Department of Electrical and Computer Systems Engineering

Transcription

1 Departent of Electrical and Coputer Systes Engineering Technical Report MECSE An Optical Fiber Dispersion Measureent Technique and Syste LN Binh and Itzhak Shraga

2 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga An Optical Fiber Dispersion Measureent Technique and Syste Le Nguyen Binh and Itzhak Shraga Departent of Electrical & Coputer Systes Engineering, Monash University, Clayton Capus, Victoria 368, AUSTRALIA Abstract We present a ethod of easureent of dispersion of guided optical ediu, the optical fibre using icrowave photonic techniques. Experiental set-up and theoretical developent of the easureent systes are described. Analytical results are copared with those obtained experientally for a length of 9.8 k standard single ode fibre. On leave fro Israel. The experiental work was conducted in Binh and Shraga Optical fibre dispersion easureent

3 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga Table of Contents Introduction...3 The external odulation and dispersion...4. The Mach-Zehnder odulator...4. The dispersion paraeter easureent Experiental Setup and Results Experiental Setup Measureent of the Mach-Zehnder Modulator Transfer Function Measureent of Dispersion Paraeter...6 REFERENCES...9 Appendix B. Theristor s Coefficients calculation for Fujitsu FLD50FCJ Laser... Appendix C: Measureent results for one SM fiber spool (9.8k) and two fiber spools (39.6k)... List of Figures Figure Typical electrode configuration for a waveguide phase odulator on insulating crystals as LiNbO 3 (a) single electrode driven odulator structure with On and OFF states (b) dual electrode type....5 Figure Typical behavior of P as a function of ψk for α=... Figure 3 Scheatic diagra of the experiental setup...4 Figure 4 Measured transission function and theoretical cos fit...6 Figure 5 Experiental results (error bars) and calculated results for fiber spool length L F =9.8k...8 Figure 6 Experiental results (error bars) and calculated results for fiber spool length L F =39.6k...9 List of Tables Table Measured paraeters...5 Table. Experiental results with one 9.8k SM fiber spool Binh and Shraga Optical fibre dispersion easureent

4 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga Introduction Modern optical counication systes deand higher and higher bandwidth and bitrates. The state of the art Counication systes use already bit-rates of up to 40 Gbit/sec per channel and DWDM systes with up to 76 channels working at this bitrate have been deonstrated []. Coercial optical counication systes use the already installed fiber-optic cables including standard Single Mode Fibers (SSMF) and.55µ Distributed Feedback (DFB) Lasers, available with ultiple wavelengths at 0.8n spacing (00GHz) or uch narrower. Usually, the optical carrier is odulated by the electrical signal using one of the two ost coon odulation techniques: direct odulation of the DFB laser or use of an external odulator. Direct odulation of the laser is the siplest approach. However when the laser ust be biased close to the threshold current point and the digital signal is superiposed in order to switch the laser optical output on and off for the and the 0 digital states. This approach introduces three separate liitations on the bit-rate: frequency chirp of the optical carrier, relaxation oscillations of the laser optical output power and bandwidth liitation due to parasitic inductance and capacitance of the laser packaging []. The relaxation oscillations of the laser and packaging parasitic inductance and capacitance liit the practical odulation frequency to 0GHz axiu, although, special designs allowed odulation frequencies up to 5GHz to be achieved. The frequency chirp liits the perforance of the optical counication systes by reducing the effective bandwidth of the fiber (or by causing a pulse broadening), especially when.55µ laser is used in conjunction with standard SM fibers. In these systes, the bit-rate*distance is liited to about 00Gbit*k/sec []. Long-haul transission of high bit-rates optical signals is ostly based on external odulation technique. The DFB laser is biased at a well-controlled DC bias and teperature, producing a very stable optical power output, both in aplitude and wavelength. The laser s optical output is passed through a separate device that odulates the optical carrier intensity the external odulator. In this way, the unwanted effects of the direct odulation of the laser are avoided and the quality of the optical signal transitted enables long-haul transission over standard SM fibers. The only liitations of the syste s bit-rate are iposed then by the attenuation and 005 Binh and Shraga Optical fibre dispersion easureent 3

5 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga dispersion of the fiber, since the standard SM fibers have significant dispersion paraeter (~8ps/n*k) at the.55µ laser wavelength. Copensation of the dispersion (using additional negative dispersion fibers) and calculation of the achievable bit-rate of optical counication systes require an accurate easureent of the fiber s dispersion paraeter. There are few types of external odulators described in the literature [3],[5]: loss odulator, directional coupler odulator, total internal reflection odulator and Mach-Zehnder odulator, the last one being one of the ost popular external odulators used. This report suarizes the theoretical background, description and results of an experient conducted in the Optical Counications and Applied Photonics Laboratory. In this experient we try to evaluate the dispersion paraeter of a standard SM fiber using an externally odulated DFB laser with λ=.55µ by a LiNbO 3 Mach-Zehnder external odulator. The external odulation and dispersion This section presents soe background inforation and theoretical approaches regarding the Mach-Zehnder interferoetric odulator behaviour and the optical fiber dispersion paraeter easureent technique.. The Mach-Zehnder odulator The Mach-Zehnder interferoetric odulator has been extensively investigated and reported in the literature since 980 s as a potential electro-optic odulator for high digital bit-rate and RF transission over optical fiber counication systes [3]-[7]. There are different types of intensity odulators described in the literature based on the linear electro-optic (Pockel) effect, which provides a change in the optical waveguide refractive index proportional to the applied electric field. As a result, a phase change occurs for the incident optical field polarized in the direction of the electrical applied field. One of the aterials ostly used for electro-optic odulators is the LiNbO 3 crystal with Ti:diffused waveguides. A waveguide phase odulator appropriate to Ti:LiNbO 3 is shown in Figure. 005 Binh and Shraga Optical fibre dispersion easureent 4

6 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga (a) (b) Figure Typical electrode configuration for a waveguide phase odulator on insulating crystals as LiNbO 3 (a) single electrode driven odulator structure with On and OFF states (b) dual electrode type. The configuration of Figure (a) is used to induce a phase change in a TE ode for X-cut Y propagating (or Y-cut X propagating) crystals while Figure (b) shows the electrode configuration for a Z-cut orientation providing axiu phase change for the TM ode. The odulator used in this work is based on a Z-cut Ti:LiNbO 3 crystal (see appendix A, for detailed data sheet), with a coplanar wave-guide structure (CPS). The way in which the phase change of the optical field transfors in intensity odulation depends upon the device geoetrical configuration and one of these configurations is the Mach-Zehnder interferoeter. The odulator shown in Figure b is of an early design, in which both ars were driven by opposite polarity voltage 005 Binh and Shraga Optical fibre dispersion easureent 5

7 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga signals. Although this approach has soe theoretical advantage by achieving a better optical signal quality (zero frequency chirp [5]), at very high frequencies, it is very difficult to atch the ipedance of the electrode to the RF source, for a broadband frequency range. Most of the high frequency odulators are ipleented with only one traveling wave-guide electrode, as shown in b, exciting one ar of the odulator, as is the one used in this work. This electrode is atched to and terinated with the sae characteristic ipedance as the signal source (typically 50Ω) so no standing waves are fored along the interaction region. In this way, a very broadband device can be built [6]. There are soe odulators on the arket with two syetrical traveling wave electrodes, allowing achieving zero chirp or other odulation schees (like Single Side Band) with a very large bandwidth at high frequencies [0]. The physics of operation has been extensively discussed in the literature [3], [5] and will only be briefly reviewed here. The guided-wave interferoeter shown in Figure odulates the light intensity due to the phase difference that is electro-optically induced between the two ars (in the traveling wave-guide electrode configuration, the phase shift is electro-optically affected in one ar only). The input power I o is divided in two halves at the input Y branch (which acts as a 3dB splitter) and travel along the two ars, having (usually) the sae physical and optical length. At the output Y branch the optical fields recobine. If the guided odes are in-phase, they will constructively interfere and excite the lowest order ode of the output waveguide. If they are exactly 80 out of phase, then they recobine to excite the first antisyetric ode, which is cut off and rapidly attenuated. Since the phase shift in the odulator s ars is affected only for the optical field polarized in the sae direction as the exciting electrical field, the Mach-Zehnder odulator is very sensitive to the polarization of the input optical field and, usually, a very stable polarized optical source is required and a Polarization Maintaining Fiber (PMF) should be used between the source and the odulator input port. Assuing an ideal device (no insertion loss), the optical field at the interferoeter output is given by [4]: EI ( jβ E L ) I ( jβl ) ( jβl ) EO = e + e = EI cos( βl )e ( ) 005 Binh and Shraga Optical fibre dispersion easureent 6

8 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga where E O is the output optical field, E I is the input optical field, β and β are the propagation constants in ar and of the interferoeter, L is the ar s length and β = ( β β ) / β = ( β + β ) / ( ) ( 3) The cosine ter in () provides the aplitude odulation while the exponential ter produces the tie dependent phase variation, or chirp. It can be seen fro () that the phase odulation can be copletely copensated if the propagation constants of the two wave-guides (ars) are changing by the sae aount and with opposite signs, using two exciting voltage signals with equal aplitude and opposite polarity. In this way one can achieve (theoretically) a zero-chirp odulator. The output intensity of the light as a function of the input intensity is given by [6], [7]: I I O I = E E O I πv = Acos ( βl) = Acos V M π (4) where A is the optical insertion loss of a practical device and V M is the odulating signal voltage. V π is the voltage required to change the output light intensity I O fro its axiu value to its iniu value and this paraeter is related to the interferoeter constants as follows: V π = λ K L (5) where λ is the optical wave-length (in vacuu) and K is a constant related to geoetrical and crystal paraeters. It is iportant to point out that V π and the phase shift is wave-length dependent so the Mach-Zehnder interferoeter acts as an optical filter as well. Assuing the odulation signal V M is a sinusoidal voltage with angular frequency ω and aplitude V superiposed on a DC voltage V B we get: V M = V B + V sin( ω t) (6) Using (4) we obtain: 005 Binh and Shraga Optical fibre dispersion easureent 7

9 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga I O AI I = = π + cos ( V Vπ B + Vsin( ω t)) = { + Bcos[ Csin( ω t) ] Dsin[ Csin( ω t) ]} (7) where B=cos(πV B /V π ), C=πV /V π, D= sin(πv B /V π ) and we used the trigonoetric relations: ( + cos ) cos θ = θ cos(a + b) = cosa cosb sina sinb (8) Using the relations: sin(xsinθ ) = n= cos( x sinθ ) = J 0 J n ( x ) + ( x ) sin ( n= J [ n ) θ ] n ( x )cos [ nθ ] (9) where J n (x) are the Bessel functions of the first kind, we can rewrite (7) as follows: IO AI I = + BJ + [ ] 0(C ) B Jn(C )cos( nω t ) D Jn (C )sin( n ) ωt (0) n= n= A particular bias voltage point of interest is at V B =V π / also known as the quadrature bias point. At this particular bias voltage, B=0, D= and (0) becoes: IO AI I = n= J n (C )sin( n [ ) ω t] () which eans that only the fundaental frequency of the odulation signal and its odd haronics are present. Further, if V =V π / (00% odulation index) then the first three coponents of the series in () are: J =0.567, J 3 =0.069 and J 5 =0.00 which eans that the 3 rd haronics aplitude is only.% of the fundaental and 5 th haronics content is only 3.9% of it. For 50% odulation index, the 3 rd haronics aplitude is only.7% of the fundaental and 5 th haronics content is only 0.0% of it. The iediate conclusion is that although the transfer function of the odulator is nonlinear (cosine square), the haronics content at the quadrature bias point is low to oderate even at very large odulation indices. 005 Binh and Shraga Optical fibre dispersion easureent 8

10 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga. The dispersion paraeter easureent The technique used in this experient is based on the analytical approach describing the behavior of SMF fibers reported by Hakki [9]. The optical signal odulated by an RF signal, using the Mach-Zehnder external odulator, is launched into the fiber. This signal is attenuated and dispersed by the fiber. The total optical power at the input and the output of the fiber (with length L F ) is easured by a photodetector (I det ) and a spectru analyzer easures the RF signal aplitude (V RF ), detected by the sae detector. Then, using the relation V P = 0log V RF RF ( LF ) I 0log (0 ) I det det ( L F (0 ) ) () we eliinate the attenuation of the fiber. The quantity P will allow us to calculate the Dispersion paraeter of the fiber, using the following theoretical approach. In the following, it is assued a syetrical two ars Mach-Zehnder odulator with both ars biased at the quadrature point and odulated by two RF signals with a phase difference of π radians, as follows: V V V = π π M = V cos( k x ); VM + V cos( k x ) (3) and V +V =V π ; k =ω /v, v=c/n 0 is the propagation velocity (c is the speed of light in vacuu). Inserting these expressions in () leads to: π EO( x) = EI cos 4 r 4 + r j( k0 x φ( x )) ( cos(k x) ) e ; φ( x) = cos(k x) (4) + π The noralized optical field in the forward traveling wave launched fro the Mach- Zehnder odulator into the fiber is given by: E O jk x = = + f ( x ) e A0 AN cos( Nk x ) EI N = E o (5) where: k = β / n = πn / λ; n fiber refraction index o o o o = (6) A 0 = a0 jb0 (7) 005 Binh and Shraga Optical fibre dispersion easureent 9

11 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga A N = a N jb N (8) 0 = J 0( ζ ) + J ( ξ ) a 0 0 = J 0( ξ ) J ( ζ ) b 0 (9) (0) a b N N nπ = cos nπ = sin + nπ sin nπ cos [ J ( ζ ) + J ( ξ )] () N N [ J ( ζ ) J ( ξ )] () N N J N (z) being the Bessel function of the first kind and order N. π( + α ) ζ = 4 π ( α ) ξ = 4 α = r = - r + r V V (3) (4) (5) (6) The paraeter, α, is called the chirp paraeter and it can be observed that for α=0 (r= or V =V ), the frequency chirp φ fro expression (4) above, is equal to zero. At the output of the fiber, the noralized optical field at any tie t, is given by: E ' ' jk = + ox jψn k ' f ( x ) e A0 AN e cos( Nkx ) N = (7) where x ' = x vt (8) λ L Dv ψ = 4π F no (9) and D is the dispersion paraeter in ps/n.k. The power associated with this field is given by: 005 Binh and Shraga Optical fibre dispersion easureent 0

12 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga P ' ' f ( x ) = PN cos( Nk x ) N =0 (30) where P 0 = A0 + A N (3) N = jψk = 0 + P Re A A e A N = * jψk N A * N + e ( N + ) (3) P = A + Re * j4ψk * jψk 4( N + ) [ A0 A e ] + Re AN AN + e (33) N = and the coefficients of higher order can be obtained in a siilar anner. In our experient, we are interested in the power contained in the fundaental odulating frequency signal, P. Therefore, P as defined in () can be evaluated as follows: P ( LF ) P = 0log P ( 0 ) (34) Assuing all the fiber and odulator paraeters (others than D) are known, one can calculate the Dispersion paraeter by easuring P at one single frequency f and use of relation (34). It turns out that expression (34) has a periodic behavior with zeroes (notches) at certain ψk values [0]. Figure shows a plot of P as a function of ψk, for r=0 and α=. Experientally, detecting the frequency of the first notch will be the ost accurate easureent, since only a Spectru analyzer is needed and the accuracy of frequency easureents with this instruent is very good. On any other point of the P graph, both frequency and attenuation need to be easured and attenuation easureents are less accurate because of power fluctuation due to laser and power eter stability and noise. In the experient detailed in the next section, we easure the notch frequency and derive the dispersion paraeter of the fiber. 005 Binh and Shraga Optical fibre dispersion easureent

13 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga Figure Typical behavior of P as a function of ψk for α= 3. Experiental Setup and Results 3. Experiental Setup The full experiental setup is shown in Figure 3. Not all the equipent was needed in all the different phases of the easureents, as will be detailed in the following paragraphs. The different coponents included in this setup are: Laser Diode Unit. This unit consists of a Fujitsu FLD50FCJ theroelectrically cooled DFB laser operating at.55µ ounted on a sall PC board allowing interconnections with the Laser Diode Controller. During the experient, the Laser was operated at 50.0 Ap and.5 C. The output power of the laser at this operational bias point was ~.5W. Laser Diode Controller. This instruent is an ILX Lightwave Model LDC-37 Controller allowing careful control over Laser Diode Current and Teperature. The theristor coefficients required for accurate teperature easureent and control, have been calculated using the Lased Diode data sheet specifications, as detailed in Appendix B. Mach-Zehnder Modulator. This is a Suitoo Ceent SCC T-MZ-.5-0 device with a >8GHz bandwidth, capable to operate at data-rates of up to 0Gbit/sec. 005 Binh and Shraga Optical fibre dispersion easureent

14 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga The device is a LiNbO 3 Z-cut Coplanar Structure (CPS) Intensity Modulator including an ebedded polarizer at the input port (see detailed Data Spec. in Appendix A). The RF+DC bias is supplied to the input electrical (SMA) connector while the output connector is loaded by a 50Ω terination. Single Mode Fiber (SMF) Spool. Two spools, 9.8k of standard SMF each (ade by Corning), have been used during the experient. All the optical interconnections are standard FC/PC connectors and adaptors. RF Signal Generator. The HP 860A Sweep Oscillator with 4 frequency bands covering the range of 0.-GHz was used (for f =00MHz, we used a different signal generator). The axiu output power of the Generator is around +0dB. Bias Tee. This device ade by Sierra Microwave Technology, odel SM470, with a -8GHz bandwidth has been used to cobine the DC Bias and the RF signal for the MZ Modulator. Photo-Detector Head. The AR-D5 Photo-Detector head ade by Antel- Optronics has a bandwidth of DC-0GHz and responsivity of ~5 A/W into 50Ω load. 005 Binh and Shraga Optical fibre dispersion easureent 3

15 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga Laser Diode C ll Laser Diode Ui FC/PC Conne RF Mach- Zehnder M d l FC/PC Conne FC/PC Conne Photo- Detector Controlle Photo- Detector Head /39.6 k SMF Bias Tee DC Power RF Apli RF Signal RF Spectru A l Figure 3 Scheatic diagra of the experiental setup Photo-Detector Controller. This unit, odel PS-05, supplies the bias voltage to the photo-detector, easures and displays the photo-detector current, which is directly proportional to the total optical power detected by the photo-detector. RF Aplifier. This aplifier (by Planar Electronics), odel PE-0-0R38-5- SFF, with 0.-GHz (-3dB bandwidth) and 0dB Gain is used in easureents where the Photo-Detector signal is close to the noise level of the Spectru Analyzer. Spectru Analyzer. The HP Spectru Analyzer, with a 9kHz-GHz bandwidth, has been used to easure the RF signal aplitudes at the input of the MZ Modulator and at the output of the Photo-Detector Head. 3. Measureent of the Mach-Zehnder Modulator Transfer Function As a first step, it is necessary to easure the odulator transfer function, the optical output power as a function of DC Bias). This easureent allows us to define the ain paraeters of the odulator as: insertion loss, V π and extinction ratio. 005 Binh and Shraga Optical fibre dispersion easureent 4

16 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga The setup used for this easureent is actually a sub-setup of full setup described above and shown in Figure 3. All the RF equipent was unnecessary as well as the SSMF spools. The Modulator was supplied with a variable DC voltage provided by the variable Laboratory DC Power Supply. The Photo-Detector was connected to the optical output of the Modulator and its current was recorded. Soe of the results are listed in Table, below and full graphs of the Modulator Transfer Curve as well as the cos approxiation are shown in Figure 4. Measured Paraeter MZ Input Optical Power (Idet) MZ Maxiu Output Power (Idet) MZ Miniu Output Power (Idet) DC Bias, V Max. Out Power DC Bias, V Min. Out Power Value (0±)µA (67±3)µA (.8±0.)µA -3.35V +.V Table Measured paraeters Using the listed above paraeters we can deterine: 67 Insertion Loss ( IL ) = 0 Log = 6. 9dB 0 V π = V V = = 4. BMIN BMAX 45 V 67 Extinction Ratio = 0 Log =. 7dB.8 The sae easured paraeters in Data Specification of this Modulator (as easured by the anufacturer) are: I.L.=3.7dB, V π =4.8V Extinction Ratio=8dB. As we can see soe degradations occurred in both the I.L and Extinction Ratio paraeters. Also, the transission function of the Modulator is shifted, so the axiu transission is achieved at 3.35V, instead of 0V. Therefore, this function can be approxiated by (4), with an additional constant phase shift Φ, as follows: IO AI I πvm = + + = πvm cos Φ cos.4 Vπ 8.9 (35) 005 Binh and Shraga Optical fibre dispersion easureent 5

17 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga Noralized Transission Vbias [V] MZ-Data cos-square approx. Figure 4 Measured transission function and theoretical cos fit As we can see the theoretical curve given in (35) gives a very good approxiation for the easured transission function of the odulator, within the operating region of V BMAX <V M <V BMIN. 3.3 Measureent of Dispersion Paraeter These easureents were done in two steps: first, we used the experiental setup shown in Figure 3, with one spool of SM fiber of 9.8 k. The Mach Zehnder Modulator was biased at the quadrature point, V B =-.35V resulting in I DET = (30±)µA. The total optical output power at the input and the output of the SM fiber spool was easured throughout the entire experient and its optical attenuation fluctuating fro (0±0.35)dB for one part of the experient to (0.8±0.4)dB for the other part of it. These sall changes in attenuation were ostly because during the experient the fiber was connected and disconnected few ties, allowing easureents of the input and output power and signal for different frequency bands of the RF signal generator. The RF signal generator frequency was swept fro 3. GHz to GHz using two bands (3.GHz-6.5GHz) and (8GHz-GHz). The output power was aintained at about +6dB (V =0.63V). The RF signal aplitude detected by the Photo-Detector Binh and Shraga Optical fibre dispersion easureent

18 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga and aplified by the RF Aplifier, was easured by the Spectru Analyzer, using its Maxiu-Hold function, with and without the SM fiber spool. The two sweeps results were stored in two separate traces and the ratio V RF (L F )/V RF (0) was calculated autoatically (using a atheatical function of the Spectru Analyzer) by subtracting the values in the two traces (the Spectru Analyzer was setup to store signal aplitudes in db). The attenuation results were anually recorded fro the Spectru Analyzer display (there was no other way of downloading the results fro the instruent). Then, taking into account the fiber attenuation, P as defined in () was obtained. The results are detailed in Appendix C. The sae procedure was repeated for a setup including two 9.8k spools of SM fiber connected one after the other, to for a 39.6k SM fiber length. The total optical attenuation of the two spools fluctuated fro (0±0.3)dB for one part of the experient to (.5±0.35)dB for the other part of it, due to the sae reasons as for one spool experient. In order to calculate the Dispersion paraeter for the fiber used in this experient, we need to plot the fiber behavior function, P and atch it with the experiental results. In our experient a single traveling wave electrode Mach-Zehnder odulator is used. To ease the algebra and without altering the end results, we can assue a non phase shifted odulator as one described by the relation (4) above. Following the theoretical approach described in Section 3., we get: π V = = β L βl cos( k x ) 4 (36) Vπ and the optical field at the output of the odulator is: E ( x ) O π V j( k x φ( x )) π V 0 cos(k x ) e ; ( x) = cos φ cos(kx) (37) 4 Vπ 4 Vπ = + EI where V - r V = V = 0.63V ; V = 0 ; r = = 0 ; α = = ; V + r π ζ V = = ; ξ = 0 V π 005 Binh and Shraga Optical fibre dispersion easureent 7

19 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga Since J 0 (0.4448)=0.95 and J 4 (0.4448)=*0-4, in the calculation of P as given by (3), we can neglect ters including the Bessel functions of order 4 and higher. We have calculated results using (35), for the above paraeters and λ=.55µ and n 0 =.47. After few iterations, we found that the best atch for both L F =9.8k and L F =39.6k is obtained at D=0.6ps/n*k. The calculations are shown in Figure 5 and 7 below, copared with the easured results. Figure 5 Experiental results (error bars) and calculated results for fiber spool length L F =9.8k The calculated results for D=0.6ps/(n*k) and L F =9.8k (see Figure 5) show a notch ( P=0) at f =(0.75±0.05)GHz (the f steps in calculation have been chosen at 0.05GHz). There is a good agreeent between the calculations and the experiental results and the iniu P is easured at (0.78±0.067)GHz (see easureent results in Appendix C). The calculated results for D=0.6ps/(n*k) and L F =39.6k (see Figure 6) show a notch ( P=0) at f =(7.55±0.05)GHz. There is a good agreeent between the calculations and the experiental results but, unfortunately, the notch could not be detected in the experient, since the RF Generator we used did not covered the 005 Binh and Shraga Optical fibre dispersion easureent 8

20 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga frequency band of 6.5GHz-8GHz. An approxiate value for this frequency can be predicted assuing a linear dependence of this value with ψk. Using this approxiation, f -notch@39.8k =f -notch@9.8k * (9.8/39.6)=7.63GHz. Figure 6 Experiental results (error bars) and calculated results for fiber spool length L F =39.6k In conclusion, this setup allows easuring with good accuracy (less than %) the frequency of the notch in P and with soe quite siple calculation the Dispersion paraeter of the fiber can be found. Moreover, for a fixed fiber length, one can calculate the notch frequency for few Dispersion paraeter values and draw a graph. Then the easured notch frequency can be placed on the graph and find iediately the corresponding Dispersion paraeter value. REFERENCES [] Farbert, G. Mohs, S. Spalter, J. P. Elbers, A. Schopflin, E. Gottwald, C. Scheerer and C. Glingener, 7 Tbits/s (76X40 Gbit/s) bi-directional interleaved transission with 50Ghz channel spacing, in Proc. ECOC, Munchen, Gerany, 000, PD.3, pp Binh and Shraga Optical fibre dispersion easureent 9

21 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga [] G. P. Agrawal, Fiber-Optic Counication Systes, ch , J. Wiley & Sons, Sec. Ed. ISBN , 997. [3] R. C. Alferness, Waveguide Electrooptic Modulators, IEEE Trans. Microwave Theory Tech., Vol. MTT-30, No. 8, Aug. 98. [4] E. L. Wooten & al. A review of Lithiu Niobate Modulators for Fiber-Optic Counications Systes, IEEE J. Selected Topics in Quantu Elect., Vol. 6, No., Jan/Feb 000, pp [5] F. Koyaa and K. Iga, Frequency chirping in external odulators, J. Lightwave Technology, Vol. 6, No., Jan. 988, pp [6] K. Kawano, T. Kitoh, H. Juoni, T. Nozawa and M. Yanagibashi, New Traveling-Wave Electrode Mach-Zehnder Optical odulator with 0GHz Bandwidth and 4.7V driving voltage at.5µ Wavelength, Electron. Lett. Vol. 5, No. 0, Sept. 989, pp [7] R. A. Becker, Broad-Band Guided-Wave Electrooptic Modulators, IEEE J. Quantu Elect., Vol. 0, No.7, July 984. [8] H. Cox, G. E. Betts and L. M. Johnson, An Analytic and Experiental Coparison of Direct and External Modulation in Analog Fiber-Optic Links, IEEE Trans. Microwave Theory Tech., Vol. MTT-38, No. 5, May 990. [9] W. Hakki, Dispersion of Microwave-Modulated Optical Signals, IEEE J. Lightwave Technology, Vol., No. 3, March 993, pp [0] G.H. Sith, D. Novak and Z. Ahed, Technique for Optical SSB Generation to overcoe Dispersion penalties in Fibre-Radio systes, Electronics Letters, Vol. 33 No., Jan Binh and Shraga Optical fibre dispersion easureent 0

22 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga Appendix B. Theristor s Coefficients calculation for Fujitsu FLD50FCJ Laser The ILX Lightwave Model LDC-37 Controller used in the experiental setup, onitors and controls the laser s teperature, using the Steinhart-Hart equation. This equation (approxiated for C=0) gives the relation between the theristor s resistance and the abient teperature, in the following for: T = A + D ln R( T ) (A) where: T- abient (easured) absolute teperature [ K] ; R(T) - Theristor s resistance at teperature T ; A, D Coefficients of the specific theristor. The Fujitsu catalog defines the laser s theristor in a different way, as follows: R ( T ) = R TR exp B T T 0 (A) where: T- abient (easured) absolute teperature [ K] ; T 0 (73+5)=98 K; R TR R(T 0 ), given in the catalog, 0kΩ; B constant, given in the catalog, After soe algebraic anipulations, (A) can be rewritten in the following for: T = T 0 B ln(r TR ) + B lnr(t) (A3) In (A3) one can identify the two constants of the Steinhart-Hart equation given in (A), as follows: A = T 0 B ln(r TR ); D = B Using the constants fro the catalog, we get: A=9.94*0-4 and B=.56* Binh and Shraga Optical fibre dispersion easureent

23 MECSE-4-005: "An Optical Fiber Dispersion Measureent Technique and Syste", LN Binh and Itzhak Shraga Appendix C: Measureent results for one SM fiber spool (9.8k) and two fiber spools (39.6k) f [GHz] 0log[V RF (L F )/V RF (0)] P [db] 0. -(9.0±0.4) +(0.4±0.6) 0. -(9.3±0.4) +(0.±0.6) 0.5 -(9.7±0.4) -(0.3±0.6).0 -(9.8±0.4) -(0.4±0.6).5 -(0.0±0.6) -(0.6±0.8).0 -(9.4±0.3) (0.0±0.5) 3.0 -(8.9±0.4) +(0.5±0.6) 4.0 -(8.9±0.4) +(0.5±0.6) 5.0 -(9.0±0.4) +(0.4±0.6) 6.0 -(7.6±0.3) +(.8±0.5) 6.5 -(6.7±0.5) +(.7±0.7) 8.0 -(6.8±0.5) +(.6±0.7) 9.0 -(6.3±0.4) +(3.±0.6) 0.0 -(5.±0.8) +(4.±.0).0 -(4.7±.3) +(4.7±.5) Table. Experiental results with one 9.8k SM fiber spool 005 Binh and Shraga Optical fibre dispersion easureent