminary experimental results of micro-cavities in Si₃N₄ waveguides realized with the focused ion beam technique are reported.     

Study on a Bessel–Gaussian beam laser

A new concept and the method are presented to obtain a laser beam output with high luminance and quality. Instead of using the conventional concept of “obtaining a single transverse mode through compressing the oscillating mode volume using a small aperture diaphragm”, the large multimode volume and the high output power are obtained by studying the physical mechanism of the expansion and coupling between a Bessel beam and a Gaussian beam. A high quality light beam (close to the diffraction limit) with high luminance and large intensity difference between the center and the edge is achieved simultaneously.     

非共振条件下高斯光束斜入射法布里-珀罗干涉仪的透射特性

基于多光束干涉原理,研究了当高斯光束的载波频率与法布里—珀罗(F P)干涉仪的谐振频率存在偏差(即非共振)时,高斯光束斜入射F P干涉仪的透射特性。结果表明,与共振情况相比,非共振条件下透射光束的峰值强度及其所对应的位置、以及光斑的大小随入射角的变化都发生了显著的改变。     

Employing injection-locked Fabry–Perot laser diodes to improve bidirectional WDM–PON performances

We proposed and demonstrated a bidirectional wavelength-division-multiplexing (WDM)–passive optical network (PON) employing injection-locked Fabry–Perot laser diodes (FP LDs) at both transmitting sites, and adaptive filters at both receiving sites. Injection-locked FP LDs, a particularly inexpensive option, are used to replace the conventional distributed feedback (DFB) LDs in WDM–PON. Adaptive filters are attractive because they can track the variations and compensate the nonlinear distortions. Transmission performance over 20 km of a standard single-mode fiber (SMF) was investigated. Improved performance of bit error rate (BER), better and clear eye diagram were achieved in our proposed WDM–PON.     

Study of cross-talk of parallel Fabry–Perot sensors in path-matching differential interferometry

Cross-talk in multiplexing parallel Fabry–Perot sensors in a path-matching differential interferometry (PMDI) can be limited by corresponding path-matching read-out systems. Nevertheless, improper design in cavity lengths of Fabry–Perots can result in serious cross-talk. This paper presents a spectrum analysis to design the parallel Fabry–Perot sensors quantitatively without cross-talk. The spectrum analysis used to solve the cross-talks in a multiple parallel Fabry–Perot system is proved to be an efficient tool. To the author's knowledge, cross-talk problems were first investigated in a multiple parallel Fabry–Perot system quantitatively and experimentally. In a spectrum analysis, the spectrum transfer function in a broadband light source and a Fabry–Perot cavity are simulated by a Gaussian distribution spectrum and a low-finesse reflectivity, respectively. After integrating the whole spectrum system with respect to the wave number, the cross-talk terms can be removed by assuming zero. It is concluded that the cavity length differences between two Fabry–Perots should be longer than the coherence length of a broadband light source to diminish cross-talk effects. Experimental results for two parallel Fabry–Perots in PMDI are presented and compared with theoretical predictions. This study shows good agreement between experimental results and theoretical predictions, indicating that spectrum analysis can be applied properly to the design of two- or multiple-parameter sensors.     

Generation of optimized wavelength-tunable optical pulse from an uncooled gain-switched Fabry–Perot semiconductor laser using optical amplifier as external light injection

We present a novel system design that can generate the optimized wavelength-tunable optical pulse streams from an uncooled gain-switched Fabry–Perot semiconductor laser using an optical amplifier as external light source. The timing jitter of gain-switched laser has been reduced from about 3 ps to 600 fs and the pulse width has been optimized by using our system. The stability of the system was also experimentally investigated. Our results show that an uncooled gain-switched FP laser system can feasibly produce the stable optical pulse trains with pulse width of 18 ps at the repetition frequency of 5 GHz during 7 h continuous working. We respectively proved the system feasibility under 1 GHz, 2.5 GHz and 5 GHz operation.     

Vectorial structure of Hermite–Laguerre–Gaussian beam in the far field

Starting from Maxwell's equations, a Hermite–Laguerre–Gaussian (HLG) beam is decomposed into the TE and TM terms by using the vector angular spectrum representation. By means of the method of stationary phase, the analytical TE and TM terms are presented in the far field. The energy flux distributions of the TE and TM terms are also investigated and depicted in the far field. The influences of the additional angle parameter and Gaussian waist width on the vectorial structure and energy flux pattern of HLG beam are also investigated. This research reveals the internal vectorial structure of HLG beam and may provide a new approach to the manipulation of laser beams.     

Propagation of high-order Bessel–Gaussian beam through a misaligned first-order optical system

The generalized diffraction integralis used to derive a generalized formula for high-order Bessel–Gaussian beams (HBGBs) through a misaligned first-order ABCD optical system. It is found that, when a HBGB propagates through a misaligned optical system, the beam shape of the output beam is unchanged. However, the center of the output beam is deviated from the optical axis, forming a decentered HBGB. The position of the output beam may be controlled by adjusting the misaligned parameters. Based on the derived formula, the diffraction patterns of HBGBs propagating through a simple misaligned lens system have been calculated numerically. These results may be useful in the application of laser beams for trapping and manipulating a wide variety of particles.     

The elliptical Laguerre–Gaussian beam and its propagation

A new kind of light beam called the elliptical Laguerre–Gaussian beam (ELGB) is proposed in this paper in terms of tensor method. The propagation formula of ELGB through axially asymmetric optical system is derived by the generalized Collins integral. By using this formula, the propagation of ELGB in free space is calculated and discussed. The results show that the propagation behavior of ELGBs is notably different from that of LGBs.     

Generalized beam propagation factor of hard-edged circular apertured diffracted Bessel–Gaussian beams

Based on the truncated second-order moments method on the cylindrical coordinate systems and the incomplete gamma function, an analytical expression of the generalized beam propagation factor (M_G² factor) of hard-edged circular apertured diffracted Bessel–Gaussian beams is derived and illustrated numerically. It is shown that the M_G² factor of hard-edged diffracted BGBs mainly depends on the truncation parameter δ and the beam parameters m and η. The results can be reduced to that for the non-truncated Bessel–Gaussian beams case and that for the truncated fundamental Gaussian beams case under certain conditions, respectively. The power fraction is also discussed analytically and numerically.     

Light Squeezing in a Fabry–Perot Cavity

A quantum mechanical model for the study of quadrature squeezing in radiation coming out of Fabry–Perot cavity containing nonlinear Kerr medium has been proposed. We have incorporated the vacuum fluctuations entering in the cavity through unused ports. The analysis has been applied to a sample of GaAs filled in the Fabry–Perot cavity and irradiated by an off-resonant Co:MgF₂ laser. Limitations on achievable squeezing due to incident pump power, interaction time, nonlinear coupling parameter and facet reflectivities have been discussed and it is seen that low reflectivity of front facet and high reflectivity of rear facet of the cavity produces substantial squeezing.     

高斯光束斜入射法布里—珀罗干涉仪的透射光强分布

基于多光束干涉原理,研究了高斯光束斜入射法布里—珀罗干涉仪的透射光强分布。结果表明,当以较大角度入射时,输出为一系列空间分离的光斑;当以较小角度入射时,输出尽管为单一光斑,但是与输入相比,其峰值强度位置发生了偏移,且光斑变大。     

Accuracy Analysis of the Fabry–Perot Etalon Based Doppler Wind Lidar

A direct detection Doppler wind lidar with the dual Fabry–Perot technique has been built in Hefei, China, and the system is described in this paper. A dual, air-spaced Fabry–Perot etalon is designed as the frequency discriminator and the transmission characteristics are measured with a stabilized cw laser and a pulse laser. The experimental data are found to be in agreement with the designed parameters. The Doppler shift is measured by taking the ratio of the transmitted intensities from the dual etalon. Analysis of the accuracy of Doppler measurement is made by considering the factors of the number of iterations in converting the measured ratio to the Doppler shift, the laser intensity fluctuation and the signal-to-noise ratio. In the sufficient signal-to-noise ratio the velocity accuracy of the Doppler lidar system is estimated to be better than 0.5 m/s.     

25 GHz interleavers made by Michelson interferometer with a Gires–Tournois etalon

We report a high-quality interleaver with frequency spacing of 25 GHz, which is made by a Michelson interferometer with a mirror replaced by a Gires–Tournois etalon. Our optimal design and elaborate manufacture assure its excellent performance. We present the analysis of performance parameters, design of structural parameters, the unique fabrication technology and testing results of this interleaver in this paper.