
Bessel Beam - mojomark
https://en.wikipedia.org/wiki/Bessel_beam
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0xfaded
My first encounter with Bessel functions was from a professor who in his youth
had built digital amplifiers -- before dsps could switch at 44k Hertz. (From
memory he had a 1k pwm)

He did it by predicting the position of the magnet in the speaker coil by
fitting a function over the last few known positions.

Bessel functions are othogonal, and their Fourier transforms are the base
polynomials band limited between -pi and pi. His argument was that by fitting
a sum of Bessel functions to a sequence captured periodic signals.

I've used this trick several times, and love the "what is this black magic"
reaction I get when showing it to others. Guess the cat's out of the bag
now...

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0xfaded
Correction, base polynomials -> chebychev polynomials

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estomagordo
I have nothing else to add than this was really cool, and almost makes me
regret not taking more than one optics class in uni.

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presscast
> a true Bessel beam cannot be created, as it is unbounded

What does "unbounded" mean in this context?

What is an example of a "bounded" beam?

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red_dinosaur
> What does "unbounded" mean in this context?

The radial intensity distribution of a Bessel beam is described by Bessel
functions, which are not square integrable (integral is not finite), see
[https://upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Be...](https://upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Bessel_Functions_%281st_Kind%2C_n%3D0%2C1%2C2%29.svg/600px-
Bessel_Functions_%281st_Kind%2C_n%3D0%2C1%2C2%29.svg.png).

Realizing a true Bessel beam would thus require infinite power.

A true Bessel beam is created by interfering (in 2D) two plane waves, see
[https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Be...](https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Bessel_beam.svg/1920px-
Bessel_beam.svg.png). You can see in the image that the "Bessel beam" area is
bounded, it is the conical shape where the beams overlap.

> What is an example of a "bounded" beam?

A "standard" Gaussian laser beam, see
[https://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/La...](https://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Laser_gaussian_profile.svg/506px-
Laser_gaussian_profile.svg.png)

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SideburnsOfDoom
> The radial intensity distribution

So, unbounded width of the beam? As opposed to unbounded length, which is
generally expected in light beams.

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SiempreViernes
Well, for truly unbounded length you need to keep the source on for infinite
time of course.

But light beams do get very long for very modest work, and properly focused
they can propagate very long distances indeed.

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SideburnsOfDoom
So, to be clear here - is the answer yes or no? Are we talking about beam
width - i.e. unbounded in a direction at right angles to the direction of
travel?

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nosjwshere
any use for this project? [https://www.cnet.com/g00/news/sending-tiny-
spacecraft-to-alp...](https://www.cnet.com/g00/news/sending-tiny-spacecraft-
to-alpha-centauri)

