Based on the weakly waveguide approximation, the eigen mode field distribution of fundamental mode step index square waveguide is suggested, and the overlap integral formula between two mode field distributions is employed, the expression of coupling efficiency between fundamental mode step index square waveguide and fiber is suggested. As the values of beam propagation factors of fundamental mode step index square waveguide and fiber are closed to unit in a certain range of normalized frequency, it is rational to express the mode field distributions of fundamental mode square waveguide and fiber by the Gaussian approximation in some range of normalized frequency. As the equivalent mode field size which defined by the geometric mean of second moment mode field size and differential operator mode field size is employed to express the waist sizes of Gaussian approximation for fundamental mode step index square waveguide and fiber, the coupling characteristics between fundamental mode step index square waveguide and fiber is discussed, and a useful optimum coupling condition is suggested. The conclusions would be beneficial to the assembling technology of optical waveguide device.
Based on the definition of beam propagation factor, the relation between beam propagation factor and normalized frequency of TE1 mode of planar waveguide is presented. As the value of beam propagation factor of TE1 mode is close to three for a certain range of normalized frequency, it is rational that the field distribution of TE1 mode of dielectric planar waveguide is expressed by the first order Hermite-Gaussian approximation. When the equivalent mode field half width expressed by the geometric mean of the two kinds of mode field half widths based on the differential operator definition and the second moment definition is employed as the waist size of Hermite-Gaussian approximation, the matching efficiency between the TE1 mode field of planar waveguide and its first order Hermite-Gaussian approximation is near to unit for a certain range of normalized frequency. For giving the characteristics of the beam propagation factor and equivalent mode field half width obviously, the fitting expressions for beam propagation factor of TE1 mode field of planar waveguide as function of normalized frequency and the equivalent mode field half width of the first order Hermite-Gaussian approximation as function of normalized frequency are suggested respectively.
As the equivalent refractive index solution and the Fraunhofer approximation of scalar diffraction integral formula are
engaged, the far field diffraction characteristics of TE0 mode symmetrical multiple quantum well planar waveguide is discussed. Based on the Fourier transform relation between the near field distribution and far field diffraction distribution, the relation among the near field half width, far field divergence half angle and beam propagation factor for non-paraxial light beam are analysed and some approximate relationship with definite physical meaning are presented.
Then, the approximate characteristics of beam propagation factor, near field half width defined by equivalent matching
efficiency and tangent value of far field divergence half angle defined by equivalent matching efficiency versus the
number of potential well layers of TE0 mode symmetrical MQW planar waveguide are presented.
Proc. SPIE. 8197, 2011 International Conference on Optical Instruments and Technology: Optical Systems and Modern Optoelectronic Instruments
KEYWORDS: Signal to noise ratio, Light emitting diodes, Optical amplifiers, LabVIEW, Interference (communication), Linear filtering, Signal processing, Electronic filtering, Signal detection, Tolerancing
In this article, it presents a suit of single channel input virtual Dual-Phase Lock-in Amplifier (DPLIA) that is constructed
by a personal computer sound card and the LabVIEW software. The virtual DPLIA is low cost and convenient to
implement. The implemented DPLIA could enhance the noise tolerance capability and lower the LOD of the optical
signal detection system. A primary benefit of this instrument is it only needs one input channel; two internal reference
signals of the digital PLL are generated in the LabVIEW software. It is easy to control and operate, the data processing
results can be saved directly to disks. This instrument will be applied in other weak signal detection systems.
Based on the eigen equation and relationship among three normalized parameters, the approximate expression between
the normalized standing parameter and the normalized frequency of TE01 mode of step index fiber is recommended.
Then, the characteristics of TE01 mode field distribution is analyzed, the approximate expression between the radial
coordinate for maximal amplitude of mode field and the normalized frequency is suggested. For the sake of clarifying
the characteristics of diffraction far field of TE01 mode of step index fiber, its expression is given according to the scalar
diffraction integral formula. Then, the approximate expression between the normalized spatial frequency for the maximal
spatial frequency spectrum and the normalized frequency is suggested. Numerical calculations show that the relative
error between approximate value and exact value are small than one percent within a large variable range and this
indicate that these approximate expressions are relatively reasonable.
For the sake of clarifying the characteristics of cylindrical travelling wave and step index fiber, the modified zero order
Hankel function, which is an approximate harmonic complex function without singularity, is recommended as the eigen
function of cylindrical travelling wave in homogeneous dielectric. As the modified zero order Neumann function avoids
the singularity in the origin of coordinate, and the concept of the essence of mode field of fiber is engaged, both of zero
order Bessel function and modified zero order Neumann function are recommend as the eigen functions of axial electric
or magnetic component in the core layer of step index fiber. Then, the analysing method of vector mode of fiber is used
for reference, a new eigen equation of step index fiber is recommended. These may provide a new method for analyzing
the characteristics of cylindrical travelling wave and step index fiber.
The diffraction far-field of planar waveguide is investigated and then rationality of the Gaussian approximation for it is
clarified based on the characteristic of its beam propagation factor. A new definition for divergence half-angle is
presented according to the maximal matching efficiency method, furthermore, relationship between the maximal
matching efficiency divergence half-angle and normalized frequency is given.
Based on the non-paraxial vectorial moment theory of light beam propagation and waveguide mode theory, the beam
parameters of single-mode fiber including mode-field radius, divergence half-angle and beam propagation factor are
analyzed and calculated. Especially, the results of beam propagation factor show that if both the core and cladding layer
fields are considered, M2>1 is always obtained and neglect of the cladding layer field will lead to M2<1. These
conclusions may be useful for further research on beam quality of fiber laser beam.
The far-field distribution of single-mode fiber is studied; the Gaussian approximation for it is analyzed based on the
characteristic of beam propagation factor and then its rationality is explained. Through researching the matching
efficiency between the far-field and Gaussian field, a new definition of divergence half-angle is presented according to
the maximal matching efficiency method; furthermore, a formula of the maximal matching efficiency divergence halfangle
as function of normalized frequency is given.
Based on the mutual coupling coefficient what derived from the method of field distribution analysis, the expressions of
coupling factor and coupling efficiency between two identical structure nonparallel straight rectangular waveguides are
suggested, and computing instances are introduced for showing the crosstalk between adjacent rectangular waveguides in
the star coupler of an AWG demultiplexer. Then, an approximation expression for computing the maximal crosstalk
between adjacent arrayed waveguides of an AWG demultiplexer is recommended. As the crosstalk between adjacent
arrayed waveguides of an AWG demultiplexer is in need of a limit, the expression for estimating the space between the
end face centers of adjacent arrayed waveguides in an AWG demultiplexer is advanced also, and a computing instance is
introduced for showing the crosstalk between adjacent arrayed waveguides in an AWG demultiplexer. Finally, based on
the Gaussian approximation for the mode field distribution of optical waveguide, the theoretical model of the spectral
response efficiency of an AWG demultiplexer is engaged, a computing instance is presented for showing the spectral
response characteristic and crosstalk characteristic of an bilateral symmetry structure AWG demultiplexer. These works
provides some help for ascertaining the basic parameters of an AWG demultiplexer.
Based on the Helmholtz's equation and energy conservation law for the travelling wave field, the actual wave function
for the TE travelling wave in the inhomogeneous dielectric is recommended, the original field distribution functions of
the TE mode in symmetrical planar waveguide core layer and cladding layers are suggested. Moreover, the virgin phase
shift for total reflection effect at the turning point is proposed, the eigen equation of a new improved WKB method for
the symmetrical planar waveguide is given. As the concept of phase delay for optical wave in the dielectric and the new
improved WKB method are engaged, the multiple quantum wells planar waveguide is considered as an equivalent of the
triplex layer waveguide, a new method for analyzing the symmetrical multiple quantum wells planar waveguide is put
forward. Several approximate formulas for computing the effective refractive index, the normalized frequency and mode
field distribution are presented. Then, found on the maximal matching efficiency method for the mode field distributions,
the expression of Gaussian approximation for the mode field distribution of single mode symmetrical multiple quantum
wells planar waveguide is present. As an example, the normalized field distributions of GaAs/GaAlAs symmetrical
multiple quantum wells planar waveguide is referred.
Based on the characteristic of vector waves which taken part in the multiple beams interference in the focal field of concave grating demultiplexer, the reversibility between emission efficiency and receiving efficiency of the optical waveguides, and the amplitude superposition theorem of multiple beams interference, an original analytic expression of simple spectral response efficiency of concave grating demultiplexer is derived. As the spectral distribution of the actual input optical signal is considered, the Gaussian function spectral distribution for example, the actual responsibility and crosstalk of the concave grating demultiplexer for this input optical signal are introduced. Several analytic expressions offer some useful foundation and novel method for analyzing the responsibility and crosstalk of concave grating demultiplexer. A computing instance of concave grating demultiplexer is given, this instance shows that the actual response efficiency characteristic curve which engaged the Gaussian function spectral distribution of input optical signal is smoother than the simple spectral response efficiency characteristic curve which ignored input optical signal spectral width, the smoothness of actual response efficiency characteristic curve and the actual responsibility are dependent on the spectral half width at one of e square of the maximal intensity of actual input optical signal.