TO DETERMINE THE NUMERICAL APERTURE OF A GIVEN OPTICAL FIBER
Submitted to: Submitted By: Mr. Rohit Verma 1. Rajesh Kumar 2. Sunil Kumar 3. Varun Sharma 4. Jaswinder Singh
INDRODUCTION TO AN OPTICAL FIBER Optical fiber: an optical fiber is a dielectric wave guide made of glass and plastic which is used to guide and confine an electromagnetic wave and work on the principle to total internal reflection (TIR). The diameter of the optical fiber may vary from 0.05 mm to 0.25mm. Construction Of An Optical Fiber:
(Where N1, N2, N3 are the refractive indexes of core, cladding and sheath respectively) Core: it is used to guide the electromagnetic waves. Located at the center of the cable mainly made of glass or sometimes from plastics it also as the highest refractive index i.e. N1. Cladding: it is used to reduce the scattering losses and provide strength t o the core. It has less refractive index than that of the core, which is the main cause of the TIR, which is required for the propagation of height through the fiber. Sheath: it is the outer most coating of the optical fiber. It protects the core and clad ding from abrasion, contamination and moisture. Requirement for making an optical fiber: 1. It must be possible to make long thin and flexible fiber using that material 2. It must be transparent at a particular wavelength in order for the fiber to guide light efficiently. 3. Physically compatible material of slightly different index of refraction must be available for core and cladding. Type Of Optical Fibers:
1. Glass Core + Glass Cladding 2. Plastic Core + Plastic Cladding 3. Glass Core + Plastic Cladding
Properties Of Different Types Of Index Fibers
Multi Mode Step Index Single Mode Step Index Fiber Multi Mode Graded Index Fiber Fiber
1 diploma of core 1 5 m. >80 m 50 60 m 2 Diameter of cladding 10. 2 2 3 Step index profile Step index profile Graded index profile. 4. Fundamental mode i.e. axial Fundamental as well as Fundamental as well as higher mode. mode. higher mode 5. Laser are used for a fine LED’s are used LED’s are used beam of light
6. NA and Ǿmax is very small so NA and Ǿmax is large NA and Ǿmax is large easier to work they are difficult to work with easier to work with with
7. Dispersion ≈0. Which is very Dispersion is 15 30 Dispersion is 2 ns/km small and is considered as 0 ns/km
8. Supports band width of 1000 20MHz Km >1 GHz km GHz Km 2 2 2 9. N max =V /2; Nmax = V /2; Nmax = V /2; V=2 πa(NA)/ λ; V=2 πa(NA)/ λ; V=2 πa(NA)/ λ; V≤2.405 V≤2.405 →1 to οο
10. Used in military application Used in short runs<1 km Used in long runs and are easy to as scattering losses are terminate, as scattering losses are less large, these are easy to in comparison terminate.
11. Most expensive Least expensive More expensive than multimode step index fiber.
NUMERICAL APERTURE OF AN OPTICAL FIBER In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. The exact definition of the term varies slightly between different areas of optics. Multimode optical fiber will only propagate light enters the fiber within a certain cone, known as the acceptance cone of the fiber. The half angle of this cone is called the acceptance angle, Ǿmax . For step index multimode fiber, the acceptance angle is determined only by the indices of refraction:
Where n f is the refractive index of the fiber core, and n c is the refractive index of the cladding This has the same form as the numerical aperture in other optical system, so it has become common to define the NA of any type of fiber to be
Where n o is the refractive index along the central axis of the fiber. Note that when this definition is used, the connection between the NA And the acceptance angle of the fiber become only an approximation. In particular manufacturers often “NA” for single –mode fiber is quite different and cannot be determined fro the indices of refraction alone. In multimode fiber, the term equilibrium numerical aperture is sometime used. This refer to the numerical aperture with respect to the extreme exit angle of a ray emerging from a fiber in which equilibrium mode distribution has been established. The numerical aperture of an optical can be expressed quantitatively as:
2 2 N1 – N2 =(n 1 +n 2)={(n 1+n 2)/2}(2 n 1) (We approximate (n 1+n 2)/2 as n 1) Hence,
Observation Table S.NO. Distance From Distance Of The NA Screen From Optical Spot Fiber
1 1.30cm 1.2cm 0.4779 2 2.25cm 2.1cm 0.4787 3 3.40cm 3.0cm 0.4934
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EXPERIMENT OBJECTIVE-: To measure the numerical aperture of the optical fiber. APPARATUS-: Fiber optical trainer kit. THEORY-: Numerical aperture of the optical fiber is maximum angle at which the light incident on the fiber end is transmitted long the fiber. The light ray should strike the fiber end within its core of acceptance else it is reflected Out of the fiber Consideration in numerical aperture measure: - It is very important that the optical source should be properly aligned with the cable and the distance from the launched point and cable be properly selected to ensure that the maximum amount of optical fiber power is transferred to the cable. PROCEDURE:
Connect the power supply to the abroad . Connect the frequency generator KHz sine wave output to input of emitter 1 current. Adjust its amplitude at 5 v. p. p. Connect one end of the fiber cable to the output socket of emitter 1 current and the other end to the N.A measurement. Hold the white screen facing such that its cut face is perpendicular to the axis of the fiber. Hold the white screen with 4 concentric circles (10,15,20,25mm diameter) vertically at a distance to make the red spot from the fiber coincide with 10mm spot. Record the distance of screen from the fiber from end perpendicular and note the diameter w of the fiber. Capture the N.A. from the formula given below. W N.A. = 4L 2 +W 2 . Vary the distance between the screen and optical fiber cable and make it coincide with one of the concentric circles. Note the distance. . Tabulate the various distance and diameter of the circle made one the white screen and compute the N.A. from the formula given below. FORMULAE Acceptance Angle And Acceptance Cone
Let’s consider the light propagation in an optical fiber. The end at which the light enters the fiber is called the launching end. Let the refractive index of the core be n 1 and the refractive index of cladding be n 2 (n 1>n 2). Let the outside medium from which the light is launched into the fiber have a refractive index n 0. Let the light ray enter the fiber at an angle θ i to the axis of the fiber. Let the refracted ray make an angle θr with the axis and strike the core cladding interface at an angle φ. If φ>θ c (critical angle), the rays undergoes TIR at the interface. As long as φ≥θc, the light remains within the fiber. Applying snell’s law to the launching face of the fiber, we get n 0Sinθi = n1Sinθr
n1 i.e. Sinθi = Sinθr n 0
n1 i.e. Sinθi = Sin(90 − φ) φ n2 n 0
n1 i.e. Sinθi = Cosφ θi θr n1 n 0
Where φ=θ c, θ i=θ max
n1 So Sinθmax = Cosθc n 0 2 2 n 2 2 n1 − n 2 Now Sinθc = so Cosθc = 1 − Sin θc = n1 n1 2 2 n1 − n 2 Hence Sinθmax = n 0 2 2 2 If (n 1 n2 )≤n 0 , then for all values of θ i<θ max TIR will occur. Assuming n0=1i.e. let the outside medium from which light is launched into the fiber be air then,
−1 2 2 θmax = Sin [ n1 − n 2 ] Numerical Aperture It is the measure of the amount of light can be accepted by a fiber. It is 2 2 defined as the Sine of the acceptance angle i.e. NA = Sin max = n1 − n 2 2 2 n1 − n 2 n( 1 − n 2 )(n1 + n 2 ) n( 1 + n 2 ) i.e. NA = n1 2 = n1 2 = n1 ≅ n1 2 n1 n1 n1 because n 1≅n2 for optical fibers.