EM resonators and applicationsCap the ends with metal plates [2] π΅ =π΅0 + β +π΅ 0 β cos...
Transcript of EM resonators and applicationsCap the ends with metal plates [2] π΅ =π΅0 + β +π΅ 0 β cos...
Waveguides (recap) [1]
1. Maxwell:
2. Expand fields into components:
πΈ π₯, π¦, π§, π‘ = πΈ0 π₯, π¦ ππ ππ‘βππ§
πΈ0 = πΈπ₯ π₯ + πΈπ¦ π¦ + πΈπ§ π§
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Waveguides (recap) [1]
3. Transverse components in terms of Ez, Bz:
(Note: replace i by βj above)4
Waveguides (recap) [1]
β’ TE Solutions of the form
π΅π§(π₯, π¦, π§, π‘) = π΅0 cosπππ₯
πcos
πππ¦
πππ(ππ‘βππ§)
i.e. a fwd travelling wave
Cut off freqs:
πππ = πππ
π
2
+π
π
2
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Cap the ends with metal plates [2]
π΅π§ = π΅0+πβπππ§ + π΅0
βππππ§ cosπππ₯
πcos
πππ¦
πππππ‘
Fwd and bkwd waves
Boundary conditions at π§ = 0, π§ = π:
π» Γ πΈπ§= βπππ΅π§
=ππΈπ₯
ππ¦β
ππΈπ¦
ππ₯= 0
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Cap the ends with metal plates [2]
This implies that π΅0+ = βπ΅0
β , ππ = ππ and :
π΅π§ = β2ππ΅0+sin
pππ§
πcos
πππ₯
πcos
πππ¦
πππππ‘
The frequency of a waveguide mode earlier was
ππ = π2 β πππ2
Now, k is restricted, so
π0 = πππ
π
2
+π
π
2
+π
π
2
Waveguide frequency 8
Losses in a resonator
β’ Perfect metal βΆ No losses
β’ Finite π β Boundary conditions get slightly modified β System supports small range of frequencies around π0
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Waveguide resonator [2]
π = π0
πΈπππππ¦ ππ‘ππππ
πππ€ππ πππ π‘
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Laser Physics in brief [5]
The presence of a photon encourages another photon to be emitted: Stimulated emission
Only 2 level system, π2
π1= exp(β
ΞπΈ
ππ)
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FastSlow
Laser Physics in brief [5]
So, the resonant frequency of the resonator must match the energy transition of the gain/laser medium!
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Gain medium in the fiber? [6]β’ Introduce a rare Earth ion into the fiber:
Called βdopingβ β Erbium Doped Fiber
Energy band diagram of πΈπ3+
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Applications [7]
β’ As a gain medium in a fiber-laser
β’ As an amplifier in fiber optics: backbone of ALL telecom!
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References
β’ [1] Griffiths, Introduction to Electrodynamics, 4th Ed. β’ [2] Ulaby et al., Fundamentals of applied electromagnetics,
6th Ed. β’ [3] http://www.hoestarinsp.com.sg/FBG1-large.jpgβ’ [4] http://spie.org/x8609.xmlβ’ [5] http://www.orc.soton.ac.uk/61.htmlβ’ [6] http://www.rp-
photonics.com/erbium_doped_gain_media.htmlβ’ [7] http://www.rp-
photonics.com/erbium_doped_fiber_amplifiers.htmlβ’ [8] http://japaneseclass.jp/trends/about/VCSEL
[9] http://www.csr.utexas.edu/grace/
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