Is Directivity Affected by Cavity Length in Laser Beams?

[sophiecentaur]

I realize that there are two factors that must affect the directivity of a laser. 1, The length of the cavity and number of reflections and 2. The aperture of the exit or the subsequent optics.

This must be related somewhat to the respective directivities of Endfire and Broadside RF transmitting antennae. The difference being in the number of wavelengths for the dimensions.
The effect of the aperture is easy to estimate but where does the length of the cavity come into it? It will clearly affect the coherence but is that just a secondary effect on the emerging wave as it goes through the exit lenses? I could see it relating to the bandwidth of the signals fed to the various elements of an RF array - although it is normal to feed them all with the same signal.

I did the Google thing about this but it seems to be either not basic enough or too basic to trigger any hits that I could spot.

 

[Simon Bridge]

You are correct - the geometry of the cavity determines the beam properties.
Compare extreme cases - CO2 gas laser in a lab on Earth and the phenomenon in the Martian atmosphere. ;)

iirc. The length of the cavity affects the photon density across the width of the cavity - makes the higher density part closer to the middle so there's more at the correct angles to go through the collimator: you get a tighter beam.

The comparison with radio is compelling but iirc not all that useful. It's been a while since I did any laser stuff - it was all the rage at my college when I did grad-school so I kinda couldn't not know about it... but it was what the alpha people did (i.e. not me so much).

You have seen the following discussion right?
https://groups.google.com/forum/#!topic/sci.physics.research/kkhEhdd4jQE

Apparently Feynman's lectures has a whole section on it!
I think the question needs to be refined - what are you trying to find out?

 

[sophiecentaur]

You have seen the following discussion right?
https://groups.google.com/forum/#!topic/sci.physics.research/kkhEhdd4jQE

Apparently Feynman's lectures has a whole section on it!
I think the question needs to be refined - what are you trying to find out?

I'm afraid that's my problem. I wanted some background before I could have anything concrete to ask.
Actually, what you wrote about the power getting confined more to the centre of the beam as the length increases is interesting. This seems to relate to 'centre weighting' of a microwave dish, which increases the beam width but improves side lobe levels. Although the dimensions in wavelengths is very different, I think it has to be relevant that the effect on acuity, due to diffraction limit of the focussing lens must be worse if the beam is concentrated near the centre. But how relevant that is . . . .

Also, what I wrote about beam width of an end fire array doesn't seem too relevant. A Yagi - type array is not improved by making it more than a very few wavelengths in length and even an array of individually fed elements is not good value, relating beam width to length. Even a cheap and cheerful laser is very many wavelengths long.

I just like to make connections between RF, with which I am fairly happy (waves always) and light, in which people reach for the photon explanation very quickly - imo, often too quickly.

 

[Andy Resnick]

I realize that there are two factors that must affect the directivity of a laser. <snip>

What do you mean by 'directivity'? The beam divergence?

 

[sophiecentaur]

I realize that there are two factors that must affect the directivity of a laser. <snip>/QUOTE]

What do you mean by 'directivity'? The beam divergence?

The angle between the 3dB points? Radiation pattern - in antenna terms.

 

[Simon Bridge]

I thought "directivity" was ambiguous too - then I looked it up and it seems a fairly consistent term when we are talking about lasers.

My intuition is that radio and laser do not link very well - that's most of what I've got left over from all the slog some years ago but I'm inclined to trust it. You may get a better understanding by comparing them though.
There are microwave frequency lasers so you can compare like with like?

The photon description happens to be much easier for lasers, in general, than the wave version - but you are right: photon models tend to be a bit of a knee-jerk response. I did a lot of my early laser stuff in the semi-classical regime.

 

[Andy Resnick]

The angle between the 3dB points? Radiation pattern - in antenna terms.

For laser light, the radiation pattern is given by the (transverse) size of the output face. By geometry- 'unfold' the cavity to see this- the beam waist is located at the exit face of the cavity; if the face of the cavity has a width of 'w', the corresponding beam divergence is approximately θ=λ/w. Note that the transverse dimension of a laser cavity is much larger than the emission wavelength, which may not be the case for radio antennas.

 

[sophiecentaur]

Absolutely. With a minimum of 10^5 ratio in wavelengths from microwaves to light, the aperture involved, in wavelengths is vey different. That formula (θ=λ/w) still applies, of course, as a starting pointy though. With reflector antennae, one of the problems is to get the illumination of the reflector right. The 'feed' in the case of a laser, will be the length of the tube, multiplied by the many reflections. This is a lot more 'ideal' than a single horn feed.

So, in the context of that other thread about focussing a laser beam at great distance, over what sort of distance can you consider directing a minimum spot, with the available optics systems? Would it always be done with lenses or would reflectors be used to advantage?

 

[Andy Resnick]

Beam steering is generally easier with a mirror- less mass to move around, for example. I don't know what sort of distance record has been set, but certainly several km within the atmosphere for directed energy weapons, and radio transmissions are still sent to Voyager spacecraft using the deep space network.

 

[sophiecentaur]

Beam steering is generally easier with a mirror- less mass to move around, for example. I don't know what sort of distance record has been set, but certainly several km within the atmosphere for directed energy weapons, and radio transmissions are still sent to Voyager spacecraft using the deep space network.

Radio is a lot better in many ways because of the achievable noise figures and the possibility of optimal channel filtering and signal processing. The inverse square law is very 'forgiving' after the first few Astronomical Units.

So, from what you say, optical comms are somewhat limited. There again, the atmosphere is a serious nuisance at high frequencies. What about outside the atmosphere?

 

[mfb]

NASA tested laser communication with a lunar probe, and the data rate (600MBit/s uplink) exceeded the radio transmission capabilities significantly.

The atmosphere can be handled with adaptive optics, in the same way our current telescopes do that for the other direction.θ=λ/w is basically the best you can get - a smaller phase space is not possible. If you put this beam into a telescope, you can use the full possible angular resolution (maybe with a small prefactor).

 

[GTOM]

"radio transmissions are still sent to Voyager spacecraft using the deep space network."

And Voyager can still send message, but it isn't really undirected, that follows 1/r2, but directed by a parabolaantenna, isn't it?

 

[sophiecentaur]

NASA tested laser communication with a lunar probe, and the data rate (600MBit/s uplink) exceeded the radio transmission capabilities significantly.

The atmosphere can be handled with adaptive optics, in the same way our current telescopes do that for the other direction.


θ=λ/w is basically the best you can get - a smaller phase space is not possible. If you put this beam into a telescope, you can use the full possible angular resolution (maybe with a small prefactor).

That's impressive. Directivity is a massive help in an optical system. For a space borne system, the available aperture for an RF system is potentially massive. I wonder how the overall RF / Optical comparison would be different then, bearing in mind the efficiency of lasers. RF receiver amplifiers can be made with very low noise temperatures. What's the equivalent situation with optical amplifiers / detectors? It's a bit chalk and cheese I know but, at some stage, there could be a switch from radio to optical, depending on the sum of all the factors involved. It's that Link Budget thing, as usual.