Laser focusing over great distances

[GTOM]

Let's suppose i want to send a message over really big (interplanetary, maybe out of the solar system) distances.

I read the Rayleigh formula, but i also read the a telescope array can give even better angular resolution.

Does that also means, instead of one giant laser focusing mirror, hundreds of smaller lasermirrors in an array even better?

What is the difference between a big mirror, or simply one with really great focal length? Is that only meant to make targeting (manufacture the mirror) easier, or somehow really compresses the beam?

 

[mfb]

The focus should always be "at infinity". A huge mirror is best, several smaller mirrors can be cheaper or easier to manufacture, but might be harder to align. The total mirror area is an important value.

 

[GTOM]

I read dielectric mirrors can achieve very high reflectivity in a narrow band with. (And that narrow band can be X-ray also.)
Does that mean one could achive TW output with a not so great mirror? Or no, since that big reflectivity also couples with sensitivity, so even when they are so efficient mirrors, you can't spare problems of "recoil"? (Problems caused by heat deformation and damage of the mirror.)

I read somewhere, that if we try to illuminate something on the Moon with laser, the spot size will have at least a km diameter. While theoratical limit of the spotsize is the angular resolution of your mirror(s) but are our present day lasers really near to this theoretical limit, or much inferior, due to focusing problems, imperfect surfaces, heat etc?

 

[sophiecentaur]

Good reflectivity is more important for avoiding overheating the mirror than in increasing range, I think. To get it in context, the difference in range for a good mirror (95%) and a damned good mirror (99%) is not a lot, in practice - just a few percent greater range - but the power absorbed by the mirror is 1/5 for the better mirror.

 

[GTOM]

I think, if we talk about the range of a long range laser, it is a combination of power output and focusing, either you focus better, or achieve a higher output, the longer it can be detected.

"Dielectric mirrors are also used to produce ultra-high reflectivity mirrors: values of 99.999% or better over a narrow range of wavelengths can be produced using special techniques. "

Does that mean i could send a TJ beam to a not so great mirror, and it would be barely heated, or i can't do it, because that much energy would still ruin the structure?

 

[mfb]

A spot size of 1km needs a primary mirror of ~20cm (WolframAlpha, I neglected the prefactor). This is roughly the limit of the atmosphere without adaptive optics. Smaller spot sizes need larger mirrors and adaptive optics (together with a good laser).The amount of power (not energy) you can send depends on the mirror size, the fraction of the power the mirror absorbs, and the amount of power the mirror can handle. Note that a smaller mirror will be more problematic - the primary mirror is not the bottleneck here.

 

[sophiecentaur]

I think, if we talk about the range of a long range laser, it is a combination of power output and focusing, either you focus better, or achieve a higher output, the longer it can be detected.

"Dielectric mirrors are also used to produce ultra-high reflectivity mirrors: values of 99.999% or better over a narrow range of wavelengths can be produced using special techniques. "

Does that mean i could send a TJ beam to a not so great mirror, and it would be barely heated, or i can't do it, because that much energy would still ruin the structure?

Do you fully (quantitatively) appreciate how the total power density delivered affects the range? Any beam follows the inverse square law (as does every form of transmission, once you are a reasonable distance from the transmitting system. A mirror with 99.999% reflectivity will deliver just 1% more power than a mirror with 99% efficiency. That represents an increase in range (all things being equal) of about 0.5%. This would be of very little consequence when compared with a difference in Gain, due to the optics (aperture etc.) which could be a factor of 200% or more (i.e double the radiated power)
The tiny increase in range could, of course, bring huge numbers of extra stars within range - but still only a small percentage of the ones that a less fancy mirror could. 'More' is a quantity that needs to be given a value before making an engineering decision.

However, the other point I made earlier about protection the mirror from overheating could be very relevant to the choice of reflecting surface.

 

[GTOM]

Thanks.

So it looks like to me, as shorter wavelengths (UV, X-ray) scatter less, they should be used, even when they are harder to reflect. (I read, 70% reflectivity at most. http://en.wikipedia.org/wiki/Optical_coating)
When they reach a really far away target, they will scatter that much, that they won't cause radiation sickness.

 

[mfb]

UV and X-rays are harder to focus. The required precision for the mirrors increases significantly, coherent X-ray mirrors would need a precision below the diameter of an atom. That is... tricky ;).
In addition, UV and X-ray lasers are hard to build.
The atmosphere is another complication - it is nearly transparent to visible light, but absorbs UV and X-rays significantly.

When they reach a really far away target, they will scatter that much, that they won't cause radiation sickness.

The reasonable detection limit is somewhere at a few photons per square meter and transmitted bit. Don't worry about radiation damage at the target.

 

[GTOM]

Well, the atmosphere can be left out, if the system is built on the Moon...

I didnt know UV and X-ray are so hard to focus, i read we already have X-ray telescopes...
So probably the best choice would be a violet, or bigger wavelength UV laser?

 

[sophiecentaur]

Well, the atmosphere can be left out, if the system is built on the Moon...

I didnt know UV and X-ray are so hard to focus, i read we already have X-ray telescopes...
So probably the best choice would be a violet, or bigger wavelength UV laser?

Have a look at the construction of an Xray telescope. Very clever construction.
You might have a problem finding a material that will act as an X ray laser. It may not be possible.

The optic spectrum covers about an octave range so going to the blue end could help (in a number of ways) to give a 2:1 advantage in directivity.

 

[mfb]

Well, the atmosphere can be left out, if the system is built on the Moon...

Sure.

I didnt know UV and X-ray are so hard to focus, i read we already have X-ray telescopes...

Those telescopes are far away from the theoretical resolution based on the wavelength. See the images of a point-like x-ray source with XMM Newton, for example. Their sides are 110 arcseconds (~2 arcminutes) long. As comparison, Wikipedia has an image of Messier 100 with a ground-based 1.5m telescope. The whole galaxy is just 7x6 arcminutes wide.

I copied both images together, they have nearly the right size per pixel. The resolution difference is huge, and the ground-based telescope is small compared to the biggest telescopes we have. The planned E-ELT will have a resolution better than the pixels in this image.

So probably the best choice would be a violet, or bigger wavelength UV laser?

Something from green to near UV, I think. Most lasers rely on the bandgap in semiconductors in some way, and interest in materials with large bandgaps (-> blue to UV) is quite new. For the same reason, X-ray lasers cannot be built in the conventional way.

You can build them like the European XFEL, but then you need a particle accelerator with a length of a few kilometers (forget the mirrors then, the beam is better).

 

[tfr000]

Google "lunar laser ranging". This is the ongoing experiment to measure the distance of the Moon using lasers.

 

[Andy Resnick]

Let's suppose i want to send a message over really big (interplanetary, maybe out of the solar system) distances.
<snip>

The design constraint is that the beam etendue (essentially the product of beam waist and divergence angle) is constant for lossless optical systems. In order to get enough power to your receiver, your beam divergence must decrease, and this means the beam waist must increase, meaning the exit pupil/mirror size must also increase.

 

[GTOM]

Thanks.

I read that free electron lasers are multiple times more efficient for converting energy to a coherent beam, than conventional lasers.
If the goal is to achieve high power output with the beam, this isn't negligable i think.

Any chance that FELs become more compact in the near future?

I read the US Navy experimented with a 70m long FEL although it meant to generate infrared beam.
Does that mean that the length of the accelerator is somewhat proportional to the generated beams frequency? (If you want to generate the shortest wavelength with the apparatus.)

 

[sophiecentaur]

The design constraint is that the beam etendue (essentially the product of beam waist and divergence angle) is constant for lossless optical systems. In order to get enough power to your receiver, your beam divergence must decrease, and this means the beam waist must increase, meaning the exit pupil/mirror size must also increase.

How far does this process operate, though? There must be a limit to how far the waist can be relied on to actually exist. It that a Lunar distance, astronomical unit, a parsec?. After that, the beam will just follow 1/r². What size of light source (length / aperture) could be be involved here?

For useful communications there is a distance limit of, perhaps 100 light years. Beyond this (in fact well short of this) the conversation gets a bit stilted. I guess the problem needs to be defined better.

 

[mfb]

I read that free electron lasers are multiple times more efficient for converting energy to a coherent beam, than conventional lasers.

For X-rays, this might be true, but I would be surprised if the same is still true in a comparison to visible and infrared lasers. Particle accelerators need a lot of power for their operation.

Any chance that FELs become more compact in the near future?

Maybe with plasma acceleration.

I read the US Navy experimented with a 70m long FEL although it meant to generate infrared beam.
Does that mean that the length of the accelerator is somewhat proportional to the generated beams frequency? (If you want to generate the shortest wavelength with the apparatus.)

It is related, higher photon energies (=shorter wavelengths) need higher electron energies.

 

[GTOM]

sophiecentaur :

"After that, the beam will just follow 1/r2."

Will it propagate in a sphere, rather than a cone?

"
For X-rays, this might be true, but I would be surprised if the same is still true in a comparison to visible and infrared lasers."

I found this one about CO2 lasers on wiki : "They are also quite efficient: the ratio of output power to pump power can be as large as 20%."

So lasers can't be really more efficient, even with FEL, and other new technology?

"The reasonable detection limit is somewhere at a few photons per square meter and transmitted bit."

Is that applies to high energy X-ray photons, or bigger wavelengths also?
Is detection dependent on both a minimal energy density, and total amount of energy collected by a large detector?

 

[sophiecentaur]

sophiecentaur :

"After that, the beam will just follow 1/r2."

Will it propagate in a sphere, rather than a cone?

"

The directivity of the source makes no difference to the rate at which the power is spread out with distance. The ISL applies for someone looking at a light, whether the light is an omnidirectional point source or the lamp is put in a blackened sphere, with a small hole pointing in just one direction. You only know about the light that comes straight at you and that follows the ISL. To find the actual power flux in a given direction you can multiply the 1/r² factor by the directivity factor of the source, in most cases. (just like projecting a film image onto a massive screen at a great distance)
But The ISL only applies with reference to this point of origin - where the beam comes together and starts to diverge. If the beam is shaped to come to a point at infinity, the ISL will not apply. However, the finite practical physical size of the source (width of lens and length of laser) introduces a diffraction limit and prevents the 'waist' of the beam from being more than a limited distance away. That was long winded but I hope you get my meaning.

I don't know enough about optics to say what the maximum reasonable distance is, to expect the waist to form. I am used to longer wavelengths - satellite dishes and other antennae, where the aperture is never very many wavelengths and the phase centre is taken as somewhere inside the confines of the antenna itself - so ISL is easy to apply when calculating the field laid down at a given distance.

 

[mfb]

I found this one about CO2 lasers on wiki : "They are also quite efficient: the ratio of output power to pump power can be as large as 20%."

Guess in which frequency range CO2 lasers are ;).

So lasers can't be really more efficient, even with FEL, and other new technology?

More than what? 20% efficiency is a lot.

"The reasonable detection limit is somewhere at a few photons per square meter and transmitted bit."

Is that applies to high energy X-ray photons, or bigger wavelengths also?
Is detection dependent on both a minimal energy density, and total amount of energy collected by a large detector?

Only for visible and near infrared light. This sensitivity relies on very good spectrometers to reduce the amount of background. I don't know how much X-ray background you get, but spectrometers there are worse.

 

[Andy Resnick]

How far does this process operate, though? <snip>

I don't understand what you mean?

 

[sophiecentaur]

I don't understand what you mean?

Sorry to be so vague but I was seeing this waist as a 'caustic' type curve with a minimum limiting width and convergence angle. I was thinking that diffraction should impose a limit but I guess it has to in some way or another.

 

[GTOM]

"More than what? 20% efficiency is a lot."

So we can generate only radio waves more efficiently? But they scatter more.

Can you give me any exact value (or scale or something like that), what can be the minimum detection threshold? Then i think i can do the math (assuming cone shaped laser propagation) how far the laser beam could be still detected.

 

[mfb]

So we can generate only radio waves more efficiently? But they scatter more.

LEDs (>40%) and gas discharge lamps (~30%) are very efficient, but it is harder to focus them in the same way you can focus lasers.

Can you give me any exact value (or scale or something like that), what can be the minimum detection threshold? Then i think i can do the math (assuming cone shaped laser propagation) how far the laser beam could be still detected.

The size of this cone is not so easy to estimate, see sophiecentaur's thread. And I don't have a full design for a receiver either.

You would first need a very good spectrometer. The Very Large Telescope has a spectrometer sensitive to deviations of 1/100 000 of the wavelength. Then you have to find a laser power and optics such that you can outshine the sun in this specific frequency range and emission cone (that is independent of distance) with pulses or a telescope so large that it can separate sun and Earth as sources (depends on the distance).

Photon efficiency of the receiver is a minor issue - just assume 50%, that is not so far away from actual designs and the other uncertainties are much more significant. Then, assuming background is negligible, you'll need on average something like 3-4 photons per bit (where for example "0-1 photons" means bit=0 and ">2 photons detected (out of expected 6-8)" means bit=1 - you can neglect overhead for error correction here).
More laser power allows a higher data rate.
A larger telescope increases the photon rate and therefore the range or data rate.

 

[GTOM]

The focus should always be "at infinity". A huge mirror is best, several smaller mirrors can be cheaper or easier to manufacture, but might be harder to align. The total mirror area is an important value.

So, just to be sure i understood correctly, while a baseline telescope's angular resolution can be like to one giant telescope, but with laser focusing, it is only the total sum of mirror areas count?

 

[mfb]

So, just to be sure i understood correctly, while a baseline telescope's angular resolution can be like to one giant telescope, but with laser focusing, it is only the total sum of mirror areas count?

Not only, but it is the relevant number. If you keep the mirror area the same but move the parts further outwards, your central beam gets a better focus, but you get more emission to somewhere else. That is nice for telescopes where you want to distinguish between features very close together, but it would not help for laser communication.

 

[GTOM]

On another site, someone keeps talking about possibilities enabled by mass energy equivalence and big laser beam density...

In the foreseeable future, could we really generate such energy densities with lasers, that the spacetime curvature done by the energy tensor, significantly helps collimating the beam over large distances?

 

[GTOM]

How big is the difference between theoretical and real world focusation? (The first one would be angular resolution of focusing device?)

I have found that site.
http://www.rp-photonics.com/gaussian_beams.html

But i don't really understand which parameter is the size of the focusing mirror?

 

[sophiecentaur]

How big is the difference between theoretical and real world focusation? (The first one would be angular resolution of focusing device?)

I have found that site.
http://www.rp-photonics.com/gaussian_beams.html

But i don't really understand which parameter is the size of the focusing mirror?

Afaics, w is the width of the aperture. It's the 'widest' aperture in the transmitter and is illuminated with a Gaussian amplitude distribution.

 

[GTOM]

Afaics, w is the width of the aperture. It's the 'widest' aperture in the transmitter and is illuminated with a Gaussian amplitude distribution.

Thanks. Sorry for my ignorance, but exactly how should i use the calculator on the bottom of the linked page, to calculate a spot size? (Distance and wavelength are clear to me, other fields not. :( I speculate about sending a laser sign to Moon from Earth low orbit with 100m focus mirror, with UV.)