1. Paraxial ray tracing for atmospheric wave propagation.

2. In this paper the transmission of paraxial light beams was analyzed based on the gradient vector potential of electromagnetic field.

3. Based on complex ray method, a paraxial approximation analysis of Gaussian beam transmission through a dielectric radome is presented.

4. To simplify the calculation, a paraxial approximation is employed when the observer is located near the beam axis.

5. Starting from paraxial wave equation, analytical propagation expressions of hyperbolic secant pulsed beams with narrowband and broadband are derived.

6. Comparing to conventional expansion, our paraxial travel time expansion increases asymmetric terms of the horizontal offset in the expression.

7. At paraxial approximation the maximum of the matching function is increasing with increased divergence angle. For different brightness of pumping light, the optimum value of the angle is obtained.

8. The derivation of the relationship between the paraxial wave equation and the complex source points is given and proved.

9. The vectorial non- paraxial behavior should be taken into consideration and the longitudinal component can not be neglected once the aperture size is comparable with or less than the wavelength.

10. By starting from the paraxial wave equation, the analytical expression of the ultrashort Hyperbolic Secant pulsed beam are deduced.

11. Numerical computations show that paraxial approximation gives almost the same accuracy in the paraxial region as complex ray method but spends much less computer time.

12. Gaussian beam method is based on the dynamic raytracing and paraxial approximation method.

13. The most important application of dynamic ray tracing is to calculate paraxial ray and Gaussian beam.

14. The flattened Gaussian beam is regarded as a whole beam, and its propagation through a paraxial optical ABCD system has been studied in detail.

15. The simple linear relationship between off-axis distance and delay time was also derived in the case of paraxial and remote transmission.

16. In the embryo an undifferentiated mesodermal component of an early trunk or tail segment or metamere, derived from paraxial mesoderm.

17. Based on the classical theory of electromagnetism, the relation and the difference between OAM and the parameter of the beam in paraxial approximation are analyzed.

18. The aperture may curtain off the light beams that deviate paraxial, the object clarity, which has the immediate have an effect on the accuracy, brightness and the depth of field and so on.

19. The propagation of ultrashort pulsed Bessel beams in free space within and beyond the paraxial approximation is studied.

20. Based on the law of refraction of light, An accurate formulate of single-spherical refraction of non- paraxial light ray was established.

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21. It is proved in a complicated optical system that the diffraction integration in terms of ray matrix element is the right solution 'for paraxial equation.

22. The Parabolic Equation method (PE) is an approximation of the wave equation, which models energy propagating in a cone centred on a preferred direction, the paraxial direction.