Question about the Peak and Average Power of a Laser

[Irishdoug]

Homework Statement

I am reading a paper and want to calculate the average power and peak power of the laser they have used in it.

Relevant Equations

Pav = Energy*rep.rate / Ppeak = Energy/pulse duration

Hi, I am reading paper that I have to give a quick presentation on. I want to calculate the average power and peak power of the laser used, a Ti:Saphire laser.

I have the wavelength they are lasing at (450nm), the repetition rate 81Mhz and the pulse duration (pulse width) of 100fs.

I have done the following calculation: $E = \frac{hc}{\lambda} = \frac{6.626x10^{-34}c}{450x10^{-9}} = 5.372x10^{-19}J$

$P_{peak} = \frac{5.372x10^{-19}J}{100x10^{-15}} = 4.417x10^{-6} J/s$
$P_{av} = Energy*Repetition Rate = 5.372x10^{-19}J (81x10^{6}Hz) = 3.6x10^{-11}J = ~0.04nJ/s$

I am unsure as to my calculations as the numbers seem incredibly small. I was expecting mW and W at least. The laser is being used in biophotonics so maybe these low powers are required, but I am unsure as I have no experience in this area. Thankyou.

 

[Steve4Physics]

Relevant Equations:: Pav = Energy*rep.rate / Ppeak = Energy/pulse duration

Hi, I am reading paper that I have to give a quick presentation on. I want to calculate the average power and peak power of the laser used, a Ti:Saphire laser.

I have the wavelength they are lasing at (450nm), the repetition rate 81Mhz and the pulse duration (pulse width) of 100fs.

I have done the following calculation: $E = \frac{hc}{\lambda} = \frac{6.626x10^{-34}c}{450x10^{-9}} = 5.372x10^{-19}J$

$P_{peak} = \frac{5.372x10^{-19}J}{100x10^{-15}} = 4.417x10^{-6} J/s$
$P_{av} = Energy*Repetition Rate = 5.372x10^{-19}J (81x10^{6}Hz) = 3.6x10^{-11}J = ~0.04nJ/s$

A few points to think about which might help...

Your formula:
“Pav = Energy*rep.rate / Ppeak = Energy/pulse duration”
can't be correct because "Energy*rep.rate / Ppeak" does not have the dimensions of power (it has no dimensions).

In your equation, what do you mean by ‘Energy’? Is it the energy in a single pulse? I think that you have used Energy = $hc/\lambda$. This is the energy in a single photon; but there are many photons in a pulse.

(To get the energy in a pulse, you would need to multiply $hc/\lambda$ by the number of photons in the pulse, This would make your answer much bigger!)

There are two ‘average powers’ and it is not clear to which you refer:
a) the average power during a single pulse; this depends on the shape of the pulse and the peak power during the pulse;
b) the average power-output over some extended time-period (during which there are many sequential pulses and time-gaps between each).

The data (wavelength, pulse repetition rate and the pulse duration) are not sufficient to calculate any type of power. You need additional data.

You have arithmetic mistakes.

Other points:
- the symbol for megahertz is MHz, not Mhz;
- if you want a multiplication sign inside a Latex expression, use \times rather than $x$. This improves readability/appearance.

 

[Irishdoug]

I apologies. The dash was meant to separate the

A few points to think about which might help...

Your formula:
“Pav = Energy*rep.rate / Ppeak = Energy/pulse duration”
can't be correct because "Energy*rep.rate / Ppeak" does not have the dimensions of power (it has no dimensions).

In your equation, what do you mean by ‘Energy’? Is it the energy in a single pulse? I think that you have used Energy = $hc/\lambda$. This is the energy in a single photon; but there are many photons in a pulse.

(To get the energy in a pulse, you would need to multiply $hc/\lambda$ by the number of photons in the pulse, This would make your answer much bigger!)

There are two ‘average powers’ and it is not clear to which you refer:
a) the average power during a single pulse; this depends on the shape of the pulse and the peak power during the pulse;
b) the average power-output over some extended time-period (during which there are many sequential pulses and time-gaps between each).

The data (wavelength, pulse repetition rate and the pulse duration) are not sufficient to calculate any type of power. You need additional data.

You have arithmetic mistakes.

Other points:
- the symbol for megahertz is MHz, not Mhz;
- if you want a multiplication sign inside a Latex expression, use \times rather than $x$. This improves readability/appearance.

Hi, sorry I stupidly used / to separate the equations. They should read $P_{av} = Energy \times rep.rate$ $P_{peak} = \frac{E}{pulse width}$.

$P_{av}$ is the energy over a period, whereas $P_{peak}$ is the energy in one single pulse. What is the additional data that I would require?

But yes I didn't take into account there are many photons in a pulse! Thankyou.

 

[Steve4Physics]

$P_{av}$ is the energy over a period, whereas $P_{peak}$ is the energy in one single pulse. What is the additional data that I would require?

You are mixing-up 'power' and 'energy' which are not the same thing. Take care to use the symbols 'E' for energy and 'P' for power.

The average power output of a laser and the energy per pulse are measured by the manufacturer. The values will be different for different makes and models. You can't calculate one without the other.

If you can identify what make/model was used, you could look for a data-sheet on the manufacturer's website. Or you could directly contact the manufacturer.

By the way, it's 'sapphire' not 'saphire'. (A very common spelling mistake!)