By Professor Carlos Gomez-Reino, Professor Maria Victoria Perez, Dr. Carmen Bao (auth.)
ISBN-10: 3642075681
ISBN-13: 9783642075681
ISBN-10: 3662047411
ISBN-13: 9783662047415
Gradient-Index (GRIN) optics presents a complete and thorough remedy on basics and functions of sunshine propagation via inhomogeneous media. The e-book can be utilized either as a lecture room textual content for college kids in physics and engineering and as a reference for experts. an outline of the phenomena, parts and know-how utilized in GRIN Optics are provided. the connection to lenses, waveguides, optical connections, spatial solitons and imaginative and prescient is tested. purposes of GRIN parts and hybrid constructions for optical connections, optical sensing and Talbot impression are analyzed.
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Extra resources for Gradient-Index Optics: Fundamentals and Applications
Sample text
5]. Our aim is to find the conditions in which the output of the optical system can be said to be an image or a Fourier transform of the object. Let us consider a complex amplitude transparency f,(x"y,). 19) Neglecting finite dimensions of the GRIN lens in a first approach, the complex amplitude distribution at the output plane is given by Eq. 20) y, )dx,dy, 9(' where K is the kernel or the impulse response of the optical system. Evaluation of K is carried out from the elements of the ray-transfer matrix of the optical system.
If Eqs. 89b) are taken into account, we conclude that the ray slope at z = zp remains constant and is proportional to the ray position at z = O. In other words, each point source of the input signal produces a parallel beam of rays at z = zp , and on these planes we have a superposition of parallel beams with different propagation directions (Fig. 2). This can be regarded as the geometrical optics interpretation of the Fourier transforming phenomenon. Finally, note that the oscillatory behavior of the elements of the ray-transfer matrix produces cyclic imaging and Fourier transforming phenomena.
For D: = 0 , the phase factor is canceled. In Eq. 3 GRIN Lens Law: Imaging and Fourier Transforming by GRIN Lens ) r- -----1'-_M_SN----'t--~) M" 55 - MT8=M 8N, .. ·,M 82 M81 Fig. 6. Cascade of GRIN optical systems. 46) where Eqs. 36) have been used. 4n ~ KFP(x, y, x;, y; ;d;)dxdydxodyo where KFP and K GL are the impulse responses for free propagation through distances d, and d~ and for propagation along a GRIN lens of thickness d, respectively. In conclusion, the diffraction of a uniform wavefront of curvature radius do on the complex amplitude transparency f,(x"y,) in the optical system shown in Fig.
Gradient-Index Optics: Fundamentals and Applications by Professor Carlos Gomez-Reino, Professor Maria Victoria Perez, Dr. Carmen Bao (auth.)
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