左手介质椭圆光波导基模传播特性

在椭圆柱坐标系中,采用分离变量方法,得出了左手介质椭圆光波导本征方程的近似解,通过数值计算,分析了椭圆波导偏心率、左手介质的电容率、磁导率对椭圆光波导基模传播特性的影响,并将左介质光波导与右手介质光波导基模特性进行对比,得出左手介质光波导的基模特性与右手介质光波导基模特性差别不大的结论.     

Propagation Characteristics of an Elliptically-cored Highly Birefringent Fiber using an Analytical Method

By using the method of separation of variables in the elliptical coordinate system, a representative formula in terms of Mathieu and modified Mathieu functions is derived and longitudinal field components for the even and odd modes are presented for the proposed fiber. The eigen value equation for the fiber to be considered is obtained by solving the fourth order determinantal equation under weak guidance condition and is given in this paper. The cutoff frequency of several lower orders modes for different eccentricities have been obtained and their propagation characteristics have been plotted. The effect of the eccentricity on the modal cutoff values and mode transmissions is discussed. Finally, the modal birefringence in the proposed fiber is also estimated.     

单模光纤折射率分布对偏振模色散的影响

利用将任意非圆柱等效为椭圆的方法分析和计算了单模光纤中包层和芯层折射率分布不同心导致的偏振模色散，得到了两个偏振模式的传输常数差△β和偏振模色散△τ与偏心比、入射光的波长、芯层半径、相对折射率差的关系曲线，为实践中昼减小单模光纤的偏振模色散提供理论上的指导。与椭圆度引起的偏振模色散相比，不同心引起的偏振模色散具有相同的数量级。     

Computing Eigen value equation and modal dispersion characteristics of an elliptical Bragg waveguide

Using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a new type of Bragg waveguide having elliptical core cross section with multilayered cladding is derived. The eigen equation is written in the form of Mathieu and the modified Mathieu functions and a dispersion relation is obtained for various modes supported by the proposed Bragg waveguide. The cutoff frequencies for several lower order even-odd modes have been calculated and their propagation characteristics are plotted. The results show that the dispersion curves are discontinuous and modes can exist only in particular wavelength bands. The effects of elliptical eccentricity on the mode cutoff values and mode transmission are addressed. Finally, the modal birefringence in the said waveguide is also estimated.     

Sound propagation in acoustically lined elliptical ducts

Sound propagation in ducts with elliptical cross-sections can be described in terms of modes characterized by Mathieu functions of orders specified by the boundary conditions. For ducts with locally reacting liners there is coupling between modes because the admissible solutions are linear combinations of Mathieu functions of different orders and the eigenvalues are roots of an infinite determinant. The amount of mode coupling depends on the eccentricity of the duct. For the case of small eccentricity of the duct, approximate general solutions are derived and an example is discussed, where solutions are found.     

Wave Properties of A Free Elliptical Helix Slow-Wave Structure with Arbitrary Eccentricity

This paper gives the investigations of the fundamental wave of a free elliptical helix slow-wave structure (SWS) with arbitrary eccentricity. The wave properties including the phase velocity characteristics, interaction impedance and the longitudinal electric field distribution of this mode has been fully studied. It is found that, when the eccentricity increases, the interaction impedance and the operating frequency of such SWS will be improved, which allows to have a higher gain and operating in a higher frequency band. Furthermore, the field configuration is different from that of a round helix; the azimuthal distribution of the E-field follows with the angular Mathieu function of the first kind, even with mode of zero. In radial, E-field is elliptical surface wave. When the eccentricity tends to zero, all the characteristics will be smoothly degenerates to the case of round helix correspondingly.     

Polarization mode dispersion and vectorial modulational instability in air-silica microstructure fiber

The birefringence of an air-silica microstructure fiber has been studied by measurement of the fiber polarization mode dispersion (PMD) over the wavelength range 545-640 nm. The experimental results are shown to be in good agreement with vectorial numerical calculations, assuming an elliptical core with an eccentricity of 7%. We also report controlled experiments studying nonlinear vectorial modulation instability in the fiber, yielding 3.9-THz modulational instability sideband shifts that are in good agreement with theoretical predictions based on the calculated fiber dispersion and PMD characteristics.     

Field analysis based on the smoothly deformed Bragg fiber

A new kind of smoothly deformed Bragg fiber structure has been proposed in this paper, and the mode field characteristics about this fiber have been analyzed. By comparing the field at different coordinates along the propagation direction, the evolution of the field for the elliptical transverse faces and the circular one is obtained. The method has also been used to detect the behavior of the elliptical Gaussian beam. This research method can be used to analyze the thermal deformation of fiber.     

Slow Wave Characteristics of Helix Structure with Elliptical Cross Section

We present a novel helix slow wave structure with an elliptical cross section shielded by an elliptical waveguide. The rf characteristics including dispersion properties, interaction impedance of zero mode in this structure have been studied in detail. The theoretical results reveal that weaker dispersion even abnormal dispersion characteristics is obtained with the increasing eccentricity of the elliptical waveguide, while the interaction impedance is enhanced by enlarging the eccentricity of elliptical helix.     

Mode competition in multi-core fiber amplifier

3D beam propagation numerical code and a newly developed optical mode solver were implemented for studies on the recently experimentally realized Yb fiber amplifier with 7-core hexagonal structure. It was found that the launched seven single-frequency beams matched with the cores converge to a wave field with permanently diminishing space beating patterns, but the result is sensitive to phases of separate beams. Namely, at a spread of phases of individual beams within a few tenths of radian, the convergence of the wave field to the in-phase mode is observed, while at phases random spread on the order of π the out-of-phase mode is dominating. Such behavior is observed at strong gain saturation in the cores. Both effects take place even if the guiding index of the cores fluctuates within a limited range. The mode solver predicts that the in-phase mode has the minimal small signal gain, and the gain of the out-of-phase mode is maximal one. This fact proves that there is no strict correlation between modal gains and amplification in strong saturated multi-core fiber. The smaller core index step significantly improves the convergence of the amplified radiation to the in-phase mode. An approach to the waveguide structure tailoring is described which assures the single in-phase mode stability.     

Analysis of Transverse Mode Formation in Quasi-Three-Level Microchip Lasers

The effects of gain guiding and thermal guiding on the cavity mode formation for quasi-three-level microchip lasers are investigated. A parameter describing the dominant guiding mechanisms at the lasing threshold is defined. Paraxial wave propagation equation for the field envelope in the gain medium with thermal-induced refractive index profile and gain profile is derived. A comparison between the calculated results and those of experiments reveals that this model is quite reasonable and applicable not only to the Yb:YAG microchip laser, but also to other quasi-three-level microchip lasers.     

Polarization properties of rectangular lattice photonic crystal fiber

In this paper, polarization properties and propagation characteristics of rectangular lattice photonic crystal fibers with elliptical air-holes are investigated by using the full-vector finite element method with anisotropic perfectly matched layers. Numerical results show that the birefringence of the fiber is induced by asymmetries of the cladding. Moreover, by adjusting its structure parameters, such as the hole pitch Λ, and the air-hole elliptical rate η, we find the optimized design parameters of the fiber with high birefringence (the order of 10⁻²) and limited polarization mode dispersion, operating in a single mode region at an appropriate wavelength range.     

Extremely large birefringence and shifting of zero dispersion wavelength of photonic crystal fibers

Three different types of photonic crystal fibers have been investigated which promise very large birefringence. The first type fiber is band gap guiding, the second index guiding, while the third type is index guiding with high refractive index circular and elliptical regions in the innermost ring. The birefringence, group velocity dispersion, modal effective index and mode field area of these fibers have been numerically estimated by employing finite difference time domain method. When elliptical regions are introduced in the first and second rings with the combination of small circular regions, each of these proposed fibers exhibits large birefringence with shifted zero dispersion point. Among these three different types of fibers, the band gap guiding photonic crystal fiber promises the largest birefringence (～5.45×10^?2) reported so far. The value of the birefringence and group velocity dispersion of these fibers can be controlled by controlling the hole pitch. Largest birefringence is achieved with a specific value of hole pitch.     

The Quantum Theory of Optical Pulses Amplification

The propagation of optical signals in optical fiber amplifier is treated with fully quantum mechanics method in this paper. The micro-Hamiltonian of the system with nonlinear effect is derived by combining spatial mode and temporal mode, and propagation equation of optical pulses in a optical fiber amplifier is derived with dispersion relation. The characteristic parameters such as gain, output power and noise figure of the amplifier are analyzed and their quantum mechanics formulas are obtained.     

Dispersion management with filtering

We present analytical and numerical results for dispersion-managed solitons in a fiber link including guiding filters and compensating gain, both taken in the distributed approximation. Stationary propagation regimes with anomalous, zero, and normal path-average dispersion (PAD) are identified. New features, compared with those of the case without filters, are the absence of a critical strength for propagation at zero and normal PAD and, instead, the existence of a critical power for stationary propagation at any PAD.     

椭圆包层光纤场的迭代近似解与漏模损耗计算

试图理论上处理椭圆包层各向异性光纤复杂的折射率分布。数学过程包括折射率分布的级数展开、δ－涵数的导数和积分以及用格林函数求解方程的迭代技术。给出了椭圆包层各向异性光纤漏模损耗的解析表达式。数值结果表明椭圆包层各向异性光纤的漏模损耗比领结型光纤小，比阶跃型各向异性光纤大；偏心率越大越有利于制造单模单偏光纤。     

Mode properties of an external-cavity laser with Gaussian gain

We analyze the mode properties of a laser with a Gaussian gain profile by using the beam propagation method. The resonance properties of the Petermann K factor and the M2 beam quality are shown to be related in the vicinity of degenerate cavity geometries. K is unity for a confocal cavity, even under conditions with strong gain guiding, while M2 is a maximum.     

Full-vector analysis of a realistic photonic crystal fiber

We analyze the guiding problem in a realistic photonic crystal fiber, using a novel full-vector modal technique. This is a biorthogonal modal method based on the non-self-adjoint character of the electromagnetic propagation in a fiber. Dispersion curves of guided modes for different fiber structural paremeters are calculated, along with the two-dimensional transverse intensity distribution of the fundamental mode. Our results match those achieved in recent experiments in which the feasibility of this type of fiber was shown.     

Central distance of interferential mode patterns of elliptical cora two-mode fiber

By means of the weakly guiding approximation, the mode spot sizes Wx and Wy of the fundamental mode along the semimajor (x-direction) and semiminor (y-direction) axes of the fiber core in elliptical core twomode fiber are discussed. The variation of their ratio value Wx/Wy with the operation wavelength λ and the length ratio a/b between the semimajor axis and the semiminor axis of the fiber core is analyzed. Based onthis analysis, the distribution figures of two-lobe interferential mode patterns are evaluated and simulated quantitatively for different phase difference changes between LPo1 and LPeven11 modes. The two-lobeinterferential mode patterns have the same profile and distribute symmetrically when the phase differenceequals π/2. Their central distance S becomes larger when WX/Wy augments gradually. Furthermore,the equation about the central distance S of the two-lobe interferential mode patterns is given when the operation wavelength varies between 0.65 and 1.31 μm, which is important to applications shuch as sensors and coupling devices between different fibers.     

Structural and wavelength dependence of mode power distribution for a broadband dispersion compensating microstructured fiber

Approximate empirical analysis of mode power distribution (MPD) carried by the fundamental mode is newly investigated based on a broadband dispersion compensating microstructured fiber (MF). The fraction of modal power in the core region, η, is defined with the help of extending the applicability of well-established classical optical fiber theories to MFs. In doing so, the influences of structural parameters and wavelength on MPD characteristics of the fundamental mode are systematically analyzed in detail based on simple physically consistent concepts of conventional fibers. As a result, it is shown that for the optimum MF design in Ref. [11] as a multimode fiber, when the number of guiding modes increases, the mode power ratio of the fundamental mode constantly increases from 69.4%; in addition, we find that as wavelength increases within 1.2-1.6 μm, mode power confinement ability of the fundamental mode is lessened for single-mode propagation, whereas for multimode propagation it becomes enhanced.