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# Power or Power Density (Irradiance)

#### BobDiaz

##### Active member
I'm trying to research the different options and I think I understand an important point, it's not just the power of the laser, but it's the power density or Irradiance that impacts the burning power.

Assume we have two 100mW lasers, both have the exact same power, but laser "A" has a beam diameter of 1.5mm and laser "B" has a beam diameter of 2.5mm. We divide the diameter by 2 to find the radius and use Pi x R^2 (Pi R Squared) to find the surface area of each beam. Last of all, we take the Power and divide it by the surface area.

Laser A: R = 0.75mm, 100mW / (3.14159... x 0.75mm^2) = 56.6mW per mm

Laser B: R = 1.25mm, 100mW / (3.14159... x 1.25mm^2) = 20.4mW per mm

As far as the math goes, it seems that a smaller beam would would have a higher amount of power per unit area and should be able to burn better. For example, I notice that those with 50mW lasers use a lens to focus the beam to a smaller point.

For any burn, like pop a balloon, light paper on fire, light a match, ... it would be interesting to know the power of the laser, the beam diameter, and was a lens used to focus the beam to a smaller point.

I must stress that using a lens does NOT increase the power and there's a slight loss in power as the beam passes through the glass or plastic. It's the density of the power that does make a difference. Focusing the power to a smaller area increases the burning power.

I'm not sure of the exact point, but it seems like those with around 75mW or lower use a lens to be able to burn things and those at or above 150mW don't need a lens to burn things. Is my estimate correct or am I wrong?

Bob Diaz

#### ultimatekaiser

##### Well-known member
Indeed. The burning occurs from the number of photons impacting the same area. It's an example of when light acts like particle, inducing heat from photons bombarding an area. The more there are in a smaller space, the more heat that is generated.

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#### DrSid

##### New member
Any diode or DPSS laser needs optics of some kind, as beam from the device itself has high divergence .. up to 40 degrees for diode lasers.
So even to get collimated (as close to parallel as possible) beam you need optics.
There is also limit to how small the spot can be. Surprisingly to get smaller dot, you need larger lens (output aperture), and/or shorter wavelength.

Check the image:

On the left there is a source, let's say laser diode.

Then there is lens. First lets follow bright red curve. That is how collimated beam looks like. The beam will look like this if the source is placed exactly at focal distance from the convex lens (yeah, assuming it is a point source, which diode laser basically is).
Such beam is parallel at the aperture (exit hole of teh apparatus), but due light diffraction it cannot be parallel forever .. it slowly changes into divergent beam, and at a distance the beam is basically a cone, with some apex angle, and with the apex on the centerline at the aperture (thin black line).
The angle is called divergence angle, and when expressed in milliRadians, or mRads, it can also be used like size at distance for small angles (which are common):
spot size = distance * divergence (in Rad).
This is due to the fact, that for very small angles (under 1 degree) angle expressed in radians equals (or is very close) to sinus and tangents of that angle.
So common 1 mRad (0.001 Rad) divergence will create spot 1m across at 1000m range.

Divergence only describes beam shape well at large distances .. where the beam is close to cone shape.

Divergence for collimated beam is governed by wavelength of the laser, and for aperture size - or in simple terms, lens diameter.
And it is divergence = wavelength / aperture size (all sizes must be in same units).
Sadly this is only ideal diffraction limited divergence .. most lens won't be able to achieve that, especially if they are strong so they can be placed close to the diode .. so then the real divergence can be somewhat bigger .. like 1.5 times, or even 2 times.
This also depends on how we measure 'spot diameter'. The energy usually falls from center of the spot with Gaussian curve .. different levels are used for defining the 'border' of the spot. So you can also see the formula multiplied by 2/PI (or PI/2 ? not sure ATM), but for our estimates it's fine as it is.

Interestingly the divergence of the collimated beam can also be used to estimate minimum spot size for close focus. That's the dark red / brown line.

Same laser, same lens. We moved the lens a bit so the beam is focused to some closer point, not parallel at aperture. It forms a waist at some distance (with collimated beam, it too has a waist .. at the aperture).

Here the beam transforms from cone to parallel .. and then to cone again. Divergence at the distance is worse, and spot at the distance will be large .. but at the waist it will be smaller then anywhere in collimated case.
It's called close focus when the beam is thinner at waist then at aperture .. or in other words, when the waist does not lie at aperture.
This is obviously how lasers are focused for data storage, and usually for burning (not always, if you cut deep, you want the beam roughly same diameter along the cutting depth).

You see how the waist of close focus beam touches the collimated beam divergence cone ? That's how it works. If you use formula for close focus, all additional distances cancels out and you came out with same formula as for ideal collimated beam divergence.

So if the divergence of collimated beam is 1mRad, it means that you won't be able to get smaller spot than 1m at 1000m using collimated beam .. but it also means you will be able to get spot about 0.1 mm at distance 100mm.

This formula is not enough for designing complex laser optics, as it only works with ideal limits .. but it is useful for basic idea about what's possible ..

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#### BobDiaz

##### Active member
DrSid,

Wow, it's far more complex than I first pictured. Close focus and smallest spot size is what I'm most interested in for burning and popping balloons. However if I can do it without adding a lens, so much the better.

After reading quite a few messages in this forum, I zeroed into the message
"TRUSTED LASER COMPANIES:
LaserBTB
Dragon Lasers
..."​

Of interest is LaserBTB, LP 515nm 532nm 1-150: 150mW model with IR filter installed

LP 515nm 532nm 1-150

Others have reported that LaserBTB either meets or exceeds specifications, so I'll go with the written specifications:

M2 factor <1.2 I have no idea what this means.

Beam divergence, full angle (mrad) <2.0 So that would be worse case of 2M diameter at 1kM, 200mm at 100M, about 20mm at 10M.

Beam Diameter at Aperture (mm) <1.5 The beam starts at 1.5mm and slowly expands from there.

Now with the right lens, I might be able to make it smaller and the shorter wavelength of green is better than red for getting to a smaller point, correct?

Thanks,

Bob Diaz

#### DrSid

##### New member
Blue would have roughly 1.5 time lower diameter, or roughly double power density then red .. if all other laser parameters would be the same. But they usually cannot be, so it is usually not as important.
What is important, is what you want to burn. Different materials absorb different wavelengths. That's why black balloons pop easily, while clean white paper is hard to burn.
Anyway .. you want high power, good divergence, short wavelength and good beam quality .. you get that in 405nm lasers. 445nm are stronger, but since they are multimode, the dot will always be bigger then ideal.
But then the power of 445nm can be a lot bigger these days, then 405nm. And one think is cutting metal, where you want to really achieve maximum power density, but if you want for example set things on fire, the dot size is not as much important, as the raw power. Most people go for 445nm if they like to burn stuff.

Green DPSS lasers are usually not ideal burners, as they are expansive per watt, and green is not as well absorbed by most materials, like 445nm or 405nm. On the other hand they usually have exceptionally good beam quality and divergence, and they excel at long range burning (where 445nm multimode lasers are just hopeless).

Reds are only good for the price, and they are relatively (again, relatively !) safer, because skin and eye tissues do not absorb red as readily, as for example 445nm.
They too have pretty good divergence however .. most marks on my walls are from my 200mW reds.

#### BobDiaz

##### Active member
Thanks for the feedback. I'm still a bit unsure and bouncing back and forth between the options. Green is nice because it's so visible per mW compared to Red or Blue. Red offers the lowest cost per watt and IR is even lower cost per watt, but I'll never see the beam and that takes the fun out of it.

I made the following chart as a joke, but there's a lot to truth to it.

In my case I really do have to watch the cost because as I go higher and higher in cost, the anger level from my wife also goes higher. After 37 years of marriage, I know how far I can push things before I'm in trouble with my wife.

I figure I get one shot at it and I'd have to wait a long time before I can purchase another. So I'm trying to get it right on the first try. My assumption is that with under 100mW, you need a lens to focus the beam to a smaller area in order to burn. With 150mW, a lens may not be required to burn some things.

Thanks,

Bob Diaz

#### DrSid

##### New member
If you want to go cheap, go for those cheap reds, 200mW. Like this one:

New Style red laser 200mW /adjustable [OLNRL200] - \$45.99 : Zen Cart!, The Art of E-commerce

It has focusable head, so you can focus it at any distance. I totally would recommend safety goggles though, especially since it's your 1st laser.

It is one of those safer lasers though .. which means you probably wont set house on fire with it or burn you hands .. it will however ruin anyone's eyesight in milliseconds .. can't help that .. if it burns, it burns ..

#### BobDiaz

##### Active member
At first I considered a red laser from biglasers:

"Flare" Red Laser Pointer 50mW - 200mW | BigLasers.com

It uses a very common battery that I can get anywhere, seemed to have good specifications, BUT after reading a lot of posts, biglasers get mixed reviews. The complaints are that the company sells second rate lasers and is really just drop shipping their product. On the plus side, others did say they responded reasonably well to problems.

The laserbtb HL 635nm 660nm is a higher cost than the one you listed, but it is a company that gets a good rating from this forum.

HL 635nm 660nm 50-300

The LP 635nm 130mW is a much lower price and takes standard AAA batteries, but I worry that the power may be too low to pop black balloons and light matches. It also lacks a focus lens, but I could always find a way to focus the beam to a point.

LP 638nm 660nm 5-130

So as I bounce around with the different choices, I'm a bit like the dog chasing his tail.