EMsource - EM sources Electromagnetic Waves and Optics 1...

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Unformatted text preview: EM sources Electromagnetic Waves and Optics 1 Generation of EM Waves Æ EM Waves in Matter Revisited • radiation of accelerated charges • resonance and dispersion • group velocity • optical properties of metals EM sources Electromagnetic Waves and Optics 2 EM radiation in one dimension • “switch on” current in xy-plane: • resulting fields: • appearance of fields delayed by ∆ t =¡z/c ( ) = > − = otherwise , ˆ , z t J i t r J r r ( ) ( ) 2 , 1 with ˆ , ˆ , cB E c ct z ct z B j t r B ct z ct z E i t r E = = > < = > < = µ ε r r r r z y x J z y • • • • • • • • • ct : = = > B E ct z r r x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x EM sources Electromagnetic Waves and Optics 3 EM Radiation by Charged Particles • charges at rest Î static E-field • charges in uniform motion Î static B-field • accelerating charges Î EM radiation – e.g., sudden shift of charge at t = 0 – new field for r < ct – distances r > ct “remember” old field – transverse E-field ¾ travelling “kink” in field lines ¾ E coplanar with accel. ¾ no “kink” parallel to accel. + + r = ct EM sources Electromagnetic Waves and Optics 4 EM Radiation by Accelerating Charge • continuous acceleration • expected properties of E-field – energy conservation: – proportional to charge: – prop. to transverse component of “historical” acceleration: – direction: a k a k a k E r r r r r r r ⊥ for strongest radiation || for radiation no coplanar , , ) , 1 for ( ˆ ˆ 4 c v kr c r t a k k r q E << >> − × × = r r π µ θ sin ) / ( c r t a E − ∝ r E 1 ∝ q E ∝ θ EM sources Electromagnetic Waves and Optics 5 EM Radiation by Oscillating Charge “far field”: r >> λ ) ( 2 , sin 4 qx p r e p E e x x t kr i t i = = ⇒ = − − ω ω θ ω π µ ) / ( sin 4 c r t a a r a q E − = ′ ′ = θ π µ E r k r θ r • B r 2 2 4 2 2 sin 32 r p c S θ ω π µ = EM sources Electromagnetic Waves and Optics...
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EMsource - EM sources Electromagnetic Waves and Optics 1...

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