Lectures on Quantum Optics and Quantum Information
Lectures on Quantum Optics and Quantum Information
Lectures on Quantum Optics and Quantum Information
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Quantizati<strong>on</strong> of the Electromagnetic Field<br />
We are not going to detail the quantizati<strong>on</strong> procedure for the free<br />
electromagnetic field, but give here the basic steps <strong>and</strong> analogies,<br />
which enable to introduce useful notati<strong>on</strong>s.<br />
More details can be found for instance in ”Introducti<strong>on</strong> to QO”.<br />
• Maxwell equati<strong>on</strong>s in vacuum (no charges, no currents)<br />
• Give the Helmholtz equati<strong>on</strong> for the E field:<br />
• Classical Plane wave decompositi<strong>on</strong> (l: 2 polarizati<strong>on</strong>s, k: wave vector)<br />
• By injecting this decompositi<strong>on</strong> into the Helmholtz equati<strong>on</strong> :