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Generalized phase matching condition for lossy periodic photonic structures.
Xuhuai Zhang1, Stephen R Forrest
1Department of Physics and Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109-1040, USA.
Optics Express
|February 23, 2010
Summary
This study generalizes phase matching for complex wave vectors, enabling analysis of light diffraction. It reveals that light exiting a lossy composite prism forms an inhomogeneous plane wave.
Area of Science:
- Optics and Photonics
- Wave Propagation
- Materials Science
Background:
- The phase matching condition is crucial for understanding wave propagation in periodic structures.
- Previous models primarily considered real transverse wave vectors, limiting analysis of dissipative or complex optical systems.
Purpose of the Study:
- To generalize the phase matching condition to complex transverse wave vectors.
- To analyze the diffraction of complex Bloch waves in composite prisms.
- To characterize the nature of light emitted into free space from such structures.
Main Methods:
- Mathematical generalization of the phase matching condition.
- Theoretical modeling of complex Bloch wave propagation.
- Analysis of wave vector transformation across periodic boundaries and interfaces.
Main Results:
- A generalized phase matching condition for complex transverse wave vectors was derived.
- The diffraction of a complex Bloch wave within a composite prism was described.
- It was shown that light exiting the prism into free space is an inhomogeneous plane wave when losses are present.
Conclusions:
- The generalized phase matching condition provides a more comprehensive framework for analyzing wave phenomena in complex optical media.
- The findings are significant for understanding light behavior in periodic structures with losses, relevant to photonic devices and metamaterials.
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