Population Inversion

لتكبير stimulated emission انقلاب التعداد شرط رئيسي لعملية الانبعاث الاستحثاثي
الضوء، وانقلاب التعداد هو توزيع للذرات على مستويات الطاقة يختلف عن التوزيع في حالة الات ا زن
الخاضع لإحصائيات ماكسويل بولتزمان، ولتوضيح فكرة انقلاب thermal equilibrium الحراري
التعداد سوف نقوم بشرح مختصر للتوزيع في حالة الات ا زن الح ا رري.
Thermal Equilibrium
From thermodynamics we know that a collection of atoms, at a
temperature T [0K], in thermodynamic equilibrium with its surrounding, is
distributed so that at each energy level there is on the average a certain
number of atoms.
The number of atoms (Ni) at specific energy level (Ei) is called Population
Number.
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The Boltzmann equation determines the relation between the population
number of a specific energy level and the temperature:
Ni = const * exp (-Ei/kT)
Ni = Population Number = number of atoms per unit volume at certain
energy level Ei.
k = Boltzmann constant: k = 1.38*1023 [Joule/0K].
Ei = Energy of level i. We assume that Ei> Ei-1.
Const = proportionality constant. It is not important when we consider
population of one level compared to the population of another level.
T = Temperature in degrees Kelvin [0K] (Absolute Temperature).
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The Boltzmann equation shows the dependence of the population number (Ni) on
the energy level (Ei) at a temperature T.
From this equation we see that:
1. The higher the temperature, the higher the population number.
2. The higher the energy level, the lower the population number.
الات ا زن الح ا رري
عند درجات الحرارة المنخفضة تكون كل الذ ا رت في المستوى الأرضي وبزيادة درجة الحرارة (بتحريك
المؤشر لليمين تثار الذ ا رت لمستويات طاقة اعلي وهذا خاضع لقانون ماكسويل بولتزمان الإحصائي عند
الات ا زن الح ا رري.
Temperature Increase
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Relative Population (N2/N1)
The relative population (N2/N1) of two energy levels E2 compared to E1
is:
N2/N1 = const* exp (-E2/kT)/ const* exp (-E1/kT)
N2/N1 = exp(-(E2-E1)/kT)
The proportionality constant (const) is canceled by division of the two
population numbers.
Conclusions:
1. The relation between two population numbers (N2/N1) does not depend
on the values of the energy levels E1 and E2, but only on the difference
between them: E2- E1.
2. For a certain energy difference, the higher the temperature, the bigger
the relative population.
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The Figure below shows the population of each energy level at
thermal equilibrium.
Population Numbers at "Normal Population"
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Example
Calculate the ratio of the population numbers (N1, N2) for the two energy
levels E2 and E1 when the material is at room temperature (3000K), and
the difference between the energy levels is 0.5 [eV]. What is the
wavelength (?) of a photon which will be emitted in the transition from E2
to E1?
Solution
When substituting the numbers in the equation, we get:
= 4 * 10-9
ومن هذه النتيجة يتبين لنا أنه عند درجة حرارة الغرفة يكون التعداد في مستوي الطاقة الأرضي
الف مليون ذرة في حين التعداد في المستوي الأول 4 ذ ا رت فقط!!!
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To calculate the wavelength:
This wavelength is in the Near Infra-Red (NIR) spectrum.
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Population Inversion
We saw that in a thermal equilibrium Bolzman equation shows us that :
N1 > N2 > N3
Thus, the population numbers of higher energy levels are smaller than
the population numbers of lower ones.
This situation is called "Normal Population". In a situation of normal
population a photon impinging on the material will be absorbed, and raise
an atom to a higher level.
By putting energy into a system of atoms, we can achieve a situation of
"Population Inversion". In population inversion, at least one of the higher
energy levels has more atoms than a lower energy level.
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An example is described in the Figure. In this situation
there are more atoms (N3) in an higher energy level (E3),
than the number of atoms (N2) in a lower energy level (E2).
The process of raising the number of excited atoms is
called "Pumping".
"Normal Population" compared to "Population Inversion".
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Three Level Laser
A schematic energy level diagram of a laser with three energy
levels is the figure below.
The two energy levels between which lasing occur are: the lower
laser energy level (E1), and the upper laser energy level (E2).
Energy level diagram in a three level laser
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