PHYS 211 Experimental Physics   Laboratory Report

Student Name: Peter

Student ID number: ---

Student email: ---

Dates of the experiment: 11 – 10 – 2001, 18 – 10 – 2001

Date of Submission: 1 – 11 – 2001

EXPERIMENT 1C   OPTICS IN WAVEGUIDES & FIBER OPTICS

Abstract

The purpose of this experiment is to determine the physical properties of optical fiber. In the first part of the experiment, the water tank was used as the waveguide. It was found that the light beam could be properly guided if it was injected from the end, but was difficult and even not possible to be guided if injected from the end. The critical angle and refractive index found in water were respectively 53^o and 1.25.

In the second part of the experiment, optical fiber was investigated. It was found that the optical fiber could be bent and broken with radius of bending 0.001m. After removing the plastic coating on the fiber, the radius of bending was found to be 0.0015. Also, a light spot was seen if light beam was injected in. There was energy loss in the power transmission in the optical fiber. The efficiency of optical fiber is 20.93%. It was observed that light after transmitting through the optical fiber was unpolarized. Some bright and dark region pattern was also observed from the optical fiber end clearly from TV monitor.

By using the steroscope and 500x microscope, the flatness of the end could be viewed and examined. Two optical fibers could be connected by fusion splicing to make a longer optical fiber.

Introduction

All matters in the nature behave as both wave and particles. The knowledge of wave is practically important because waves are used in a wide range of application. Two of the main applications are in communication and energy delivery. The optical fiber investigated in this experiment is a kind of dielectric waveguide, so that the wave can be guided properly between two points through the fiber.

Optical fiber is the medium in which communication signals are transmitted from one location to another in the form of light guided through thin fibers of glass or plastics. These signals are digital pulses or continuously modulated analog streams of light representing information, such as voice information, data information, computer information and video information.

These information can be sent on metallic wires like twisted pair and coax, and through the air on microwave frequencies. The reason for using optical fiber is that it has certain advantages over any metallic conductor or microwave.

The main advantage of optical fiber is that it can transmit more information in longer distance with less time. In addition, it is not affected by interference of electromagnetic radiation, which makes it possible to information with less noise and error. There are also some other applications of optical fiber that are not possible with metallic condition. These include senor or scientific application, medical or surgical application, industrial application and image transmission.

The experiment gives more understanding of optical fiber. From the structure of the optical fiber, it can explain how the light can be propagated in the fiber. Also, the polarization effect, the properties of the signal after fiber transmission, characteristics of the optical fiber in order to have a perfect transmission and the transmission in a small core fiber were investigated.

Theory

When a light beam strikes an object, some or all of the light will bounce off, the light is said to be reflected. If the surface is smooth and polished, regular reflection will occur.

By the law of reflection, the angle of incidence is equal to the angle of reflection:

i = R    ------ (1)

where i is the angle of incident and R is the angle of reflection. (Figure 1)

When light strikes a surface as shown in Figure 2, part of the light will be reflected and part of it will be absorbed as shown by the penetrating ray.

Before looking at the relationship of the angle of incidence to the angle of refraction, the refractive index is given below:

n = c / v    ------ (2)

where c is the speed of light in vacuum and v is the speed of light in the medium.

When a light ray traveling in a medium strikes a second medium, they have the relationship given by:   

n₁ sin i = n₂ sin r    ------ (3)

As shown in Figure 3, when the angle of incidence increases to a value called critical angleθ_c, the refracted ray just grazes the surface and travels parallel to it. At this point, the angle of refraction is 90^o. Substituting to (3), we have

                      n₂ sin i = n₁ sin 90^o

                       sinθ_c = n₁ / n₂    ------ (4)

Therefore, for any light ray whose angle of incidence is greater than this critical angle, total internal reflection occurs. By equation (4), n₁ should be larger than n₂, which means that the incidence medium is denser than the second medium. Hence, total internal reflection only occurs when light rays travel from denser medium to less denser medium.

Optical fiber consists of a light-carrying core surrounded by a cladding that traps the light in the core by total internal reflection. Figure 4 shows the structure of optical fiber and Figure 5 illustrates the propagation of light in optical fiber.

By making the core of the fiber of a material; with higher refractive index, the light in the core can be totally reflected at the boundary of the cladding for all the light striking greater that the critical angle. The critical angle is determined by the difference in the composition of the materials used in the core and cladding.

In Figure 6, when the optical fiber is bent, the X surface will extend and the Y surface will compress. Therefore, stain = ΔL / L

                         = [2π(R + r) - 2πR] / 2πR

                         = r / R                        ------ (5)

whereΔL is the length difference in the outer and inner surface, L is the length of optical fiber when straight, R is the radius from bending center to X surface and r is the radius from bending center to center of the fiber.

In Figure 7, assume that n₂ = 1 for simplicity. The propagation of the guided wave along the z axis is:           k_lz = k₁ cosθ

where k₁ = 2p / λ_m withλ_m =λ_o / n₁ is the wavelength inside the waveguide. Clearly the angle of obliquenessθcan only take on values from zero to a maximum θ_m set by the critical angle according to: cosθ_m = sin φ_c = 1 / n_1.

Therefore, θ_m determines the minimum value of k_lz:   k_lz,min = k₁ cosθ_m.

This implies:   k_lz,min < k_lz < k_l.

Figure 8 shown the Diagram of where the parameter locate.

Furthermore, for the wave to propagate, we must have constructive interference amongst all the multiple reflected waves. According to the geometry, we have:

(2d / sinθ)(1 – cos 2θ) = iλ_m  ( i = 0, 1, 2, …)

Since θ<θ_m, the maximum number of nodes is:

M = 4 d n₁ sinθ_m /λ_o = 4 d (n₁² – 1)^1/2 /λ_o     ------ (6)

Magnifying glass is a kind of convex lens, the size of the image is larger than the original object if the object is placed between the lens and the focus point of the lens. The magnification is     m = v / u    ------ (7)

where u and v are respectively the object distance and the image distance away from the lens. The simple formula for a convex lens is:

1/u + 1/v = 1/f      ------ (8)       where f is the focal length.

Figure 9 shows the light diagram for convex lens.

Experimental Methods

(1)   Making waveguide out of water

A long tank was filled up with water. The laser beam was injected through one end surface as in Figure 10 and through the side surface as in Figure 11. The range of incident angles was measured over which the laser beam can be guided. The above steps were repeated to investigate whether it is possible to use a dry and clean empty tank to guide the laser beam. The refractive index of water was then calculated from the critical angle measured.

(5) Optical fiber material – bending and cleaving

A glass fiber sample called fiber-1 was used in the experiment. The fiber was bent and tried to measure the radius of the bending at which the fiber broke. The plastic coating on the fiber was then removed using a simple razor blade. The fiber was bent again and the radius of bending was measured at which the fiber broke.

Another 50 microns fiber was given. The plastic coating of the fiber was first removed using a simple razor blade. The fiber was then scribed with a fiber cleaver and broken by pulling. In order to get a reasonably flat surface, the flatness of the surface that fiber was inspected at least two times under a steroscope and the 500x microscope. Also, a 50μm fiber was given which was cleaved by TA using a professional fiber cleaver. The flatness of the surface that fiber was examined under a steroscope and the 500x microscope.

(6) The injection of light into the optical fiber

The experimental setup is shown in Figures 12 and 13. Optical fiber sample called fiber-2 was used. One fiber chunk was put into the chuck holder next to laser while another side was put into the chunk holder next to the detector.

The laser power was measured with the power meter. The laser beam was then focused onto the fiber end by positioning the fiber end near the focus points of the lens (~1.2cm) A piece of paper was put at the other end of the fiber to see whether some laser was delivered through the fiber.

Focused light was injected to fiber instead of laser. The fiber end was first moved to the position of the focused spot that the core area covered the whole area of the focused spot. The power meter was then used to monitor the output light from the end of the fiber for quantitative measurement. The position of the power meter was adjusted so that it collected most of the light coming out from the optical fiber. Then the position of the input end of the fiber was slowly adjusted so that the intensity of the guided light detected by the power meter is a maximum. The power of the guided light was estimated from the measured value of the power meter and the efficiency of the injection was calculated.

(7) Optical paths inside the waveguide (optical modes)

The lens, the output fiber end and the CCD camera were put in position shown in Figure 14. The output fiber end was illuminated using a torch lamp and the image can be observed on the TV monitor. Each component was slowly adjusted so that a clearer image can be seen. Then the position of the output fiber was finely adjusted using positioner-II until a very clear image was obtained. From the TV monitor, the image of the laser coming out was observed.

Then the laser light emerged from the fiber end was investigated. The position of the output fiber end was moved away from the image plate by a small amount in the direction away from the lens by turning the knob surrounding the fiber chunk. The corresponding change was observed and recorded in the pattern on TV monitor. The above steps were repeated with turning the same knob further away from the image.

(8) Change of polarization direction inside the fiber

The laser light to be injected was polarized by putting a polarizer between the output of the HeNe laser and the input port of the optical fiber. Therefore the direction of polarization was examined by emerging another polarizer between the output end and the magnifying lens.

(9) Joining optical fibers – connectorizing and splicing optical fiber

The fiber connector and splicing method were used to connect the fibers together. In the experiment, the fusion splicing was used. The two fiber ends was positioned together and was melted to fuse them together.

Result

(1) Making waveguide out of water

The path of the laser when injected from the end in the tank filled with water is shown in Figure 15. Total internal reflection occurs inside the tank.

The critical angle from the water tank, θ_c = 53^o + 1^o

The angle of incident from air to water, θ_i = 65^o + 1^o

The range of the incident angle over which laser could be guided was from -65^o + 1^o to 65^o + 1^o.

Since the refractive index of air is 1, [5]

By equation (4), the refractive index of water is: sinθ_c = n₂ / n₁

                                       sin 53^o = 1 / n₁

                                           n₁ = 1.252

The error of the refractive index of the is: (cosθ_c / sinθ_c ) = δn₂ / n₂ +δn₁ / n₁

                      (cos 53^o / sin 53^o)( 0.5π/ 180^o) = 0 /1 +δn₁ / 1.252

δn₁ = 0.0136

Therefore, the refractive index of water is 1.25 + 0.01.

If the laser beam was injected from the side, it is not possible to guide the laser. The ray propagated in the path shown in Figure 16. It was observed that no total inside reflection occurred in the water tank, though some reflection did occur in the tank. Also, light spot was detected outside the water tank, indicating that the some laser beam pass through the wall of the tank.

When an empty tank was used, it is also not possible to guide the light. Light was able to observed from the side but not able to observed from the end of the tank.

(5) Optical fiber material – bending and cleaving

It is found that the optical fiber can be bent and the radius of bending at which the fiber broke was 0.0010 + 0.0005m. After removing the plastic coating on the fiber, the radius of bending was measured to be 0.0015 + 0.0005m.

The maximum strain with plastic coating = (50 + 125 + 1000) x 10^-6 / 0.001

                                 = 1.175

Error in maximum strain with plastic coating:

                          δσ/σ=δR / R

                       δσ/ 1.175 = 0.0005 / 0.001

                             δσ= 0.5875

Hence, the maximum strain with plastic coating is 1.2 + 0.6.

The maximum strain without plastic coating = (50 + 125) x 10^-6 / 0.0015

                                 = 0.1167

Error in maximum strain without plastic coating:

                          δσ/σ=δR / R

                       δσ/ 0.1167 = 0.0005 / 0.0015

                             δσ= 0.0389

Hence, the maximum strain with plastic coating is 0.12 + 0.4.

Under a steroscope, when a fiber was broken with a fiber cleaver, the breaking point is not flat enough.

(6) The injection of light into the optical fiber

After adjusting the suitable position of the fiber, a bright light spot was seen when a paper was placed at the other end of the fiber.

Power of incoming laser beam = 0.707μW

Percentage error of measurement by power meter is 2%.

Therefore error in power of the laser beam = 0.707μx 2% = 0.01414μW

Hence the power of incoming laser beam is 0.71 + 0.01μW.

Power of the laser beam after passing through the fiber = 0.148μW

Error in power of the laser beam = 0.148μx 2% = 0.00296μW

Hence the power of laser beam after passing through the fiber is 0.148 + 0.003μW.

Efficiency of the fiber = (0.148 / 0.707) x 100% = 20.93%

Error in efficiency:          δE / E =δW_I / W_I +δW_O / W_O

                      δE / 20.93 = 0.01414 / 0.707 + 0.00293 / 0.148

                            δE = 0.833

Hence the efficiency of the fiber is 20.9% + 0.8%.

Therefore, we can conclude that there is considerable energy loss during transmission through the fiber. 

(7) Optical paths inside the waveguide (optical modes)

When a laser was delivered through the fiber, a bright light spot was observed on the paper at the other end of the fiber.

By using a CCD camera, the image of the laser light after passing through the fiber was observed on the television.

The observed image of the light is shown in Figure 17.

The image of the laser beam spot after turning the knob surrounding the fiber chunk was magnified and the bright and dark region was changed a little only.

(8) Change of polarization direction inside the fiber

When the incoming light was horizontally polarized, it was observed that image was seen and no change on the television with CCD camera was found regardless of what the direction of the second polarizer at the fiber end was.

When the incoming light was vertically polarized, image was seen and no change on the television with CCD camera was found regardless of what the direction of the second polarizer at the fiber end was.

Therefore, although the incoming light was polarized, the output light was unpolarized. It shows that the input light was linearly polarized but not the output one.

(9) Joining optical fibers – connectorizing and splicing optical fiber

A fusion splicer was used to join the two fiber splicing. After the joining process, the fiber was observed on the screen and the result is shown in Figure 18.

The fibers were joining properly. There was very little flaw at the joining point of the fibers. If there were flaw, leakage would occur there.

Discussion

Part I

(1) Making waveguide out of water

When laser was injected as shown Figure 10, light was refracted in water. From the experiment, it was found that when the incident light was between –65^o to 65^o, no light spot can be seen at the side of the tank but seen at the other side only. It is because total internal reflection occurred there.

When the light was refracted to water, the ray then hit the wall of the tank and totally reflects if ray travels from denser medium to less dense medium and the angle of that ray was larger than the critical angle of water, that is 53^o found in the experiment. If it is smaller than the critical angle, ray will partially reflected vack to the water tank and partially refract outward. Therefore, the angle of incident of laser is important. And it can be determined by combining equations (3) and (4).

                        n₁ sin i = n₂ sin r

                         sinθ_c = n₁ / n₂

Sinceθ_c = 90^o – r,         n₁ sin i = n₂ cosθ_c

Hence,                  1 / sin i = tanθ_c

Total internal reflection only occurs when the ray travels from denser medium to less dense medium. From equation (4), sinθ_c cannot be greater than 1, thus it is not possible to have total internal reflection when n₂ is larger than n₁.

From the experiment, it was also found that the refractive index of water is 1.25+0.01, while the actual value if refractive index of water is 1.33. [5] There is a considerable difference between the two values and the actual value is outside the range. Actually, the path for the laser beam is shown in Figure 19, in which plastic has highest refractive index than that of air. Therefore when the laser beam was injected with angle between –65^o to 65^o, it was refracted first in plastic and then to water. Ray 2 then strikes to the edge of water and plastic. Since water is less dense than plastic, the rain will mainly refract to the plastic. And since plastic is denser than that of air outside, if the angle of incident of the ray 3 is larger than the critical angle of plastic, the ray will reflect back and back to the edge of water and plastic. Although the plastic has higher refractive index than that of water, the angle of incidence of ray 4 is smaller than the critical angle in plastic. Therefore the ray 5 refracts in the water again the whole process is then repeated.

When the laser was injected from the side, it was impossible to guide the laser beam inside the water. This is because no matter what the angle of incidence is, the refracted angle is smaller than the critical angle of plastic. And since the ray is larger than the critical angle of plastic, the ray then refracts to the water. Finally, the ray will refract to plastic and then to air again. Similarly, by equation (4) again, when the incident angle from air tends to 90^o, the refracted angle will tend to the critical angle of the plastic. And by injecting laser with smaller incident angle, the refracted angle will be smaller according to equation (3). Therefore there is no way to have total internal reflection if the laser beam is injected from the side.

Although there is no total internal reflection when the laser beam is injected from the side, the beam could also be seen in the tank. It is because there is reflection and refraction at the same time when laser beam penetrates from one medium to another. Therefore, when the laser beam travels to the edge of water and the plastic wall, some of the light beam was refracted as shown in Figure 20.

When laser was injected to the empty water tank, it was impossible to guide the laser beam inside the tank. It is because as the empty tank is filled with air, the laser beam injected will first refract to the plastic wall and then refract to air in the tank. The ray will then refract to the plastic wall and refract to air outside the tank. From equation (3), n₁ sin i = n₂ sin r. Since n₁ = n₂, we have i = r. The incident angle of the laser beam is equal to the angle of the outcoming beam in air of the empty tank. Therefore there is no total internal reflection in plastic wall.

For the error source of this part of the experiment, the laser beam was scattered in all direction due to the rough surface of the plastic wall. Also, the total internal reflection occurs at the plastic and air interface but not the plastic and water interface, so the value of the measured critical angle of water was not accurate.

For the improvement, the plastic wall should be as thin as possible, so that the effect of refractive index of plastics is minimized. Besides, the surface of the plastic wall should be polished so that the laser beam will not scatter away in all direction.

Part II – Optical fiber

There are two basic types of optical fiber, multimode and single mode. Multimode fiber means that light can travel in many different paths through the core of the fiber, entering and leaving the fiber at various angles. Two types of multimode fiber exists, single index and grade index, distinguished by the index profile of their core and how light travel in them, and one type of single mode fiber, as shown in Figure 21.

In the experiment parts (5) to (9), a 50-micron core optical fiber was used. It is a kind of multimode fiber. [5] Light travels in straight lines in the fiber, reflecting off the core and cladding interface. The numerical aperture can be determined by the difference in the indices of refraction of the core and cladding and can be calculated by equation (3).

It is found that after removing the plastic coating on the fiber, the fiber is easier to break on bending. Therefore, the purpose of having a layer of plastic coating on the fiber is to increase its strength, so that it is not easy to break when bent. Also, plastic coating provides scratch protection for the glass below. It also adds the mechanical strength of the fiber and protects it from moisture damaging. In addition, the plastic coating cushions the fiber when it is pressed against irregular surface. Finally, the jacket compensates for some of the contractions and expansion caused by temperature variations. Thus the optical fiber can be used with longer time.

It is important to have a flat fiber end when injecting light beam to fiber. This is because light may be scattered at the edge of the fiber end and so the original signal may get loss or distortion. The fiber end is said to be ‘flat’ if it does not have a ‘saw’ surface. It should be smooth at the edge of the fiber end. Also, the edge of fiber end should be perpendicular to the side of the fiber.

In the experiment, it was found that the efficiency of a 50μm fiber was just 20.9%. It seems that there was large portion of power loss in the fiber. Figures 22 and 23 show that after passing the laser beam to the convex lens, laser with different angle of incidence will be injected to the fiber, Since part of the laser beam may have angle of incidence larger than the critical angle of glass core after refraction, they may refract again to the cladding region and be lost by radiation.

Also, bending of fiber may lead to leakage of laser beam. The incident angles will be different as illustrated in Figure 24 when bending. In this case, even if the incident angle of the first reflection is larger than the critical angle, other incident angles may not. Therefore the light may not be properly guided. 

When the radius of bending increases, higher the chances of incident angle is smaller than the critical angle as shown in Figure 25.

Moreover, core area fiber does not cover the whole laser spot after focusing by the convex lens. Some of the laser beam did not enter the fiber and get loss. Also, some beam was reflected at the fiber end as shown in Figure 26.

As light waves travel down the optical fiber, they lose part of the energy because of various light absorbing compounds in fiber. Dirt comes to the fiber and impurities will cause parts of the optical signal to be lost due to scattering or absorption causing attenuation of the signal.

In order to have a maximum efficiency, it is better to use a narrow laser beam, so that the angle of incident of laser after focusing is lower and so only total internal reflection occurred in fiber. The radius of bending should be as small as possible, so that the leakage during transmission is minimized. Also, position the fiber end so that it can cover the whole area of laser spot, maximum power injected can be obtained. Moreover, the fiber end can be cleaned with alcohol to remove any dirt before use.

(7) Optical paths inside the waveguide

From the experiment, it was observed that some bright and dark region appeared on the television. It is because interference occurred in the fiber.

In traveling down the optical, each ray of the light may be reflected hundreds or thousands of times. The rays reflected at high angle (with higher mode) must travel at a greater distance than the low angle rays (with lower mode) to each the end of the fiber. Because of this long distance, the higher mode ray arrives later than the lower mode ray. Phase difference between them causes signal distortion when getting the result at the end of the fiber as shown in Figure 27. [2] Actually, there are more than two modes in fiber and can be determined by equation (6).

By equation (7), m = v / u, object distance is inversely proportional to magnification. When v increases, m will increase. Therefore, when the output side of fiber end moves closer to the lens, the image on the television will larger. While the fiber moves away from the lens, the image will be smaller.

(8) Change of polarization direction inside the fiber

As in Figure 28, since the laser beam reflected in fiber more than hundreds times, so the polarization direction may change in fiber, and so the resulting laser beam is unpolarized. [1]

(9) Joining optical fiber by fusion splicing

There will be a great power loss if light pass through a non-perfect splice joint fiber. Figure 29 lists the most cases why having such power loss.

Another loss mechanism is back reflection or refraction and is measured as optical return loss. As the light travels through the fiber, passing through splices, finally arriving at the end point, some of light is reflected back by fiber end faces at those man-made points as shown in Figure 30. [6] 

Other Sources of Error:

Most sources of error have been mentioned in the above discussion. One other source of error is that when recording the value of incoming and outcoming laser beam, the environment is not dark enough. Then the detector may record a higher value.

To improve the accuracy, it is necessary to turn off other light source before taking readings.

Conclusion

After doing the experiment, it is found that in order to have total internal reflection, the laser beam should be injected from denser medium to less dense medium and the angle of incidence should be larger than the critical angle of incidence of the medium. The critical angle of water was found to be 53^o + 1^o and the refractive index of water is 1.25 + 0.01.

Also, the propagation of the laser beam is due to the total internal reflection in the optical fiber. The plastic coating on the fiber is mainly for protecting the optical fiber from bending. Also, it was found that the efficiency of 50μm optical fiber was is 20.9% + 0.8%. This shows that the power loss in fiber transmission is very high. Moreover, it was observed that there was interference in the fiber with different mode of laser beam and distortion appeared. Although the input laser beam is polarized, the output laser beam is unpolarized. Also, two fibers can be joined together by fusion splicing to form a long optical fiber.

As optical fiber is important for transmission of signal in modern society, the value of efficiency would be much higher than that found in the experiment. But we still need to find ways to improve the effectiveness of transmission of signal through optical fiber.

Reference

[1] Fiber optical system, first edition, Bypierre Halley, page 35-46

[2] Fiber optics, second edition, Robert Hossm, page 28-31

[3] Fiber optics, second edition, Robert Hossm, page 78-83

[4] An introduction to optical fibers, third edition, Allen Cherin, page 76-86

[5] Fiber optic technician’s manual, Jim Hayes, page 15-24

[6] Fiber optic technician’s manual, Jim Hayes, page 75-76

[7] Handout of Experiment 1C of PHYS211

Figure Captions 

Figure 1: Reflection

Figure 2: Refraction

Figure 3: Total internal reflection

Figure 4: Optical fiber construction

Figure 5: Light propagation in optical fiber

Figure 6: Bending an optical fiber

Figure 7: Propagation by multiple reflection in a linear waveguide.

Figure 8: Diagram of where the parameter locate

Figure9: Light diagram for convex lens

Figure 10: Injection from the end

Figure 11: Injection from the side

Figure 12: Input side of the setup

Figure 13: Out put side of the setup

Figure 14: Imaging of the near-field profile

Figure 15: Ray travels in the water tank when injected from the end

Figure 16: Ray travels in the water tank when injected from the side

Figure 17: Image of the laser beam after passing through the fiber

Figure 18: Joining two fibers

Figure 19: The path of the light beam when injected from the end of the water tank

Figure 20: Path of the laser beam when injected from the side.

Figure 21: The three types of optical fiber

Figure 22: Angle of incidence of light so that only total internal reflection occurs

Figure 23: Reflection and Refraction of ray on cylindrical core cladding surface

Figure 24: Bending loss

Figure 25: Bending loss for small radius

Figure 26: Injection loss

Figure 27: Fiber dispersion

Figure 28: On the plane of cross section of the rod

Figure 29: Splice loss factor

Figure 30: Optical return loss

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