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Investigating Optical Tunnelling Phenomenon with Glass Prisms

Experiment investigates conditions for light not being totally internally reflected between glass prisms. Utilizes centimeter waves and visible light to analyze effects based on parameters like wavelength, refraction index, and prism distance.

luke-boyer
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Investigating Optical Tunnelling Phenomenon with Glass Prisms

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  1. Problem 15. Optical Tunnelling

  2. Problem Take two glass prisms separated by a small gap. Investigate under what conditions light incident at angles greater than the critical angle is not totally internally reflected.

  3. Experiment • Two measurement ranges: • Centimeter waves – accurate measuring • Visile light – obtaining the effect • Parameters: • Waveelngth of the light used • Refraction index of prisms and medium in the gap • Polarization • Distance between prisms

  4. 1. Centimeter waves • Wavelength: 3 cm • Polarization: linear, electrical field perpendicular to plane of propagation • Prism refraction index: 1.5 (paraffin) • Measurements: • Intensity of tunneled waves • Intenzity of reflected waves in dependence on prism distance • Measured – voltage in the detector • Voltage – proportional to field!

  5. Centimeter waves cont. • Apparatus schematic: detector Radiation source Translation system multimeter

  6. Centimeter waves cont.

  7. Centimeter waves cont. Tunelled field:

  8. 2. Visible light • Wavelenght: 780 nm • Polarization: linear • electric field perpendicular to plane of propagation • Prism index of refraction: 1.48 (measured) • Measurements: • Intensity of tunneled waves • Intensity of reflected waves • Intensity measurement: photodiode • Voltage – proportional to square of field!

  9. 2. Visible light • Measurement in time • A slow motor (0.5 r/min) moves the translator • Voltage sampling at the diode every 1/50 of a second • The signal grows in time • Change of prism distance: v – translator speed t – elapsed time

  10. Visible light cont. • Apparatus schematic: Slow motor + translation laser prisms Data receiving computer oscilloscope

  11. Visible light cont.

  12. Explanation • Huygens principle: Every atom ˝through˝ which light passes is a source of light identical to the incident light  Electromagnetic waves in dielectrics – the resultant of interference of the initial wave and all scattered waves

  13. Explanation cont. • At total reflection – the reflected ray is the only interference maximum • Behind the reflection plane – destructive interference, but only far away from the plane • Close to the plane (distances of the order of the wavelength) the waves haven’t interfered completely and a decaying field exists

  14. Explanation cont. • That field decays fast due to interference • If a prism is put into the field – a new interference maximum can be formed in the prism • A new, tunnelled wave is formed in the prism • The energy of the reflected wave becomes smaller

  15. Maxwell equations E – electric field B – magnetic field induction P – polarization c – speed of light in a vacuum ε0 – vacuum permittivity

  16. Plane wave solutions Electrical field: E0 – amplitude ω – frequency t – time k – wave vector r - radiusvector Magnetic field:

  17. Geometry of the problem y Incident wave d E1 k1 Prism 1 Prism 2 φ φ x n1 n0 n0 Er Et' kt' kr Reflected wave Tunnelled wave

  18. Boundary conditions • If the electric field is perpendicular to the wave vector plane: E10, Er0, Et0– amplitudes of the incident, reflected and transmitted waves k1x, krx, ktx– x components of the wave vectors of the incident, reflected and transmitted waves

  19. Boundary conditions cont. • For the wave vectors: k1y, kty– y components of the incident and transmitted wave vectors n0 – prism index of refraction n1 – medium between prisms index of refraction

  20. Solution • If the incident angle is greater than the reflection angle, Snell’s law gives • x – component of the wave vector is a pure imaginary => the wave propagates along the plane • => the amplitude decays exponentially φ – incident angle

  21. Solution cont. • The field in the second prism: d – prism distance λ – vacuum wavelegth of incident light Θ – decay coefficient

  22. Comparation – decay coefficient • Centimeter waves: • Optical range:

  23. Comparationcont. • Agreement is relatively good • Error causes: • Imprecise prism refraction index values • In optical range: • Prism surface defects and dust • Motor precision ...

  24. Conclusion • We have obtained, measured and modelled optical tunnelling • It may be said: The only condition for light incident on a prism plane with an angle greater than the critical angle not reflecting completely is to put another prism plane next to the original plane to a distance of the order of the wavelength used

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