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I have a 5 mW laser pen powered by a 1000 mAh 3.7 volt battery that takes over 2 hours to recharge. It drains it in 15 minutes. Why is it only called 5 milliwatts output if it is consuming 14.8 W?

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closed as off-topic by ACuriousMind, Danu, Kyle Kanos, user36790, Gert Mar 24 '16 at 3:24

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    $\begingroup$ Shhhh! If they sold it as a 14 W laser the FDA would make them label it as a class 4 (highly dangerous) device. $\endgroup$ – The Photon Jan 17 '15 at 5:16
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    $\begingroup$ At the risk of asking you to think about it, do you really believe all the input power is converted into laser light? Lasers, like (for example) automobile engines, are rated by their useful output, not their total energy input. $\endgroup$ – Carl Witthoft Jan 17 '15 at 13:31
  • $\begingroup$ I would then wonder why it lights up a room equally as brightly as a lightbulb if it only uses one eight thousandth of the power. $\endgroup$ – Waffle Jan 17 '15 at 17:19
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    $\begingroup$ Lightbulbs do get very hot, but seeing as the laser's battery is being used up similarly to the power consumption rate of a lightbulb, why does the pen itself not burn my hand if so little of the energy is actually converted to light? $\endgroup$ – Waffle Jan 17 '15 at 21:59
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    $\begingroup$ I'm voting to close this question as off-topic because it is asking about equipment (mal)functioning and not about physics. $\endgroup$ – Danu Mar 23 '16 at 8:25
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It's 5 mW optical power. The rest is wasted on other forms, practically all of it being heat.

Your figure for efficiency seems somewhat small for diode laser, but I work with old German Zeiss ILA-120A argon ion laser. Power consumption is 16kW (yes - 16000W or $16*10^3$W) and useful output is 3W. Now that's poor efficiency. But it has excellent stability, and linewidth are orders of magnitude smaller than those for diode lasers.

And as afternote - there is quantity called slope efficiency defined. Lasers have thresholds. Once you are above threshold output power is proportional to pumping power (with offset of course). Efficiency is the slope of graph output power vs pump power - hence the name. I'm not aware of any typical laser exceeding 40%.

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You never measured the current the device drained, so there is no way to whether know the battery is working properly or if it truly holds 1000ma hours. If in fact in a perfect world it does provide a current as stated, in 15 minutes drain time, it would be draining at a very high rate. which is many times more, what it should be for a 5mw laser (about 10ma to run). I suspect the battery is faulty or there is a short to ground.

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Electromagnetic waves carry energy, in free space there is an energy density like: $$\frac{\epsilon_0}{2}\vec{E}\cdot\vec{E}+\frac{1}{2\mu_0}\vec{B}\cdot\vec{B}.$$

A travelling wave can be in phase and sinusoidal, at the frequency of the wave (not the frequency of the power supply). Each little finite segment of the travelling wave come from a little bit in the past and a little bit behind. So eventually you can trace it back to the generation of the laser. So for a small interval of time, the laser itself is generating the wave, and sometimes it puts more energy into the wave than at other times.

So the power going from the laser system into the travelling wave also varies sinusoudally. But since it depends on the energy density which goes like the wave squared, it is always nonnegative, has twice the frequency, and has a peak power that is twice the average power.

That's an analysis of the power from the energy carried by the travelling wave as it leaves, and it has to come from the laser system. But the laser system can draw power from the wall outlet at a totally different rate. For instance it might power a fan to exhaust some heat, some of the wall; power might be lost as heat, and the laser system could spend a long time getting ready to lase, spending time and energy to get the population inverted, putting things in meta-stable states.

During that time, the energy of the laser system could be increasing, and some could be being exhausted as heat, and that can happen long before the laser starts to lase, and hence before any light starts to come out.

Energy has a source and a destination, what's coming into the laser system either flows out or increases the total energy in the laser system. What comes out either decreases the total energy of the laser system, or fails to only because even more energy is flowing in.

There are multiple ways for energy to flow out, heat being an example. There are multiple places for energy to be stored within the system (though eventually that might all turn in to heat if we wait long enough). Some of that storage (for the population inversion) is even required.

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