King Fahd University of Petroleum and Minerals. Electrical Engineering Department EE 420. Fiber Optics Communication.

Transcription

1 King Fahd University f Petrleum and Minerals Electrical Engineering Department EE 420 Fiber Optics Cmmunicatin Labratry Manual July 2005

2 2 PREFACE This manual cntains ten labratry experiments t be perfrmed by students taking the ptical fiber cmmunicatin curse (EE 420). The varius experiments included in this manual are designed t enrich the student experience in the field f fiber ptics cmmunicatin and t cmpliment and imprve understanding f the varius cncepts studied in the classrm lectures. The experiments range frm intrductry nes in which the student learns basic cncepts such as ptical pwer measurement t mre advanced experiments, such as experiments that utilize the ptical time dmain reflectmeter (OTDR) in fiber ptics measurements. The experiments are designed, whenever pssible, t be theretically verifiable. This is imprtant nt nly fr gaining practical experience, but als t give students cnfidence in the thery studied in the classrm lecture. In additin, in the design f thse experiments, lengthy and repetitive prcedures are avided, whenever pssible. Repetitive measurements are nly dne when such measurements are essential fr theretical interpretatin and verificatin f the experimental results. A lt f effrt has been made t simplify and clarify the experimental prcedure and t insure smth cnduct f the experimental measurements. The students are strngly encuraged t read the intrductry part f each experiment ahead f time, befre attending the labratry. Each experiment cntains an ample and clear intrductin t the experiment, which shuld facilitate understanding, cnducting and interpretatin f the experimental wrk. Students at the senir level are expected t submit prfessinally-written labratry reprts. T help the student prepare prfessinal quality reprts, a guide has been develped and included in Appendix A alng with a sample reprt. The EE 420 students are strngly encuraged t read this guide and the sample reprt, because they stress and clarify a number f basic ideas that are frequently neglected r misunderstd by ur students. Because a number f EE 420 labratry experiments utilize laser surces, a labratry safety prcedure has been included at the end f this manual. I wuld like t thank Mr. Hameed Frazi, Mr. Jey Espinsa and Mr. Ibrahim Al- Rashid f the EE department fr prviding invaluable help during the hardware setup f the varius experiments fund in this manual. Husain A. Al-Jamid Prfessr, EE Department July, 2005

3 3 TABLE OF CONTENTS Experiment 1: Optical Pwer Measurements Experiment 2: The HeNe Laser Intensity Prfile: Thery and Experimental Verificatin.10 Experiment 3: Light Plarizatin and Fcal Length f Thin Lenses..22 Experiment 4: Determinatin f the Acceptance Angle and Numerical Aperture f Optical Fibers...30 Experiment 5: Light Cupling t Multimde Graded Index Fibers 38 Experiment 6: Fiber Misalignment Lss Measurement...47 Experiment 7: Fiber Splicing and Intrductin t the OTDR..54 Experiment 8: OTDR Measurement f Fiber Length, Attenuatin and Splice Lss..63 Experiment 9: Characteristics f the Light-Emitting Dide.69 Experiment 10: Characteristics f the Phtdide 76 Appendix A: Guideline fr Preparing Labratry Reprts...88 Appendix B: Units f Optical Pwer 97 Appendix C: Operatin f Optical Pwer Meters 100 Labratry Safety 102

4 4 EXPERIMENT 1 OPTICAL POWER MEASUREMENT OBJECTIVES: The bjectives f this experiment are t understand the basic cncepts f ptical pwer measurements using ptical pwer meters, the difference between calibrated and nn-calibrated ptical pwer meters, the prper use f the varius ptical pwer units and cnversin between thse units. In rder t gain experience with ptical pwer measurement, the ptical pwer lss due t micrscpe glass slides will be determined experimentally using a nn-calibrated ptical pwer meter. The experimental results will be cmpared with thery. EQUIPMENT: 1. Optical Pwer Meter: INFOS, Mdel # M HeNe Laser: Cherent, Mdel # One glass micrscpe slide, marked with 8 circles. 3. Five glass micrscpe slides, each marked with a single circle. 4. Glass slide hlder. 5. Labratry jack. 6. Shrt ptical bench (abut 1/4 meter lng). 7. Hrizntal and vertical translatin stages assembled n a bench base. PRELAB ASSIGNMENT: Read appendices B and C thrughly in rder t prepare fr this labratry experiment. The infrmatin cntained in appendices B and C prvide basic backgrund fr ptical pwer measurement, which is imprtant fr understanding this experiment and future experiments. Befre the experimental part f this experiment, the labratry instructr will briefly explain appendix B and C, but it s yur respnsibility t fully understand their cntents. INTRODUCTION: It is well-knwn that when an ptical beam is incident nrmally frm a medium with refractive index n 1 nt anther medium with refractive index n 2, part f the beam is reflected and part f it is transmitted (see Figure 1). Nte that the incident beam encunters a single interface nly. The reflectivity R 1 and transmissivity T 1 in this case are given by: R P n n r Pi n1 n2 2 (1)

5 5 P T 1 R 4nn t Pi ( n1 n2) (2) Reflected Transmitted Incident n 1 n 2 Figure 1: Reflectin and Transmissin f Light at a Single Interface. Where P i, P r and respectively. The subscripts in 1 single interface. P t dente the incident, reflected and transmitted pwers, R and T 1 dente reflectin and transmissin thrugh a The situatin becmes mre invlved when light passes thrugh a slab f material with a nn-zer thickness d, as shwn in Figure 2. The refractive index f the slab is assumed t be n 2 and the refractive index f the surrunding material is assumed t be n 1. This type f prblem is different frm the single interface prblem shwn in Figure1, because in this particular case, the light beam encunters tw parallel interfaces, leading t multiple reflectins inside the slab. Incident n 2 Transmitted n 1 Reflected d n 1 Figure 2: Reflectin and Transmissin f Light at Tw Parallel Interfaces. Accrding t thery, the transmissivity T 2 f the slab shwn in Figure 2 is given by: T P (1 R ) (3) P R R 2 t i (1 1) 4 1sin

6 6 Where R 1 is the reflectivity f a single interface, which is given by equatin (1), kn2d (2 / ) n2d and is the free space wavelength. The subscript in T 2 indicates the presence f tw parallel interfaces. Accrding t equatin (3), when the parameter is a multiple f (i.e. k n2d 0,, 2, 3,... ) the transmissivity reaches a maximum value f 1. Hwever, when is an dd multiple f /2 (i.e. k n2 d / 2, 3 / 2, 5 / 2,...) the transmissivity reaches a minimum value f transmissivity T 2 f the slab always lies in the range: (1 R) /(1 R). Thus the (1 R ) /(1 R ) T 1 (4) Let us assume that the slab is made f glass ( n ) and the surrunding medium is air ( n ). Using equatin (1) results in R Then using equatin (4), it is easy t shw that T 2 lies in the range: T 1.0 (5) 2 Using equatin (5), we can calculate range f the pwer lss in db that an ptical beam encunters when passing thrugh a slab f glass (see appendix B): 10lg(0.852) 10lg(1.0) db Lss db db 0 db (6) Lss In this experiment, the pwer lss due t a glass slab in the frm f a micrscpe slide will be measured in db. Because the thickness d f the micrscpe slide is nt unifrm acrss the slide, the parameter changes value depending n the lcatin where the light beam passes thrugh the slide. This means that the pwer lss caused by the glass slide is als nt unifrm. Hwever, accrding t thery this lss must always lie in the range given by equatin (6). Als accrding t equatin (6), the mean lss f the glass slide equals ( )/ db. The gain an insight int hw the slide thickness effect the transmissivity, let us nte that a /2 change in the parameter can cause the transmissivity t change frm maximum t minimum r vice versa. Fr /2 kn2 d, we have d ( / 2) /( kn2) /(4 n2) /(4 1.5) 0.11m. Thus a very small change in d can lead t large changes in the transmitted pwer. This experiment cnsists f tw main parts. In part A, the ptical pwer lss experienced by a light beam as it passes thrugh different lcatins f the same glass slide will be measured. In part B, the ptical pwer lss due t a number f glass slides, separated by air gaps will be measured. Nte that in part B, ptical pwer readings will be repeated using different meter wavelength settings. One bjective f part B is find ut if the meter setting has an effect n the ptical lss measurements.

7 7 PROCEDURE: PART A: 1- Turn n the ptical pwer meter and the HeNe Laser. Wait fr abut 15 minutes in rder fr the HeNe laser utput t stabilize. 2- In the ptical pwer meter, select 0.85 m and the dbm scale. [The ptical pwer meter is clearly nt calibrated, because the HeNe laser has a wavelength f m]. 3- Align the Laser and the pwer meter fr maximum meter reading. This gives the value f P i in dbm, recrd it in table 1. [Take extra care nt t mve the laser surce r the pwer meter after yu take this reading]. 4- Insert the glass slide (the glass slide marked with 8 circles) between the laser surce and the pwer meter (see Figure 3). The slide shuld be psitined s that the laser beam passes thrugh circle number 1. [The glass slide must be kept clean, by hlding the slide n the sides nly]. 5- Recrd the pwer meter reading in table 1 in the clumn marked P. Glass Slide HeNe Laser P i P Optical Pwer Meter Figure 3: A Glass Slide Inserted between the Laser Surce and the Optical Pwer Meter. 6- Repeat step 5, when the light passes thrugh circles number 2 thrugh Calculate and recrd the pwer lss in db ( dblss Pi P) fr each f the 8 cases. 8- Calculate the average experimental db lss and recrd its value in table Plt the db Lss versus circle number. 10- Cmpare the experimental results btained in table 1 with the theretical range f the db pwer lss [as predicted by equatin (6)]. Are the results within the predicted range? 11- Cmpare the average theretical and average experimental db pwer lsses. 12- Discuss the results, write cmments and sme cnclusins.

8 8 Circle Number P (dbm) Theretical Average db lss db db P dbm Lss Experimental Average db lss i Table 1: Input and Output Pwers in dbm when Light Passes thrugh Different Lcatins f the Micrscpe Glass Slide. PART B: 1- Leave the ptical pwer meter setting at 0.85 m and the dbm scale. 2- Remve the slide used in part A. 3- Align the Laser and the pwer meter fr maximum meter reading. Recrd the meter reading in table Insert the glass slide # 1 between the laser surce and the pwer meter. The slide shuld be psitined s that the laser beam passes thrugh the circle. 5- Insure that the laser beam passes (as clse as pssible) thrugh the center f the circle. 6- Recrd the pwer meter reading in table 2 in the clumn marked P. 7- Add slide # 2 (d nt remve slide # 1). Recrd the meter reading in table Keep adding new slides, ne at a time and recrd the meter reading in table 2, until yu finish inserting all the five slides prvided. 9- Calculate the db lss in each case and recrd the values in table Plt the db Lss versus the ttal number f slides used. 11- Change the pwer meter setting t m. 12- Remve all the slides. 13- Repeat steps 3 thrugh 10 using the new meter setting. Add the slides in the same previus rder, slide 1 first, fllwed by slide 2 and s n. 14- Discuss and cmpare the results btained in tables 2 and 3. Des the db lss measurement depend n the pwer meter setting? Write sme cnclusins.

9 9 Slide Number P (dbm) db P dbm Lss i Table 2: Input and Output Pwers in dbm when Light Passes thrugh a Number f Micrscpe Glass Slides. The Optical Pwer Meter is Set at 0.85m. Slide Number P (dbm) db P dbm Lss i Table 3: Input and Output Pwers in dbm when Light Passes thrugh a Number f Micrscpe Glass Slides. The Optical Pwer Meter is Set at 1.310m. QUESTIONS: Make sure yu read Appendix B, befre yu answer these questins. 1- Cnvert 0dBm t: a) mw b) W & c) W 2- Cnvert 0.1 mw t: a) db b) dbm & c) db 3- Cnvert 0.3W t: a) db b) dbm & c) db 4- A 2.5 mw ptical beam passes thrugh a lssy ptical element. If the lss f the element is 10 db, calculate the utput pwer in mw and in dbm. 5- The input t a lssy element is 25dB an the utput pwer is 14dB. Calculate the db element lss.

10 10 EXPERIMENT 2 THE HENE LASER INTENSITY PROFILE: THEORY AND EXPERIMENTAL VERIFICATION OBJECTIVES: The bjectives f this experiment are t measure the transverse intensity prfile f the HeNe laser, the angle f divergence as well as t measure the dependence f the spt size and the peak intensity n distance. The experimental results are t be cmpared with theretical predictins. EQUIPMENT: 1. Optical pwer meter: INFOS, Mdel # M HeNe laser: Cherent, Mdel # Hrizntal and vertical stages assembled n a shrt ptical bench (abut 1/4 meter lng). This assembly is required t hld the HeNe laser. 4- Apprximately 2 meter lng multimde fiber (cre diameter = 50 m, Orange Clr). 5. Mells Grit hrizntal and vertical translatin stages, (0.01 mm reslutin) with a fiber hlder assembled n a Mells Grit bench base. PRE-LAB ASSIGNMENT: Read the intrductin t this labratry experiment befre yu attend the lab. This intrductin intrduces imprtant theretical backgrunds which are necessary fr understanding and interpreting the experimental results. INTRODUCTION: The light emitted by a HeNe laser surce fllws apprximately a Gaussian intensity distributin in the transverse directin, which is given by: 2 2 I r I e (1) 2 r / w () max Where r is the radial crdinate, w is the Gaussian beam spt size and I max is the maximum intensity, which ccurs at the beam center r 0. The spt size w is als 2 2 called the 1/e distance, because the intensity drps by a factr 1/ e when we mve a distance w frm the beam center. Figure 1 shws a plt f the Gaussian 2 2 intensity prfile I( r) 10exp( 2 r / 2 ). The maximum intensity Imax 10 and the spt size w 2. The hrizntal dashed line indicates the clearly shws the spt size t be w / e level, which When a Gaussian beam prpagates in a hmgeneus medium, such as air, the spt size w increases with distance and the peak intensity I drps. Electrmagnetic max

11 Intensity I 11 thery actually predicts that the intensity f a Gaussian beam prpagating in a hmgeneus medium is given by (see Figure 2): I( r, z) I ( z) e r / w ( z) max (2) Radial Distance r Figure 1: Gaussian Intensity Distributin in the Radial Directin. Where the z - varying peak intensity I () max z and spt size wz () (in free space) are given by: I z I w w z (3) 2 2 max ( ) max (0) (0) / ( ) 2 z w 2 w( z) (0) 1 w (0) (4) Where is the wavelength and z is the directin f Gaussian beam prpagatin. I (0) max and w (0) are respectively, the peak intensity and spt size at z 0 (see Figure 2). The spt size w (0) is als knwn as the minimum r initial spt size. The asympttic angle f divergence f the Gaussian beam is given by: w(0) w (5) Fr HeNe lasers, the angle f divergence is very small, much smaller than 1 degree. 2 2 Accrding t equatin (3), fr large values f z, i.e. [ z/ w (0)] 1, the spt wz () becmes a linear functin f z : z w( z) w(0) 1 z / w(0) z 2 w (0) 2 (6) Als fr large values f z, frm equatins (3) and (4), we can cnclude that the peak intensity I () z becmes prprtinal t 2 max 1/ z.

12 12 In this experiment, we will scan the laser beam emitted by a HeNe laser in rder t measure its intensity prfile in the transverse directin (acrss the beam). An ptical fiber with a sufficiently small cre diameter (much smaller than the measured beam spt size, i.e. d w) will be used in rder t insure that nly a small fiber prtin f the beam pwer is detected by the pwer meter, as seen in Figure 3. This is dne t insure high reslutin f measurement. If we use a fiber whse diameter is cmparable t the beam spt size, the results we btain will be pr. In this experiment the fiber used has a cre diameter f 50 m, which is much smaller the spt size that we will be measuring. 2 wz ( ) 2 w(0) 2w z Figure 2: Illustratin f Gaussian Beam Expansin, Shwing the Initial Spt Size w (0) and the Definitin f the Distance z. Output End f the Laser Optical Fiber HeNe Laser 2 w (0) Optical Pwer Meter z Figure 3: An Optical Fiber Used fr Scanning the Laser Intensity Prfile at a Fixed Distance z frm the Laser Output End. PROCEDURE: [IMPORTANT: INSURE THAT THE UNCONNECTED END OF THE FIBER HAS BEEN RECENTLY CLEAVED AND CLEANED BEFORE YOU BEGIN]. 1- Turn the HeNe laser surce and leave it n fr abut 15 minutes in rder fr it t stabilize.

13 13 2- Cnnect ptical fiber t the ptical pwer meter. D nt remve the fiber frm the pwer meter and d nt mve the ptical pwer meter while taking measurements. 3- Set the ptical pwer meter t the dbm scale and chse 0.85 m 850 nm. 4- Attached the pen end f the fiber t the fiber hlder and psitin tip at a distance z 0.5 cm r less frm the laser utput end. [Be careful that the fiber s tip des nt tuch the laser, because that may break the fiber]. 5- Mve the fiber s tip bth in the hrizntal and vertical directins until yu btain maximum pwer reading. 6- The fiber tip is nw lcated at the beam s center ( r 0 ). 7- Recrd the maximum pwer in the secnd clumn f table 1 in the rw marked r 0. The meter is expected t register abut 15dBm (r a few dbms higher). [If yur meter registers much less pwer, cnsult with yur labratry instructr. This may be due t a pr cnnectr which is used t cnnect the fiber t the ptical pwer meter]. 8- Scan the beam nly in the hrizntal directin in the range ( 0.5 r 0.5 mm ) using a step f 0.02 mm. [Fr the Mells Grit translatin stage micrmeter, 1turn = 0.5 mm]. This means that the distance between the individual marks f the Mills Grit translatin stage is 0.01 mm. Recrd the pwer (in dbm) in the secnd clumn f table Repeat steps 4 thrugh 8 fr z 20, 40, and 80 cm and recrd the measured pwers in the secnd clumn f tables 2, 3 and 4, respectively. [Nte that tables 2, 3 and 4 have different step sizes and different ranges]. REPORT REQUIREMENTS: 1- Cnvert the pwers recrded in the secnd clumn f tables 1 thrugh 4 t mw and recrd the results in the third clumn f each table. 2- Nrmalize the pwers calculated in clumn 3 f the each table by dividing by the maximum pwer in each case. Recrd the values in clumn 4 f each table. This clumn nw cntains the nrmalized pwer P (r equivalently the nrmalized intensity I N ). 3- Plt the nrmalized intensity I N versus the radial distance fr each f the fur cases n the same graph. By definitin, the maximum intensity seen in the resulting graphs shuld equal t unity. 4- Cmment n and discuss the resulting graphs. Hw clse t Gaussian is the nrmalized intensity prfile fr each case? Des the spt size appear t increase with the distance frm the laser end? 5- Cmment n and discuss the dependence f the peak pwer (in mw) n distance frm the laser end. 6- In rder t cmpare the experimental and theretical results, we need first t accurately calculate the spt sizes w 0, w 1, w 2 and w 3 crrespnding respectively t the distances z0 0.5 cm 0cm, z1 20 cm, z2 40 cm and z3 80 cm. Use a Gaussian functin fit t calculate the spt size in each case. This can be dne as fllws, using matlab: A - Plt the nrmalized intensity (clumn 4 f the table) versus the radial distance r. N

14 B - Prgram and plt the nrmalized Gaussian functin exp[ 2( r r ) / w ] (in the same figure) versus r. C - Initially set the radial shift parameter r t zer and try several values f w t btain the best pssible graphical fit between the experimental data f clumn 4 and the nrmalized Gaussian functin. If necessary, adjust the value f r t btain the best pssible Gaussian fit. The value f w which results in the best pssible fit between the tw graphs crrespnds t the Gaussian spt size. If dne crrectly, this prcedure gives accurate values f the spt size. Accurate spt size is necessary fr the cnsistent results. 7- Plt the experimentally determined nrmalized intensity and the crrespnding Gaussian fit n the same figure fr each f the fur cases. 8- Recrd the values f w, w 1, w 2 and w 3 btained frm the Gaussian fit prcedure in table Use the measured value f w(0) w t theretically predict the values f w 1, w 2 and w 3 using equatin 4. Recrd the results in table 5. Cmpare the theretical and measured values f w 1, w 2 and w 3. [use m ]. 10- Plt wz () versus z fr z 0cm using the theretical and experimental data n the same graph. 11- Plt the experimentally measured peak pwer (in linear units) versus z and cmment n the resulting graph. Des the peak intensity increase r decrease with z? 12- Demnstrate that the measured peak pwer in mw (at the Gaussian beam center) 2 is prprtinal t 1/ w. 13- Calculate in radians and in degrees using the knwn value f w and equatin 5. Is much smaller than 1? 14- Discuss and cmment n the results including the symmetry f the laser beam intensity prfile and write sme cnclusins. Radial Distance (mm) [Beam is Scanned Hrizntally] P (dbm) P (mw) IN PN (Unit-less)

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16 Table 1: Optical Pwer Versus Radial Distance r. The Distance between the HeNe Laser Output End and the Fiber Input End is z 0.5cm 0cm. Radial Distance (mm) [Beam is Scanned Hrizntally] P (dbm) P (mw) IN PN (Unit-less)

17 Table 2: Optical Pwer Versus Radial Distance r. The Distance between the HeNe Laser Output End and the Fiber Input End is z 20cm.

18 18 Radial Distance (mm) [Beam is Scanned Hrizntally] P (dbm) P (mw) IN PN (Unit-less)

19 Table 3: Optical Pwer Versus Radial Distance r. The Distance between the HeNe Laser Output End and the Fiber Input End is z 40cm. Radial Distance (mm) [Beam is Scanned Hrizntally] P (dbm) P (mw) IN PN (Unit-less)

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21 Table 4: Optical Pwer Versus Radial Distance r. The Distance between the HeNe Laser Output End and the Fiber Input End is z 80cm. z (cm) wz ()[mm] [Theretical] wz () [mm] [Experimental] Table 5: Theretical and Measured Gaussian Spt Sizes. QUESTIONS: 1- Based n the experimental data, what shuld be the spt size at a distance f 100 m frm the laser utput end? 2- Using the experimental data, estimate the distance at which the spt size equals 5 cm. 3- Des the angle f divergence increase r decrease when the wavelength increases? 4- Estimate the distance beynd which wz () becmes a linear functin f z. Use the 2 2 cnditin [ z/ w (0)] Based n yur answer t part 4, d yu expect the values f wz () measured in this experiment t increase linearly with z? Justify yur answer. 6- A Gaussian beam has a peak intensity f r 2w ( V / m ), calculate its intensity at

22 22 EXPERIMENT 3 LIGHT POLARIZATION AND FOCAL LENGTH OF THIN LENSES OBJECTIVES: This experiment cnsists f tw separate parts, parts A and B. Part A has tw bjectives. The first bjective is t determine whether r nt a given beam f light is plarized. The secnd bjective is t experimentally verify the angular dependence f the transmitted ptical pwer when a beam f light passes thrugh a plarizer/analyzer pair. The bjective f part B is t experimentally verify the thin lens frmula by experimentally finding the fcal lens f a given thin lens by imaging. PART A: EQUIPMENT REQUIRED 1. Optical pwer meter: INFOS, Mdel # M HeNe laser: Cherent, Mdel # ¼ m ptical bench. 4. Hlder. 5. Labratry Jack. 6. Tw linear plarizers. INTRODUCTION: A linear plarizer is characterized by a pass axis with a blck axis at 90 degree with respect t the pass axis as shwn in Figure 1. Light Plarizer Pass Axis 90 Blck Axis Figure 1: A linear Plarizer with Pass Axis at 90-Degree with Respect t the Blck Axis. When light beam pass thrugh an ideal linear plarizer, the electric field vectre cmpnent parallel t the pass axis passes thrugh the plarizer withut lss. Hwever, the beam s electric field vectr cmpnent parallel t the blck axis des

23 23 nt pass at all thrugh the ideal linear plarizer. In this experiment we use a linear plarizer and assume that it apprximates the peratin f the ideal linear plarizer. Nw cnsider a linearly plarized light beam prpagating in air in the z - directin, with an electric field given by: E E a E e a E e jkz jkz i x x y y (1) Where E x and E y are the field amplitudes in the x and y directins, respectively and k is the free space phase cnstant. This beam will be used as input t the plarizer. Let us situate the plarizer in the x y plane (nrmal t the beam s directin f prpagatin z ) and rtate the plarizer such that its pass axis becmes parallel t the y - axis (see Figure 2). The Blck axis is nt shwn, because we knw it is always at 90 with respect t the pass axis. As shwn in Figure 2 (a), the input electric field vectr makes an angle with respect t the pass axis f the plarizer. The utput electric field vectr is shwn in Figure 2(b), after the beam passes thrugh the linear plarizer. It is clear that nly the y - cmpnent f the field vectr passes thrugh the plarizer, while the x - cmpnent is blcked, resulting in the utput electric field: E a E e jk z (2) y y This represents a beam linearly plarized in the y - directin. Pass Axis Pass Axis E i E (a) (b) Figure 2: Input and Output Electric Field Vectrs when a Linearly Plarized Light Beam Passes Thrugh a Linear Plarizer. The Input Electric Field Vectr is at Angle with Respect t the Pass Axis f the Plarizer. Fr the case cnsidered abve, the amplitude f the input electric field and utput 2 2 electric fields are respectively given by: E E E and E Ey which are related by the simple relatinship: i x y

24 24 E E cs (3) i Since the electrmagnetic pwer is prprtinal t the square f the electric field, we can easily predict the rati f the utput t input pwer: E 2 P 2 ( ) cs (4) E P i i Equatin (4) is valid nly fr the ideal linear plarizer shwn in Figures 1 and 2. Hwever, we can still use equatin (4) fr practical linear plarizers prvided we interpret P i t be the maximum utput pwer P,max P( 0) that can pass thrugh the plarizer (i.e. when 0). Thus fr a practical linear plarizer, we have: P ( ) P,max 2 PN cs (5) Where P N is the nrmalized utput pwer. In this part f the experiment (part A), we will perfrm ptical pwer measurements t verify the validity f equatin (5). Frm the pint f view f plarizatin, there are tw types f lasers. Either they are linearly plarized r randmly plarized. A linearly plarized laser means that the electric field vectr f the laser has a specific and fixed directin. In the case f a randmly plarized laser, the electric field vectr cntinually and rapidly changes directin in a randm manner. Sunlight is anther example f a randmly plarized light. In this experiment, we will find ut whether the HeNe laser surce in the EE 420 labratry is linearly r randmly plarized. During this part f the experiment, it is imprtant t distinguish between the tw angles and p. The angle = angle between the input electric field vectr and the pass axis f the plarizer, exactly as defined in Figure 2 (a). Hwever, p simply represents the reading f the plarizer dial. The plarizer dial used in the EE 420 labratry has the fllwing range p PROCEDURE: [IMPRTANT: FOR THIS PART OF THE EXPERIMENT, THE LASER MUST BE TURNED ON FOR AT LEAST ONE HOUR BRFORE RELIABLE MEASUREMENTS CAN BE TAKEN]. 1- Place a plarizer between the HeNe laser surce and the ptical pwer meter as shwn in Figure 3. Adjust the plarizer rientatin s that the beam passes nrmal t the plarizer and as clse as pssible t the center f the plarizer.

25 25 Plarizer Aperture HeNe Laser Optical Pwer Meter Figure 3: Setup Used fr Examining the Plarizatin f the HeNe Laser Surce Using a Linear Plarizer Placed Between the Laser and an Optical Pwer Meter. 2- Turn n the pwer meter and select the dbm scale and 0.85 m. 3- Insure that an apprpriate aperture is used at the input end f the pwer meter t minimize the effect f the ambient light. The pwer meter cver can be used an aperture. 4- Set the plarizer angle p t zer degrees. 5- Adjust the psitin f the pwer meter fr maximum meter reading. 6- Recrd the ptical pwer in dbm in the secnd clumn f table Set the plarizer dial t 10 p and recrd the dbm pwer in table Repeat step 7 fr 20, 30,...,90. p 9- Cvert the dbm pwer t mw and recrd the values in the third clumn f table Calculate the crrespnding nrmalized pwer P N and recrd its value in clumn 4 f table Plt a graph that shws the variatin f P N with p. At this pint the distinctin between p and is nt imprtant. 12- Using this graph, cmment n the variatin f P N with p. Is the HeNe laser linearly plarized r randmly plarized? 13- Place anther plarizer between the HeNe laser surce and the ptical pwer meter as shwn in Figure 4. The plarizer n the right-hand-side is nw called analyzer, because it is used t analyze the linearly plarized light that emerges frm the plarizer. 14- Insure that the light beam passes as clse t the center f bth the plarizer and analyzer. 15- Set the analyzer angle p t Rtate the dial f the plarizer until the pwer received is minimum. The reading f the plarizer angle is nt imprtant, s we d nt need t recrd it. Since the pwer received by the meter is minimum, we are nw sure that the linearly plarized light makes an angle 90 with respect t the analyzer pass axis. 17- Recrd the dbm meter reading in the third clumn f table 2 (use the bttm rw, which crrespnds t 90 p ). 18- Rtate the analyzer dial t 80 p and recrd the meter reading in the third clumn f table 2. [D nt change the plarizer angle].

26 26 p (Degrees) 0 P (dbm) P (mw) P N (Unit-less) Table 1: Measured Optical Pwer Variatin with the Plarizer Angle Single Plarizer is Used. p when a 19- Repeat step 18, fr p 70, 60, 50,., 10, 0, 350, 340, 330,., 270 and 280 degrees. [Nte that the angle 350 is equivalent t 10, 340 is p equivalent t 20 and s n]. 20- Cnvert the meter reading recrded in clumn 3 t mw and recrd the values in clumn 4 f table Divide by the maximum pwer t cnvert the data f clumn 4 t nrmalized pwer and recrd the resulting nrmalized pwer P N in clumn 5 f table Plt P N versus Plt equatin (5) [ PN cs ] in the same figure. 24- Calculate the relative errr between the experimental and theretical values f P N. 25- Discuss and cmment n the results. Write sme cnclusins. p

27 27 Plarizer Analyzer HeNe Laser Optical Pwer Meter Linearly-Plarized Light Figure 4: Plarizer/Analyzer Pair Placed between the HeNe Laser Surce and the Optical Pwer Meter. The Laser Light is Linearly Plarized by the Plarizer Befre it Passes Thrugh the Analyzer. p (Degrees) (Degrees) P (dbm) P (mw) P N (Unit-less) Table 2: Measured Optical Pwer with Arrangement. fr the Plarizer/Analyzer Pair

28 28 PART B: EQUIPMENT REQUIRED 1- White light surce. 2-1 m ptical bench. 3- White Screen. 4- Lens Hlder. 5- Lens (fcal length f 10cm ). 6- Lens (unknwn fcal length). 7- Object with hlder. INTRODUCTION: In this part f experiment we will use the well-knwn thin lens frmula: (6) f d d i t experimentally measure the fcal length f a thin lens, where f, d and d i are respectively the fcal length f the lens, the bject distance and the image distance (see Figure 5 in the prcedure sectin). After frming an image, we will measure the distances d and d i, frm which the fcal length f the lens can easily be determined, using equatin (6). We will d tw separate measurements. The first measurement will be dne using a lens having a fcal length f 10 cm. The measured value f f will then be cmpared with the knwn value. In the secnd measurement, the fcal length f the thin length is unknwn and we are expected t determine it experimentally. In ding this experiment, it is helpful t recall that a real image can be frmed nly if d f. PROCEDURE 1- Insert a lens f fcal length f 10cm between the bject and the screen, as shwn in Figure Adjust the intensity f the white light surce in rder t reduce glare. 3- Set the bject distance t d 12cm. 4- Change the distance d i until a sharp image is frmed n the screen. 5- Recrd the value f d i in table Calculate the value f the fcal length using equatin (6) and recrd it in table 3. Cmment n hw clse this value is t f 10cm. Cmment n the surces f errr if any. Discuss the results and write sme cnclusins. 7- Using the abve prcedure, determine the fcal length f the lens supplied t yu by the labratry instructr and recrd the experimental value in table 3. Write a cnclusin.

29 29 Bicnvex Thin Lens Screen White Light Surce Object Image d d i Figure 5: Image Frmatin Using a Thin Bicnvex Lens. Lens Fcal Length d (cm) 10 cm 12 Unknwn d i (cm) f experimental (cm) Table 3: Imaging Data fr the Knwn and Unknwn Lenses. QUESTIONS: 1- Fr the plarizer/analyzer arrangement, calculate (theretically) the angle such that the transmitted pwer is 50% f the maximum pwer. 2- Fr the plarizer/analyzer arrangement, calculate (theretically) the angle such that the transmitted pwer is 6 db belw the maximum pwer. 3- Fr the plarizer/analyzer arrangement, calculate (theretically) the rati f the transmitted electric field ( fr 30 ) t the maximum pssible electric field. 4- Briefly suggest a simple methd that can be dne t shw that sunlight is nt linearly plarized. Yu can use nly ne plarizer. 5- A thin lens having a knwn fcal length f 5cm is used fr the frmatin f a real image n a screen. If yu want t frm an image at 45 cm frm the lens, hw far frm the lens must the bject be placed? What is the resulting magnificatin?

30 30 EXPERIMENT 4 DETERMINATION OF THE ACCEPTANCE ANGLE AND NUMERICAL APERTURE OF OPTICAL FIBERS OBJECTIVES: The bjective f this experiment is t measure the acceptance angle in air (frm which the numerical aperture can be determined) f tw types f multimde graded index (GI) ptical fibers. The axis f the ptical fiber will be rtated with respect t an incident laser beam fr this purpse. EQUIPMENT REQUIRED 1- Optical pwer meter: INFOS, Mdel # M HeNe laser: Cherent, Mdel # Optical bench (¼ m). 4- Hrizntal and vertical stages (Used t carry and align the HeNe laser). 5- Labratry jack. 6- Rtatinal stage with aluminum adapter plate. 7- Apprximately 2m lng, 50 m graded-index fiber (Orange Clr). NA = Apprximately 5m lng, 62.5 m graded-index fiber (Gray Clr). NA = Optical fiber hlder. 10- Meter stick. PRELAB ASSIGNMENT Read the intrductin t this experiment, befre yu attend the labratry. INTRODUCTION: Cnsider a step-index (SI) ptical fiber with a cre and cladding refractive indices n 1 and n 2, respectively. Als assume that the SI fiber terminates at a medium f refractive index n, as shwn in Figure 1. n 2 n 1 Cladding Cre Fiber s Input Plane Cre Axis n Terminating Medium Figure 1: The Acceptance Angle f an SI Optical Fiber. The acceptance angle and numerical aperture (NA) f the SI fiber are given by (see Figure 1):

31 31 NA n sin n n (1) This well-knwn relatin hwever, des nt apply t graded-index (GI) ptical fibers, because the cre refractive f GI fibers decreases with the distance r frm the fiber cre axis. Fr a GI fiber, with an nn-unifrm (graded) cre refractive index n 2 () r and unifrm cladding index n 2, equatin (1) is mdified t: NA n sin n ( r) n (2) Which means that fr GI fibers, bth NA and are decreasing functins f r. The refractive index nr () has a maximum value f n 1 at the cre axis ( r 0 ) and the minimum value f n 2 at the cre-cladding bundary ( r a). Thus the cre refractive index has the fllwing range: n n() r n (3) 1 2 Thus the numerical aperture and the acceptance angle have the fllwing ranges: 0 NA n n (4) sin ( n1 n2 / n ) (5) The definitin f the acceptance angle [given either by equatins (1) fr SI fibers r (2) fr GI fibers] is based n ray thery, which is an apprximate thery. Equatins (1) and (2) als d nt tell us hw t directly measure the acceptance angle experimentally. Hw can we then measure the acceptance angle f a given fiber? A pssible direct methd is illustrated in Figure 2. A laser beam is cupled t an ptical fiber an angle with respect t the cre axis f the fiber. Pwer Meter Input Plane Fiber n Cre Axis Laser Beam Figure 2: Methd Used fr Measuring the Acceptance Angle f an Optical Fiber. When 0, maximum pwer is cupled the fiber. When increases beynd zer, the cupled pwer start t decrease. The acceptance angle is reached when the pwer is reduced by 13 db with respect t the maximum.

32 32 The experimental setup is shwn in Figure 3. A 50 m multimde GI fiber will be used in this experiment. As shwn in the figure, the fiber s tip needs t be placed as clse as pssible t the center f rtatin f the rtatinal stage. If the fiber s tip is misplaced, the experimental measurements will be pr, as will be explained later. The fiber hlder and the stainless adapter plate are nt shwn in Figure 3. Rtatinal Stage Pwer Meter GI Fiber Laser Beam Fiber s Tip Placed at the Center f Rtatin (COR) and at the Beam s Center HeNe Laser Figure 3: Basic Experimental Setup Used fr Measurement f the Acceptance Angle. In this experiment, it is imprtant t make sure f the fllwing: 1) The fiber s tip shuld be in the exact center f the laser beam (see Figure 3). 2) The fiber s tip shuld be lcated exactly at the center f rtatin f the rtatinal stage. If this is nt dne accurately, then when the stage is rtated, the fiber s tip will mve away frm the beam s center, resulting in errneus results, because the laser intensity prfile is nn-unifrm. By keeping a sufficiently lng separatin between the fiber s tip and the laser beam, results in laser beam expansin, which tends t reduce the errr due t dislcating the fiber s tip. 3) The laser beam must be prperly aligned. The means that the laser beam s and the fiber s axes must cincide with each ther. In this experiment, we will measure the acceptance angle f tw GI ptical fibers, which bth f which have a variable the acceptance angle in the radial directin r. The experimental methd explained abve can be used t estimate the average acceptance angle f a GI fiber. It cannt be used t measure () r, the variatin f the acceptance angle as a functin f r. PROCEDURE: [IMPORTANT: INSURE THAT BOTH ENDS OF THE TWO FIBERS HAVE BEEN RECENTLY AND PROPERLY CLEAVED, OTHERWISE LARGE EXPERIMENATL ERRORS MAY OCCUR]. 1- Turn the laser n and place its utput end apprximately 1m frm the rtatinal stage. 2- Align the laser. Fr laser alignment use the fllwing simple prcedure:

33 33 - Establish a cnvenient reference straight line axis n the ptical table. - Mve the meter stick alng the reference axis and bring it clse t the laser beam utput end. Mark the psitin where the laser beam center hits the meter stick. - Mve the stick away frm the laser and again mark the psitin where the laser beam center hits the stick. [When the laser is aligned the laser shuld hit the stick in the same psitin]. - If necessary rtate the laser in the plane parallel t the ptical table and in the plane nrmal t the ptical table, until the laser beam hits the meter stick at the same psitin, regardless f its psitin alng the reference axis. 3- Cnnect the 50 m ptical fiber (range clr) t the ptical pwer meter. Turn the pwer meter n and set it t the dbm scale and 0.85 m. 4- Place the fiber int the fiber hlder and insure that the fiber s tip is as clse as pssible t the COR f the rtatinal stage (white dt) befre yu tighten the screws the fiber hlder t the adapter plate. Take extra care t d this. It helps if yu lk frm abve. 5- Release the stpper f the rtatinal stage. Then rtate the stage s that the fiber s axis is apprximately parallel t the beam (r parallel t the reference axis). 6- Mve the hrizntal and vertical stages until the laser hits the fiber s tip. 7- Adjust the hrizntal and vertical stages fr maximum meter reading in rder t insure that fiber s tip is lcated exactly at the center f the laser beam. 8- T insure that the fiber s tip is lcated at the center f rtatin, rtate the stage clckwise and cunterclckwise t and check if the fiber s tip stays at the beam s center regardless f the angle f rtatin. 9- Adjust the angle f rtatin fr maximum meter reading. Nw, this means that 0. Recrd the meter reading in at the bttm f clumn 2 f table Turn the rtatinal stage clckwise using a step f 2. Recrd the meter s reading in the secnd clumn f table Rtate the stage back t the psitin f maximum pwer. Then repeat step 10 using cunterclckwise rtatin with a step f 2. Recrd the values in the frth clumn f table Cnvert the meter readings t mw and then calculate the nrmalized pwer P N and recrd the values in table Plt a graph shwing P N versus. 14- Cmment n the resulting graph including symmetry. 15- As discussed in the intrductin, the acceptance angle is reached when the received pwer is 13 db belw the maximum. Thus, fr the nrmalized pwer P, the acceptance angle crrespnds t PN 0.05, since by definitin, the maximum value f P is unity. Using the same graph, estimate the values f the acceptance N angle and, which crrespnd t psitive and negative angles, respectively. Then find the final estimate f the acceptance angle, using ( ) / Use the result btained in the previus step t estimate the numerical aperture f the fiber. Cmpare the resulting value with the fiber s manufacturer s data. 17- Repeat steps 3-16 fr the 62.5 m fiber (Gray Clr). Recrd the results in tables 3 and 4. N

34 Cmpare the acceptance angles and the numerical apertures f the tw types f fibers. Discuss the experimental results; write apprpriate cmments and sme cnclusins. (Degrees) P (dbm) (Degrees) P (dbm) Table 1: Variatin f the Received Optical Pwer in dbm Versus Angle fr the 50 m GI Optical Fiber. (Degrees) P (mw) P N (Degrees) P (mw) P N

35 Table 2: Variatin f the Nrmalized Optical Pwer versus Angle fr the 50 m GI Optical Fiber. (Degrees) P (dbm) (Degrees) P (dbm)

36 Table 3: Variatin f the Received Optical Pwer in dbm Versus Angle fr the 62.5 m GI Optical Fiber. (Degrees) P (mw) P N (Degrees) P (mw) P N Table 4: Variatin f the Nrmalized Optical Pwer versus Angle fr the 62.5 m GI Optical Fiber.

37 37 QUESTIONS: 1- Using the experimental data fr the 50 m GI ptical fiber, find the angle at which the pwer drps t 20 db belw the maximum. Use the average f the psitive and negative angles t find the answer. 2- Suppse we had a unifrm laser beam, instead f the nn-unifrm laser beam used in this experiment. Des this cmplicate r simplify the experimental setup? Explain. 3- Given an ptical fiber with NA Calculate the acceptance angle f the fiber when it is terminated in water ( nwater 1.33 ).

38 38 EXPERIMENT 5 LIGHT COUPLING TO MULTIMODE GRADED INDEX FIBERS OBJECTIVES: The bjective f this experiment is t cuple HeNe laser light t a multimde grade index fiber. Bth direct and lens cupling will be dne. The cupling efficiency is t be measured in each case and the experimental results are t be cmpared with theretical predictin. EQUIPMENT REQUIRED 1- Optical pwer meter: INFOS, Mdel # M HeNe laser: Cherent, Mdel # n a hrizntal and translatin stage, all assembled n a ¼ m bench. 3- Mells Grit hrizntal and vertical translatin stages, (0.01 mm reslutin) with a fiber hlder assembled n a Mells Grit bench base. 4- GI 50 m ptical fiber [Orange]. Abut 2 meter lng. 5- Thin lens ( f 5cm ). 6- Lens hlder. 7- Translatin stage assembled n ¼ m bench: Ealing Electr-Optics. PRELAB ASSIGNMENT: Read the intrductin t this experiment befre attending the labratry. INTRODUCTION: In this experiment HeNe laser light will be first cupled directly t a 50 m GI ptical fiber. This will be fllwed by indirect cupling by fcusing the laser light int the GI fiber using a thin lens. Let us turn ur attentin first t the direct cupling f a laser beam t a highly multimde GI fiber f cre radius a, as shwn in Figure 1. Electrmagnetic thery predicts that the cupling efficiency in this case is given by the simple relatinship: 2 2 ( a / w ) fr a w (1) Where w is the laser spt size (assumed t be Gaussian) and a is the cre radius f the fiber. The crrespnding db lss in this case is given by: db a w a w 2 lss 10lg 10lg( / ) 20lg( / ) (2) In this experiment we will verify the theretical predictin f equatin (2), by cupling a laser beam f knwn pwer and measure the resulting db lss in the case f direct laser/ fiber cupling. This methd tends t cuple part f the light pwer int

39 39 the cladding mdes f the fiber. Cladding mdes are very lssy mdes, which decay after few meters r few tens f meters depending n the type f fiber and methd f excitatin. The fiber used in this experiment is relatively shrt, s there is a strng pssibility that the measured fiber transmissin efficiency, in the case f direct cupling, will be smewhat higher than the predictin f equatin (1). This als means that the experimental db lss may be smewhat smaller than the predictin f equatin (2). We can use the theretical and experimental cupling efficiencies t rughly estimate the ptical pwer cupled t the cladding mdes (and ultimately reaching the pwer meter) in the case f direct cupling. Gaussian Laser Beam 2w 2a Multimde GI fiber HeNe Laser Surce z Figure 1: Direct Cupling f the HeNe Laser Surce t a Multimde GI Fiber f Cre Radius a. LASER/FIBER LENS COUPLING: Based n equatin (1), when the laser spt size w is reduced, the cupling efficiency increases. One way t reduce w is by fcusing the laser beam using a lens, befre the light is cupled int the fiber input end, as shwn in Figure 2. f 2w Fiber ' 2w Figure 2: Laser/Fiber Lens Cupling. In thery, we can btain a maximum efficiency f 1 if we reduce the laser spt size frm w t ' w and match it t the radius a 25 m f the GI fiber ' (i.e. w a 25m ). T successfully achieve this task, we need first t design the

40 40 lens cupling system. The Gaussian spt size given by the well-knwn relatinship: ' w at the fcal pint (see Figure 2) is ' w f (3) w Frm experiment 2, we have measured the minimum spt size w (at z 0) f the HeNe laser and fund it t be w 0.28 mm. Using this spt size, alng with equatin (3), we can find the fcal length f the lens required t fcus this spt size int ' w 25m, as fllws: ' f ww/ (2510 m) ( m) /( m) 3.47 cm The nearest available lens has a fcal length f 5cm. Thus, we will use this lens in ' this experiment. Hwever, if we use this lens, the fcused spt size w will be larger ' than the target spt size w 25m (see equatin 3). What shuld be the value f w ' that can be fcused int w 25m when a lens f fcal length f 5cm is used? Using equatin (3), the answer is w 0.4 mm. This spt size can be btained if we increase the distance z frm the laser utput end t the lens, since the Gaussian beam emitted by the laser expands with z. Previus experimental results shw that at z 37cm, the spt size is w 0.4 mm (see experiment 2). This methd f excitatin tends nt t excite the cladding mdes, prvided the beam is prperly fcused directly int the fiber s cre and the spt size is reduced t match the cre radius. PROCEDURE: HENE LASER TOTAL POWER MEASUREMENT: 1- Turn n the HeNe laser and wait fr it t stabilize. 2- Remve the cver f the ptical pwer meter. 3- Measure the ttal pwer emitted by the laser surce. Because the sensr f the pwer meter has a smaller area than the laser beam, yu need t first partially fcus the laser light int the light sensitive area f the pwer meter. D nt verly fcus the light int the light sensitive area f the meter, because this causes sensr saturatin and leads t meter readings that are less than the actual pwer. T measure the ttal pwer emitted by the laser, use the fllwing prcedure (Refer t Figure 3): - Place the lens at abut 20 cm frm the laser utput end. - Place the light sensitive area f the meter at abut L 9cm frm the lens. [Insure that the laser beam size is slightly smaller than the dimensin f the light sensitive area. The light sensitive area must capture all the laser light]. - Turn the pwer meter n and set it t dbm and 0.85 m and recrd the meter s reading in table 1.

41 41 - Repeat the abve fr L 8,7, 6and 4cm. Recrd the values in table 1 4- Take the maximum f the five readings in table 1 and call it P l and recrd its value in table 1. Als recrd the same value f P l in table 2. f 5cm Plane f the Light Sensitive Area Laser Beam Optical Pwer Meter L Figure 3: Arrangement Used t Measure The Ttal Pwer f the HeNe Laser Surce. L 9cm L 8cm L 7cm L 6cm L 4cm Maximum ( P l ) Ttal Laser Pwer (dbm) Table 1: Ttal Laser Pwer Measurement. LASER/FIBER DIRECT COUPLING: [IMPORTANT: INSURE THAT THE FIBER HAS BEEN RECENTLY CLEAVED AND CLEANED BEFORE YOU BEGIN. IF THE FIBER IS NOT PROPERLY CLEAVED, EXTREMELY LARGE EXPERIMENTAL ERRORS WILL RESULT]. 1- Cnnect the fiber t the fiber s hlder n the hrizntal/vertical translatin stage (Stage XY) and adjust the distance between the laser t the fiber s tip t z 37cm (see Figure 4). 2- Cnnect the ther end f the fiber t the pwer meter and insure it is set t the same previus setting. 3- Mve stage XY in bth the hrizntal and vertical directins until yu btain maximum meter reading (as yu did in experiment 2). The fiber nw shuld be