1B24 Waves Optics and Acoustics Lecture 5 of 33 (UCL)

Page 1

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t λ

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n

Typical variation of refractive index

Frequency

Refractive index Absorption Limiting value = 1

Infrared

Visible

Ultraviolet

X-ray

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«Wr

Two Superposed Waves a . cos ω 1 . t

y ω 1,ω 2,k 1,k 2,x,t

k 1 .x

a . cos ω 2 . t

k 2 .x

Take the angular frequencies to be 10 .π and 11.5 . π , wavevectors to be 10 . π and 12 . π 2 1

0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 2

time t=0 2 1

0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 2

time t=0.15

The carrier has edged slightly ahead of the envelope.

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Groupv.mcd

1

04/02/99 12:29

10 . π 11.5 . π Phase velocity : = 0.977 10 . π 12 . π 11.5 10 Group velocity: = 0.75 12 10

We expect the envelope to lag behind

2 1

0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 2

{/ OTs3:<2e7°ÂœÂžÂ?™l>=<ÂĄyÂœyRN7'UK4HL 7dI}CG0tUe:<‚§7 28‚§03Ue7 _ U8OT=<7oCG4 a37-U x U8RN0ÂŤC OT=<s.I8R<7'> 4H282eOP7 2ž4H=N_ 7-=;aH7 zT03‚¼7°4bI 4ƒz€4XIK7 2„I8OPL 7Hl The carrier wavelength is

2 .π = 0.182 11 . π

By t 0.4 the envelope has travelled to x 0.3 but the carrier has moved to x 0.4 , i.e. the carrier is ahead by half a wavelength.

œžÂ?ÂŤWIs Groupv.mcd

2

04/02/99 12:30

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