Week of 9/11

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Here is a great resource for mathematics and Mathematica:  [http://mathworld.wolfram.com/ Mathworld, the on-line free mathematics encyclopedia]
 
Here is a great resource for mathematics and Mathematica:  [http://mathworld.wolfram.com/ Mathworld, the on-line free mathematics encyclopedia]
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{{mathematica|filename=Resonance.nb|title=amplitude and phase spectrum of a single resonance.}}
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{{PDF|filename=9_11_06.pdf|title=9/11/06 lecture notes}}
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----
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'''9/13/06:  More on the Fabry-Perot etalon'''
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<math>E_t = (E_0 t^2) e^{i \omega L/c} + r^2 (E_0 t^2) e^{i \omega 3L/c}  + r^4 (E_0 t^2) e^{i \omega 5L/c} .... \,</math>
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or
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<math>E_t = (E_0 t^2) e^{i \omega L/c}\left[ 1 + r^2  e^{i \omega 2L/c}  + r^4  e^{i \omega 4L/c} ...\right] </math>
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Hence
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<math>E_t = (E_0 t^2) e^{i \omega L/c} \frac{ 1 - r^2m e^{i \omega 2mL/c}} {1 - r^2m e^{i \omega 2L/c}}</math>
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Take the limit as the number of bounces goes to infinity, then take <math>|E_t|^2</math>  and We get:
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<math>I_t/I_i = \frac{1}{1+ K \sin^2(L \omega/c)}</math>
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where <math>K = 2r/(1-r)^2</math>  and <math>r</math> is the reflectivity of the mirror.
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For more details see the [http://mesoscopic.mines.edu/preprints/time_frequency.pdf  tutorial on spectroscopy and interferometry]
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{{mathematica|filename=Fabryperot.nb|title=Amplitude spectrum of a Fabry-Perot etalon}}
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{{PDF|filename=9_13_06.pdf|title=9/13/06 lecture notes}}
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[http://scitation.aip.org/publications/myBrowseAZ.jsp    The American Institute of Phyics On-line Journal Publishing Service]
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Here you will find many free journals to brows.  The
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[http://scitation.aip.org/ajp/ American Journal of Phyiscs] is especially good for students to read.  As long as you are logged into
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a campus machine (138.67.xxx.xxx ip address) you can download pdf copies of papers for free.
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----
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{{mathematica|filename=Matrix_examples.nb|title=A Mathematica example on matrices}}
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{{PDF|filename=9_15_06.pdf|title=9/15/06 lecture notes}}

Latest revision as of 16:58, 15 September 2006

Here is a great resource for mathematics and Mathematica: Mathworld, the on-line free mathematics encyclopedia


Mathematica.png Download amplitude and phase spectrum of a single resonance.
Pdf.png Download 9/11/06 lecture notes



9/13/06: More on the Fabry-Perot etalon


E_t = (E_0 t^2) e^{i \omega L/c} + r^2 (E_0 t^2) e^{i \omega 3L/c} + r^4 (E_0 t^2) e^{i \omega 5L/c} .... \,

or

E_t = (E_0 t^2) e^{i \omega L/c}\left[ 1 + r^2 e^{i \omega 2L/c} + r^4 e^{i \omega 4L/c} ...\right]

Hence

E_t = (E_0 t^2) e^{i \omega L/c} \frac{ 1 - r^2m e^{i \omega 2mL/c}} {1 - r^2m e^{i \omega 2L/c}}

Take the limit as the number of bounces goes to infinity, then take | Et | 2 and We get:

I_t/I_i = \frac{1}{1+ K \sin^2(L \omega/c)}

where K = 2r / (1 − r)2 and r is the reflectivity of the mirror.

For more details see the tutorial on spectroscopy and interferometry

Mathematica.png Download Amplitude spectrum of a Fabry-Perot etalon


Pdf.png Download 9/13/06 lecture notes

The American Institute of Phyics On-line Journal Publishing Service Here you will find many free journals to brows. The American Journal of Phyiscs is especially good for students to read. As long as you are logged into a campus machine (138.67.xxx.xxx ip address) you can download pdf copies of papers for free.

Mathematica.png Download A Mathematica example on matrices


Pdf.png Download 9/15/06 lecture notes
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