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Transformations of Functions III

Transformations of Functions III

Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...

Transformation

Transformation

Microbial communities are dynamic environments where cell lysis releases free DNA into the surroundings. Other cells can take up this extracellular DNA through a process known as transformation.When a cell incorporates this foreign DNA into its genome, resulting in genetic modification, the process is known as transformation. Cells capable of this process are termed competent. Competence can be natural, as observed in certain bacteria and archaea, or artificially induced in the...

Confocal Fluorescence Microscopy

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Confocal microscopy is an advanced microscopic technique. The prime advantage of the confocal microscope over other microscopy techniques is its ability to block the out-of-focus light from the illuminated samples using pinholes. It is widely used with fluorescence optics to obtain high-resolution, sharp contrast images. Unlike optical microscopes, confocal microscopes use a focused beam of light laser to scan the entire sample surface at different z-planes. These microscopes are, therefore,...

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Updated: May 20, 2026

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

Recent advances in transformation optics.

Yongmin Liu¹, Xiang Zhang

¹NSF Nanoscale Science and Engineering Center-NSEC, 3112 Etcheverry Hall, University of California, Berkeley, CA 94720, USA.

|August 1, 2012

Summary

This summary is machine-generated.

Transformation optics manipulates electromagnetic waves for novel devices like cloaks and lenses. This review covers recent advances in designing and fabricating these nanoscale optical tools.

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Area of Science:

Optics and Photonics
Electromagnetism
Materials Science

Background:

Transformation optics offers a framework for controlling electromagnetic wave propagation.
Recent years have seen significant advancements, enabling previously theoretical devices.

Purpose of the Study:

To review recent progress in transformation optics.
To highlight key devices and their fabrication at optical frequencies.

Main Methods:

Theoretical design principles of transformation optics.
Fabrication and characterization techniques for nanoscale optical devices.
Analysis of specific devices: carpet cloak, Janus lens, plasmonic cloak.

Main Results:

Demonstration of devices that manipulate light at the nanoscale.
Successful implementation of cloaking and advanced lensing functionalities.
Experimental validation of theoretical designs.

Conclusions:

Transformation optics is a powerful tool for creating novel optical devices.
Nanoscale light manipulation is advancing rapidly.
Future research directions include overcoming current challenges and exploring new applications.