Li, R. Gallawa, and I. Goyal, "Vector and quasi-vector solutions for optical waveguide modes using efficient Galerkin's method with Hermite-Gauss basis functions," J. Wang, Z.
Zhang, and J. Meunier, "Improved Ritz-Galerkin method for field distribution of graded-index optical fibers," Microw. Gallawa, R.
Purchase Progress in Optics, Volume 51 - 1st Edition. Print Book & E-Book. ISBN , Read the latest chapters of Progress in Optics at ecmerweaha.tk, Elsevier's leading platform of peer-reviewed scholarly literature.
Goyal, Y. Tu, and A. Rasmussen, T. Povlsen, A. Bjarklev, O. Lumholt, B. Pedersen, and K. Rottwitt, "Detailed comparison of two approximate methods for the solution of the scalar wave-equation for a rectangular optical wave-guide," J.
Beyne, and G. Lightwave Technol. Since , he is a full professor at The American University in Cairo. Shahoei, H. Chen, "A microwave photonic approach for simultaneous interrogation of multiple fiber Bragg grating temperature sensors," Applied Optics, vol. Established seller since Couny , P.
Barai, S. Sharma, "Wavelet-Galerkin solver for the analysis of optical waveguides," J. A , Vol. Erteza, I. Goodman, "A scalar variational analysis of rectangular dielectric waveguides using Hermite-Gaussian modal approximations," J. Hosain, "An accurate splice loss analysis for single-mode graded-index fibers with mismatched parameters," J. Silvestre, E. Pinheiro-Ortega, P. Andres, J. Miret, and A. Ortigosa-Blanch, "Analytical evaluation of chromatic dispersion in photonic crystal fibers," Opt.
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Xu, and Z. Li, "A note on computing eigenvector derivatives with distinct and repeated eigenvalues," Commun. Cho, J. Sun, and R. Fleming, J. Abramowitz, M. Yamada, R. Fernandez, F.
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bbmpay.veritrans.co.id/mujeres-solteras-en-torremayor.php Ex-library, With usual stamps and markings, In good all round condition. No dust jacket. Published by North-Holland About this Item: North-Holland, They can also be found in other compact systems, such as fluorescence micro-endoscopes for application in deep tissue imaging 1 , 4 , 8. Procedures for fabrication of GRIN lenses are well established: an ion-exchange process creates a rotationally symmetric index profile in the glass rod. There is however an undesirable side effect: the process also introduces a concomitant intrinsic birefringence that maintains the same rotational symmetry 9 , 10 see Fig.
This gradually changing birefringence profile exhibits the following properties: 1 the magnitude of the retardance is constant at a given radius, 2 the retardance increases with increasing radius; and 3 the slow axis is oriented in the radial direction. These properties mean that the GRIN lens behaves like a spatially variant waveplate array, providing a continuum of birefringence states that can manipulate the polarization and phase of a light beam see Fig. Here, through better understanding of these phenomena, we have drawn upon these previously undesirable GRIN lens properties to build new light manipulation structures to extend the applications of traditional GRIN lens systems GLSs.
Such combinations of elements introduce myriad possibilities for structuring the phase and polarization profiles of beams and foci. We describe here several aspects that enable novel extra functionality in GLSs. We also demonstrate that, by proper choice of the interstitial optics of the cascade, we can use azimuthal or radial polarization light fields at the GRIN lens input to enhance the axial resolution.
This capability can facilitate GLS-based label-free endoscopic diagnosis of structural changes in tissue, with clear applications to cancer detection. Great interest has developed in vector light fields that contain complex phase and polarization structures, whether in the focal or pupil domains. Of special interests are those containing singularities, as they promise unprecedented capabilities for applications ranging from classical to quantum optics 11 , 12 , 13 , 14 , 15 , 16 , Examples include various complex vector beams that have non-uniform polarization distribution across the transverse plane 18 , 19 , 20 , 21 , 22 or beams with helicoidal wave fronts that carry orbital angular momentum OAM 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , or indeed their combinations as VVBs 32 , Currently, such beams can be generated by using a range of modulation devices, such as spatial light modulators, q-plates 34 , metasurfaces 35 , segmented waveplates 36 , or Fresnel-reflected cones The focusing properties of the GRIN lens arise due to the refractive index-led dynamic phase that accounts for the sinusoidal ray trace using scalar theory.
However, the birefringence means that vector effects must be considered. Furthermore, the lens is capable of manipulating the light through the introduction of a geometric Pancharatnam—Berry phase PB phase To the best of our knowledge, this is the first time that the PB phase and its corresponding effects have been considered for GLSs. Examples of beam generation are shown in Fig. The two spirals in the interferogram iv and the phase profile v indicated that the light beam contained two units of OAM.
This concept can be extended further.
It is important to realize that the spatial modulation effects described here are not confined to controlling the beam profile for the corresponding GLSs. As beam modulations can also be harnessed in many imaging methods to enhance spatial resolution or other imaging properties 19 , 20 , 40 , GRIN lens cascades have expected benefits in various GLSs. Indeed, we can show that through understanding these previously unwanted birefringence phenomena, it is possible to improve the performance of current GLSs, specifically as used for scanning micro-endoscopy.
Previous research has shown that GLS used in biomedical imaging can suffer from a lower than expected axial resolution; normally this is attributed to spherical aberration 41 , 42 , We show here that this problematic phenomenon can be also introduced by the inherent birefringence of the GRIN lens via the induced spatial polarization aberration. Furthermore, through understanding of these phenomena, we present a possible solution based upon specific polarization light fields that improves the axial resolution.
These two modes—which are azimuthal and radial linearly polarized light fields—experience their own refractive index profiles n o r and n e r , which are still approximately quadratic with r , but have different magnitudes. Hence, their focusing strength is different and the corresponding focusing pitch within the GRIN lens is different. For this reason, other input states that are a combination of these eigenmodes—including uniform polarization states—create a superposition of both axially offset foci that lead to the elongated focus.
However, this problem can be avoided if a single eigenmode is used. To verify this proposition experimentally, we first measured the focus of GRIN lens when the input was a mixture of the two eigenmodes, using uniform circular polarization at the input Fig.
The focal spot was elongated along the axis, with full-width at half-maximum FWHM of The inclusion of a spatially variant half waveplate SHWP into the cascade, combined with appropriate input polarization, permitted generation of the two eigenmodes. The pupil fields at the output, as well as the axial PSF, were measured. We can see in Fig. Note that the foci for the individual eigenmodes were ring shaped in the lateral plane, with zero intensity along the axis due to the phase singularity introduced by the SHWP in the cascade. In a practical imaging system, this effect could be compensated using an appropriate helicoidal phase plate 44 , or an alternative method for preparation of the input polarization state.
Our observations show that enhanced axial resolution can be obtained in a GLS by modulation of the focus through the appropriate configuration of the input polarization and phase state. As shown in the previous section, there is a complex interdependence of the focal field and the polarization state of the input beam, as processed through the GRIN lens cascade. This dependence provides further opportunities to harness the birefringence properties of the GRIN lens as parallel analysis channels for polarization sensing.
The primary ability of the GRIN lens as a focusing device is due to its continuously varying, rotationally symmetric refractive index distribution 9 , As already discussed, this is accompanied by the gradually varying birefringence distribution. As a high degree of symmetry is required for focusing, this means that the birefringence distribution is also highly symmetric. This provides a continuous, non-pixellated, range of analysis channels that could be used for polarimetry.