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File:Uklon2D.gif

Uklon2D.gif(800 × 456 pixels, file size: 2.01 MB, MIME type: image/gif, looped, 49 frames, 4.9 s)

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Slovenščina: Animacija prikazuje propagacijo dvo-dimenzionalnega Gaussovega valovnega paketa, ki uboga valovno enačbo. Če imenujemo os propagacije "z-os", potem navpična "y-os" predstavlja magnitudo jakosti električnega polja.

Začetni paket je sestavljen iz monokromatskih ravnih valov, ki so vsi polarizirani v isti smeri, vendar se vsi ne propagirajo vzdolž z-osi. Ker je začetni paket omejen vzdolž x-osi, ki je pravokotna na os propagacije paketa, se vzdolž te osi s časom razleze. Razširitev povzročijo ravni valovi, ki se ne propagirajo vzdolž z-osi (smeri propagacije paketa). Ožji kot je paket vzdolž x-osi na začetku, več takšnih ravnih valov vsebuje, hitreje se razleze.

Pojavu, ki ga redko slišimo razloženega na tak način, pravimo uklon. Ponavadi se uklon razlaga s Huygensovim načelom, ki je dober približek za analitično računanje.

Simulacija je izdelana v Wolfram Mathematici 9.0 in temelji na numerični integraciji propagirajočih-se ravnih valov, ki sestavljajo valovni paket na začetku. Animacija sestoji iz 49 sličic. Izračun vsake je trajal približno 13 minut.
English: The animation demonstrates the propagation of a two-dimensional Gaussian wave packet, which obeys the wave equation. If we name the axis of propagation the "z-axis", then the vertical "y-axis" represents the magnitude of the electric field.

The initial packet is composed of monochromatic plane waves, which are all polarized in the same direction, though not all are propagating along the z-axis. Because the inital packet is confined along the x-axis, which is transverse to the direction of propagation of the packet, it disperses with time along this axis. The dispersion is caused by the plane waves which do not propagate along the z-axis (the axis of packet propagation). The narrower the packet is in the begining, more of such plane waves it consists of, the quicker it disperses.

This effect, which is seldomly explained this way, is called diffraction. Usually it is described via the Huygens principle, which is a good approximation for analytical computations.

The simulation is written in Wolfram Mathematica 9.0 and bases on numerical integration of propagating plane waves, which form the inital wave packet. The animation consists of 49 frames. Each frame took approximately 13 minutes to compute.
Date
Source Own work
Author Marko Petek

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current02:46, 5 June 2015Thumbnail for version as of 02:46, 5 June 2015800 × 456 (2.01 MB)Marko Petek (talk | contribs)User created page with UploadWizard
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