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We develop an analytic approach for reflection of light at a temporal boundary inside a dispersive medium and derive frequency-dependent expressions for the reflection and transmission coefficients. Using the analytic results, we study the temporal reflection of an optical pulse and show that our results agree fully with a numerical approach used earlier. Our approach provides approximate analytic expressions for the electric fields of the reflected and transmitted pulses. Whereas the width of the transmitted pulse is modified, the reflected pulse is a mirrored version of the incident pulse. When a part of the incident spectrum lies in the region of total internal reflection, both the reflected and transmitted pulses are distorted considerably.
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Impact of the boundary’s sharpness on temporal reflection in dispersive media
We investigate the impact of the finite rise time of a spatiotemporal boundary inside a dispersive medium used for reflection and refraction of optical pulses. We develop a matrix approach in the frequency domain for analyzing such spatiotemporal boundaries and use it to show that the frequency range over which reflection can occur is reduced as the rise time increases. We also show that total internal reflection can occur even for boundaries with long rise times. This feature suggests that spatiotemporal waveguides can be realized through cross-phase modulation even when pump pulses have relatively long rise and fall times.
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- Award ID(s):
- 1933328
- PAR ID:
- 10287061
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optics Letters
- Volume:
- 46
- Issue:
- 16
- ISSN:
- 0146-9592; OPLEDP
- Format(s):
- Medium: X Size: Article No. 4053
- Size(s):
- Article No. 4053
- Sponsoring Org:
- National Science Foundation
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