A laser produces a beam of a single frequency or monochromatic light because of the collective light emission from many atoms. When the optical media in which the beam is of correct geometry, the resulting light beam is also coherent. In this case, it means the waves of light are traveling together with their associated waves in phase with each other. The name laser is an acronym for  Light Amplification by Stimulated Emission of Radiation. This results in a beam of light that is very directional with high intensity.

Lasers are widely used in medical science, the music industry, and engineering.  Laser light is so well defined it can be focused to a point concentrating its energy.

 Before you begin, be sure to review the following resource: 

 (1) How a Laser Works – YouTube 

 

In this case study, you are going to apply what you know about light wave properties to investigate the nature of particular laser operation.  In the scenario provided, you are going to determine the following quantities:

  • The laser’s energy per photon.
  • The pulse energy for the laser during a specific time interval. 
  • The number of photons in a single laser pulse.

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The following is a demonstration of the calculations you will perform during this case study assignment. 

A laser is used in eye surgery to weld a torn retina back into place. The laser’s wavelength is 514 nm (λ)(λ) and its power is 1.5 watts in each laser pulse.  During the surgery, the laser is pulsed for 50 ms.

During that pulse, what is the average energy of the laser? How many photons are produced?

The laser wavelength is given.  We want to find the frequency using the speed of light (c) equation. 

c=λfc=λf

Solving for frequency, and inserting the values for the speed of light and the given wavelength, we the get the following:

f=cλ=3×108ms514×10−9m=5.84×1014Hzf=cλ=3×108ms514×10−9m=5.84×1014Hz

To find the energy of each photon in the laser beam, we have to use the following formula that relates energy to frequency via Planck’s constant h =6.63× 10-34 Js.

E=hfE=hf

The energy of each photon would then be:

E=hf=(6.63×10−34J⋅s)(5.84×1014Hz)=3.87×10−19JE=hf=(6.63×10−34J⋅s)(5.84×1014Hz)=3.87×10−19J

It is important to note that this is the energy of a single photon in the laser beam!

The Energy of the pulse is defined by the product of the pulse power and the time so 

E=Pt=(1.5W)(50×10−3s)=0.075JE=Pt=(1.5W)(50×10−3s)=0.075J

Then the energy of each pulse is 0.075 Joules. The number photons n in each beam pulse can be found by dividing the pulse energy by the energy of a single photon:   

E=0.075J3.87×10−19J=1.94×1017E=0.075J3.87×10−19J=1.94×1017

n =1.94×1017  is the number of photons produced in this pulse.

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Given the results of this exercise above, let’s evaluate the situation below.

A neodymium YAG laser is used to repair glaucoma damage in another patient. Its wavelength = 1064 nm and produces an Energy of 4.1X10-3 joules. How many photons does it produce?  If its power is also 1.5 watts. How long is its pulse length?

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