Laser Modes

Laser Modes أنماط الليزر
علمنا من المحاض ا رت السابقة أنه للحصول على الليزر نستخدم التغذية العكسية بواسطة الم ا ريا وذلك
لتكبير الشعاع الضوئي خلال مروره بالوسط المشع لليزر، لهذه الم ا ريا دور في التأثير على الإشعاع
longitudinal الكهرومغناطيسي داخل المكبر حيث ينتج نوعين من الأنماط تعرف بالأنماط الطولية
transverse modes والأنماط المستعرضة modes
Longitudinal modes only specific frequencies are possible inside the optical
cavity of a laser, according to standing wave condition.
Transverse modes are created in cross section of the beam, perpendicular
to the optical axis of the laser.
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Longitudinal modes (Axial Modes)
Using Fabry-Perot interferometer one can observe that the
output of the laser beam consists of a number of discrete
frequency components. These modes are known as
longitudinal modes or axial modes. These modes are
created inside the optical resonator between the two
mirrors.
إن السبب يعود في تكون هذه الأنماط يعود إلى تكون أمواج موقوفة
بين المرآتين. وكما نعلم أن الأمواج الموقوفة تتكون standing wave
نتيجة لتداخل موجتين لهما نفس التردد وتنتش ا رن في اتجاهين متعاكسين في
المسافة بين المرآتين. وكمثال على هذه الأمواج الوتر الموسيقي في الجيتار.
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Standing waves in a laser
In a laser an optical cavity is created by two mirrors at both ends
of the laser.
These mirrors serve two goals:
1. They increase the length of the active medium, by making
the beam pass through it many times.
2. They determine the boundary conditions for the
electromagnetic fields inside the laser cavity.
The axis connecting the centers of these mirrors and
perpendicular to them is called Optical Axis of the laser. The
laser beam is ejected out of the laser in the direction of the
optical axis.
An electromagnetic wave which move inside the laser cavity from
right to left, is reflected by the left mirror, and move to the
right until it is reflected from the right mirror, and so on.
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Conditions for Standing Waves
Two waves of the same frequency and amplitude are moving in
opposite directions, which is the condition for creating a standing
wave.
standing waves, must fulfill the condition:
L = q ?q/2
L = Length of the optical cavity.
q = Number of the mode, which is equal to the number of half
wavelengths inside the optical cavity. The first mode contains
half a wavelength, the second mode 2 halves (one) wavelength.
?q = Wavelength of mode m inside the laser cavity.
In fact the number of modes (q) in most laser is very large. For
Example if the central wavelength is 500nm and the mirror
separation is 25cm , q has a value of 1000000, since q can be any
integer, there are many possible wavelengths within the laser
transition shape.
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Example: The length of an optical cavity is 25 cm. Calculate the
frequencies ?q and wavelengths ?q of the following modes:
1. q =1
2. q = 10
3. q = 100
4. q = 106
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The separation between axial modes
If the First mode is q
Then
L = q ?q / 2
If the Second mode is q+1
Then
L = (q+1) ?q+1 / 2
It is more convenient to refer to the axial modes by their frequency
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The separation between neighboring frequencies is equal to C/2L i.e.
dependent only on the separation between mirrors and independent of q.
For L=25cm The separation between neighboring frequencies is 6x108sec-1.
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ملاحظات
وذلك L تزداد عدد الأنماط تحت منحنى الحصيلة كلما زاد طول مكبر الليزر
L لأن الفاصل بين الأنماط يقل بزيادة
It is clear that a single mode laser can be made by reducing the
length of the cavity, such that only one longitudinal mode will
remain under the fluorescence curve with GL>1.
عدد الأنماط التي يمكن أن تنتج ليزر تلك التي يتحقق عندھا شرط
الحصيلة أكبر من أو يساوي الخسارة كما ھو واضح في المنطقة الملونة
في الشكل أعلاه.
للحصول على عدد الأنماط التي يمكن أن تكبر تحت منحنى الحصيلة
C/2L على المسافة بين نمطين Laser bandwidth نقسم
The approximate number of possible laser modes is given by the
width of the Laser bandwidth divided by the distance between
adjacent modes:
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Example
The length of the optical cavity in He-Ne laser is 30 cm. The
emitted wavelength is 0.6328 ?m. Calculate:
1. The difference in frequency between adjacent longitudinal
modes.
2. The number of the emitted longitudinal mode at this
wavelength.
3. The laser frequency.
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