Electromagnetic (EM) spectrum

1. Electromagnetic (EM) spectrum non-ionizing radiation ionizing radiation 1 EHz 1018 1 Hz 1 kHz 103 1 MHz 106 1 GHz 109 1 THz 1012 1 PHz 1015 300 Mm 300 km 300 m 0.3 m 0.3 mm 300 nm 0.3 nm electric power supply cellular phone 750 nm 400 nm g-rays X-RAY/CT MRI PET ULTRASOUND — not EM radiation

2. 0 0 1 2 3 4 5 6 7 8 9 x 1014 BLACKBODY RADIATION 4000 K spectral energy density 3000 K 2000 K 1000 K frequency (Hz)

3. FUNCTIONAL FORMS OF EM RADIATION IT COULD BE A DIRAC DELTA PULSE: d (t-t1) IT COULD BE A HARMONIC WAVE: sin (w t) ARBITRARY FUNCTION OF t

4. HARMONIC WAVES sin (wt) = sin (w (t-r/c)) = sin (wt-wr/c)= sin (wt –kr) Temporal frequency in rad/s w Spatial frequency in rad/m k = w/c frequency in cycles/sec n = w/2p Wave number (m-1) k = k/2p Period in time in s T =1/n =2p/w Period in space in m l = 1/k = 2p/k

5. EM RADIATION fixed temporal coordinate fixed spatial coordinate Period in time T=1/n Period in space l=2p/k

6. 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Superposition of waves (same w) U(t) t/p t/p constructive interference destructive interference

7. Superposition of waves (same w) • frequency stays constant • amplitude and phase may be different U1 ~ U2 interferometric measurement: (assume initial Dfi = 0) Df = 2p/l (x1 – x2)

8. 0 0 5 10 15 20 25 0 10 20 30 40 50 60 70 80 90 100 Superposition of waves (different w) U(t) t/p t/p beat frequency U1 = cos(w1t) U2 = cos(w2t) w = w1 – w2

9. Superposition of harmonic waves“ARBITRARY WAVEFORMS” 0 0 0.5 1 1.5 2 2.5 3 t/p

10. 0 50 100 150 200 250 300 0 -0.1 -0.05 0 0.05 0.1 0.15 Time vs. frequency Gaussian Spectrum Gaussian Decay Frequency Time Lorentzian Spectrum Exponential Decay Dirac Delta Function ?