By Andrey S. Ostrovsky

ISBN-10: 0819463507

ISBN-13: 9780819463500

This ebook offers a unmarried resource of data at the challenge of coherent-mode representations in optics, together with new views on its capability functions. specifically, the ''light string'' and the ''light capillary'' beams will be advantageously utilized in communications, measurements, microelectronics and microsurgery; the quick set of rules for bilinear transforms might be effectively utilized to machine simulation and layout of optical structures with in part coherent illumination.

**Contents**

- Preface

- Coherent-Mode illustration of Optical Fields and assets

- Coherent-Mode illustration of Optical structures

- Coherent-Mode illustration of Propagation-Invariant Fields

- Coherent-Mode Representations in Radiometry

- substitute Coherent-Mode illustration of a Planar resource

- References

- writer Index

- topic Index

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**Extra info for Coherent-Mode Representations in Optics (SPIE Press Monograph Vol. PM164)**

**Sample text**

44) µ=−∞ we obtain WII (ρ1 , θ1 , ρ2 , θ2 ) = J0 2πr0 ρ21 + ρ22 − 2ρ1 ρ2 cos (θ1 − θ2 ) 1/2 . 3), the field with the cross-spectral density function given by Eq. 9 To clarify the physical nature of the propagation-invariant fields of the second kind, we calculate the 4D Fourier transform of Eq. 45). It may be readily shown that WII (r1 , φ1 , r2 , φ2 ) = δ (r1 − r0 ) δ (r2 − r0 ) δ (φ1 − φ2 ) . 46) Hence, we come to the following conclusion: the Bessel-correlated beam represents the superposition of the plane waves, whose wave vectors lie on the conical surface with the vertex angle γ = tan−1 [(k/2πr0 )2 − 1]−1/2 ; these waves are completely uncorrelated in the azimuthal direction.

For a Fourier-transforming lens, we used a high-quality single lens with a 50-mm diameter and a focal length of 300 mm. We registered the transverse intensity distribution of the generated beam at different distances z behind the back focal plane of the Fourier-transforming lens. To provide a solid statistical average of the registered data, we used an exposure time of several seconds. The results of the experiment are shown in Fig. 7. As one can see from this figure, the generated beam may be approximately identified as the light string beam.

43) may be obtained if we put r0n = r0 2 |q |2 . 44) µ=−∞ we obtain WII (ρ1 , θ1 , ρ2 , θ2 ) = J0 2πr0 ρ21 + ρ22 − 2ρ1 ρ2 cos (θ1 − θ2 ) 1/2 . 3), the field with the cross-spectral density function given by Eq. 9 To clarify the physical nature of the propagation-invariant fields of the second kind, we calculate the 4D Fourier transform of Eq. 45). It may be readily shown that WII (r1 , φ1 , r2 , φ2 ) = δ (r1 − r0 ) δ (r2 − r0 ) δ (φ1 − φ2 ) . 46) Hence, we come to the following conclusion: the Bessel-correlated beam represents the superposition of the plane waves, whose wave vectors lie on the conical surface with the vertex angle γ = tan−1 [(k/2πr0 )2 − 1]−1/2 ; these waves are completely uncorrelated in the azimuthal direction.

### Coherent-Mode Representations in Optics (SPIE Press Monograph Vol. PM164) by Andrey S. Ostrovsky

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