Lect30_[Compatibility_Mode]

Lect30_[Compatibility_Mode] - Physics 344 Foundations of...

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Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir Applications Their Applications Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Shuo Liu Office: PHYS 283 [email protected] Office Hours: If you have questions, just email us to make an ppointment. e enjoy talking about physics! appointment. We enjoy talking about physics! Notices: Midterm II at 8:00pm, Thursday, December 2 in MSEE B012
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The Energy of Cavity Fields Last lecture we began the wave-model analysis of the distribution of field energy stored in a resonant cavity in order to complete our blending of the wave and photon models of light into a quantum mechanics of single photon states of the electromagnetic field. Recall that we can represent generic cavity fields as superpositions of modal (,) s i n ( ) s i n ( ) yn n n n Ex t E kx t ωδ =+ fields, each with their own amplitude and phase, () 1 n=1 sin( ) sin( ) cos( ) n nn n n n t t αω β ω = ≡+ with or, equivalently, cos( ) n E α δ = and sin( ) n E = 222 n E = + and tan( ) n n n = 1 c o s ( )c o s ( ) cos( ) cos( ) sin( ) zn n n n n n n n cB x t E k x t t t = ≡− n=1
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We established that when a single cavity mode is excited, the n th mode, say, sin( )sin( ) yn n nn EE k x t ω δ = + the cavity fields are s( ) cos( ) n E k x t + cos( zn n n Bk c ωδ and the energy density in the cavity is 22 00 ) cos(2 ) cos(2( )) xt E E kx t ε + + ( , ) )cos(2( 44 n n n uxt ++ If we consider using a photomultiplier tube to detect photons in a cavity excited in this way, we do not resolve the very high frequency variation of this uantity which averages away and we measure quantity, which averages away, and we measure () 2 (,) n E α β <> = = + If we consider the total field energy stored in the cavity, we should find that it is constant because our model of the cavity’s mirrors neglects the tiny resistive losses in their highly conductive metal surfaces.
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To verify this we compute the energy stored by integrating the energy density 22 00 ( , ) cos(2 )cos(2( )) 44 nn n n n uxt E E kx t ε ω δ =+ + over the cavity’s volume. The structure of the mode fields were determined assuming that the mirrors forming the cavity were of infinite extent. However, the field structure of a mode remains essentially the same provided that the mirror’s breadth is far larger than the mode’s wavelength. In that case, diffraction effects like those discussed in section 24.4 of the M&I text are negligible.
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue.

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Lect30_[Compatibility_Mode] - Physics 344 Foundations of...

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