PHY 102, Spring 2015, Workshop #10
Lasers
Physics 102
Workshop #10
Name: ____________________________________
Lab Partner(s): ____________________________
Instructor: _______________
Time of Workshop: ________
The name LASER is an acronym for Light Amplification by the Stimulated Emission of Radiation. The
atomic process that directly produces laser action is known as stimulated emission. A necessary
condition for this process to occur is that the atom is initially in an excited state. Stimulated emission is
one of two processes in which an atom can make a transition to a state of lower energy. The other
process is spontaneous emission. The following section will help you understand the difference
between spontaneous emission and stimulated emission.
Spontaneous and Stimulated Emission
In spontaneous emission, the atom in an excited state (E2) makes the transition to a lower energy level
(E1), at random without the aid of any stimulant. Since the atom has lower energy after the transition is
completed, the lost atomic energy (energy difference between excited and ground states E = E2 – E1)
must be converted into some other energy form. In this case, it is light. That is, a photon is created with
a frequency determined by the Einstein-Planck relation E=h·f.
In contrast, stimulated emission requires the presence of an external photon with energy E=. E2 – E1.
The atom is again initially in an excited state E2. The external photon then stimulates the transition
of the atom from the initial state of energy E2 to the final state of energy E1.
Thus, two photons emerge after the transition: the original external photon and one that was produced in
the transition, since total energy has to be conserved. Both photons will have the same energy E = E2 E1. Hence, by the relation E = hf, both photons must have the same frequency f.
It can also be shown that both photons travel in the same direction and have the same phase. This last
property is called coherence.
We can draw these transitions by depicting an energy level diagram. In all such diagrams, the energy
level increases, as we go upward. Photons are illustrated by wavy lines
whose arrow
head indicates if the photon is entering or leaving the system. Transitions are indicated (like in the
Energy diagram of the emission form the Hydrogen atom last week), by vertical arrows pointing from
the initial energy level of the system to the final energy level of the system.
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PHY 102, Spring 2015, Workshop #10
1. Complete the figure below. Draw the incoming and outgoing photon(s) and the arrow indicating the
direction of the transition as appropriate for the different physical processes.
2. In the space below, state, in your own words, some of the basic differences between spontaneous and
stimulated emission.
2. Both the absorption of light and stimulated emission are examples of resonance. To see this, note
that for both processes, it is necessary to have an incoming photon of light. This is the driver. Let its
frequency be fd. An atom has also its own natural frequencies according to the possible transitions
between its energy levels (Et = hft !). We recall from the 1st workshop that resonance is a phenomenon
that occurs when the frequency of the driver matches one of the natural frequencies of the system. In
such a situation there is strong interaction between driver and system.
Explain, in a short paragraph below, (between two and four sentences) why
a) absorption is an example of resonance.
b) stimulated emission is an example of resonance.
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PHY 102, Spring 2015, Workshop #10
The Ruby Laser
The ruby laser was the very first laser and was invented in 1960. The ruby mineral (corundum) is
aluminum oxide with a small amount (about 0.05%) of chromium. It is the chromium that gives ruby it
characteristic pinkish-red color by absorbing green and blue light. The Cr3+ ions are also the atoms that
participate in the laser action. The figures below show a schematic of the Ruby Laser, the transitions
between the involved energy levels and its excitation spectra.
Schematic of the Ruby Laser
Energy Levels and Excitation Spectra of the Ruby Laser
There are three states of the Cr ions that need to be considered. The diagram for the energy levels of
these three states is given below.
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PHY 102, Spring 2015, Workshop #10
Initially, the Cr3+ ions are in the ground state. Its energy can be denoted as E0. For simplicity, the energy
of this state is chosen to be zero. The first process required is the excitation of most of these Cr ions to
an excited state whose energy is 2.25 eV.
To produce this excitation, photons impinge on the ruby material (Blue and Green light) and are absorpt.
This process is called optical pumping.
3. Find the frequency fpumping required for this impinging radiation to drive the Cr3+ ions to the excited
state. (Planck’s constant h = 6.6 x 10-34 joule-seconds. 1eV = 1.6 x 10-19 Joules.).
In a short time, most of the Cr ions now have the excited-state energy of 2.25 eV. They then seek a state
of lower energy. To do this, the ions very quickly make an extremely rapid transition to a lower excited
state whose energy is 1.79 eV. This is labeled as the metastable state in the previous figure.
4. This transition to the metastable state is a radiation-less transition, i.e. no photons are emitted.
However, the overall energy of the system needs to be conserved. Can you explain what happened to the
missing energy?
The metastable energy state is an important characteristic of the material. Metastable means that the
probability for spontaneous emission is very small. In fact, it will stay in this state for about 4
milliseconds until spontaneous emission will occur. This may seem like a short time, to you, but, for an
atom it is a very long time. Usually an atom will stay no longer than 10-12 seconds in an excited state
before it spontaneously emits a photon and relaxes back into the ground state. Eventually, however,
spontaneous emission does also occur from a metastable state, a photon is produced and the Cr+3 ion is
back in its ground state.
5. Find the frequency f of this photon produced during spontaneous emission due to the transition from
the metastable state into the ground state. What color is it?
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PHY 102, Spring 2015, Workshop #10
6. The term population inversion refers to any situation in which the population of an excited state
exceeds that of the ground state. In the case for Ruby Laser that means that more Cr+3 ions are in an
excited state then are in the ground state shortly after pumping has begun. Explain why this inversion
occurs and identify the state that has greater population than the ground state.
As mentioned before, there is spontaneous emission from the metastable state to the ground state, after
about a millisecond. The emitted photon travels through the ruby material and stimulates other Cr+3 ions
to drop down to the ground state. Because the probability for stimulated emission is much greater than
that for spontaneous emission, Laser action follows: From each stimulated emission event two photons
emerge that induce further stimulated emission and the process of stimulated emission cascades. An
intense, coherent beam of light is produced. This is laser light.
7. Describe at least two differences between light produced by a laser, and the light produced by an
ordinary light bulb:
8. The term monochromatic refers to light of one color. More precisely, it refers to light of one
frequency. Is laser light monochromatic? Please explain your answer.
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PHY 102, Spring 2015, Workshop #10
The ruby laser is an example of an optically pumped laser. That is, there must be impinging light, in
order to begin the process that leads to laser light. For any such laser the wavelength of the light that is
used for the pumping is shorter than the wavelength of the light produced by the laser.
9. Can you reason why this has to be always the case for an optically pumped laser? Please explain:
Lasing Cycle of the Ruby Laser.
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PHY 102, Spring 2015, Workshop #10
10. At this point we have reviewed the physical principles of the essential steps that lead to the final
emission of laser light from a Ruby Laser. Using the figure on the previous page, please explain the full
lasing cycle of the Ruby Laser.

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PHY 102, Spring 2015, Workshop #10
11. Equipped with the basic understanding of the working principles of a laser, we can build now our
own. In the diagram below, four energy levels of an atom are drawn: the lowest level (the ground state
E0) and three excited states (E1, E2 and E3). The highest level E3 and the level E1 are unstable states, i.e.
an electron excited to these levels remains there for no more than 10-12 seconds. The energy level E2 is a
metastable state.
Which of the lettered transitions on the diagram below would you use for optical pumping of the laser?
Which transition(s) are the best candidate(s) for the actual production of laser light by stimulated
emission? Please explain your answers.
E3
E2
E
F
E1
A
E0
B
C
D
G
Ground State
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H