DIFFERENTIAL MODE DELAY (DMD) FOR MULTIMODE FIBER TYPES AND ITS RELATIONSHIP TO MEASURED PERFORMANCE Rick Pimpinella and Al Brunsting Fiber Research Department Panduit Corp., Orland Park, IL 60427 determined by the fiber’s bit error rate (BER). Optical pulses are launched into the MMF core at precisely controlled offsets from the fiber axis and have fast rise and fall times, referred to as restricted launch conditions, compared to overfilled launched conditions using an LED. Emerging pulses from the MMF are measured and saved in the time domain (voltage vs. time) by a fast received and data storage device. We will show that the DMD measurements correlate with MMF length, fiber type, and the corresponding BER. Abstract – With the introduction of Vertical Cavity Surface Emitting Lasers (VCSEL’s) used with multimode fiber (MMF), Differential Mode Delay (DMD), modal interference effects and the influence of connector interfaces are found to reduce the observed bandwidth of multimode fibers (MMF’s). In this study the performance of three example MMF’s is characterized by measuring DMD and is compared to Bit Error Rate (BER) measurements on the same three fibers. Fiber length is also considered. Controlling the spatial locations of the launch pulses, we develop methods aimed to certify the performance of optical fiber for 10Gb/s Ethernet. The source for these measurements was an 850nm VCSEL. 2. PERFORMANCE OF MULTIMODE FIBERS (MMF) 2.1 Refractive index profile The refractive index of the MMF core varies as a function of distance from the core axis (refractive index profile). The specific shape of the refractive index profile in the core has a significant effect on the distribution of the guided optical power in the fiber. But more importantly, the index profile profoundly influences the velocities of the various propagating modes, which results in dispersion. A parabolic index distribution nearly equalizes the group velocities of the propagating modes and fiber manufacturers strive to optimize the specific index distribution to minimize dispersion. ©2005 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications, (060.2270) Fiber characterization, (060.2300) Fiber measurements. 1. INTRODUCTION It is now clear that of the bandwidth of a significant fraction of legacy MMF and laser-based transceivers (such as VCSELs) does not support data rates up to 10-Gb/s and lengths of 300-m. This is due mostly to the design of these fibers which were optimized for lower bit rates and light emitting diode (LED) transmitters. The fiber cores were designed to be overfilled and thereby the LEDs couple optical power into all, or nearly all, of the fiber modes. However, when the small spot from a VCSEL illuminates a fiber core, optical power is coupled into a small fraction of the available modes (several hundred). The actual supported bandwidth of installed legacy MMF, using laserbased transceivers, can be (and usually is) unpredictable. A general refractive-index profile is given by Eq. (1). n(r ) = {n clad ] α 1/ 2 r < rcore r ≥ rcore (1) where ∆ is the relative refractive index difference between core and cladding and given by ∆ = 0.5.(ncore2 - nclad2)/ ncore2. The power law parameter is α. A set of perturbed refractive index profiles, relative to Equation (1), has been proposed to describe MMF that is representative of installed fiber [2]. Even though these perturbations were used for 1300nm and a core diameter of 62.5µm a similar set of perturbations can be generated for 850nm and a core diameter of 50.0µm to describe those corresponding applications. In ref. 1 the effects of perturbed refractive index profiles on DMD-type results were simulated and shown to be significantly dependent on the refractive index profile and amount of offset launch [2]. New laser optimized MMF supports these higher data rates up to 300-m, specified as OM-3 by ISO 11801 and 850-nm Laser Optimized 50 micron (850 LO 50) by TIA. The only accepted way to characterize these high bandwidth MMF’s is with DMD measurements. See, for example, ref. [1]. This paper will describe such DMD measurements and relate the results to measured MMF performance as OFC/NFOEC Conference [ ncore ⋅ 1 − 2 ⋅ ∆ ⋅ (r rcore ) 1 2005 Technical Proceedings DMD measurements, described in Section 3, are similar to these offset launch conditions. differences in modal output in combination with the optical properties of MMF result in an observed modified behavior for VCSEL signal propagation. For 10GbE systems, the dispersion and interference effects acting on the propagating modes can significantly degrade signal performance, thereby limiting the maximum transmission distances to a few hundred meters. The dispersion and interference effects result in several optical power penalties that reduce the system’s overall optical power budget. 2.2 Vertical Cavity Surface Emitting lasers (VCSELs). In MMF systems the optical source is traditionally an LED and depending on the material system, operates at either long or short wavelengths (1310nm or 850nm respectively). Unlike Fabry-Perot (FP) and Distributed Feedback (DFB) lasers, LED’s are mainly surface emitting devices, having a broad spectral output with large numerical aperture (NA). The large core diameters in MMF (50µm, 62.5µm and larger) are designed to efficiently couple the LED output power. The LED output overfills the MMF core resulting in an Overfilled Launch (OFL) condition. For an OFL condition the performance of MMF is limited to relatively low bit rates (< 650Mb/s) and, modal dispersion is relatively well behaved. 2.3 Bit error rate (BER) Flawless propagation of bits of data through the fiber link is the ultimate design goal of the MMF in that optical link. For our purposes there are two basic measures of this transport performance: (1) the number of bit errors compared to the total number of bits transmitted (BER) per unit time and (2) the speed of the bits passing through the fiber (data rate in bits/sec). Here we will focus on BER. State-of-the-art high-speed multimode systems such as 10Gigabit Ethernet (10GbE) use newer devices known as VCSEL’s. They, like LED’s, are surface emitting devices; however, the internal structure of the VCSEL comprises a layer of multiple quantum wells between Bragg Reflectors forming a laser cavity. Hence, although the device is a surface emitter, the output of the VSCEL is similar to that of the more traditional edge-emitting laser. The light emission of the VCSEL is from a single longitudinal mode, although multiple transverse modes with slightly different wavelengths are supported due to the lateral cavity diameter. In Fig. 1 consider digital pulses (bits) being launched into a MMF, represented by “initial pulses”. The mean optical power of the (zero, one) bit is (p0, p1), W. There is noise on these pulses, pnoise. After the pulses have propagated through the MMF they suffer distortions due to differential mode delay and other effects, represented by “final pulses”. Additional noise is present in the final pulses. The difference between p1 and p0 for the (initial, final) pulses is (OMAinitial, OMAfinal) or optical modulation amplitude. There are two bimodal distributions of optical powers for both the p1 and p0 pulses, shown on the right side of Fig. 1. The logic of the associated circuitry is programmed to decide if a given propagated pulse is a 1 or a 0. A comparison is made between the detected optical power of a given pulse within a given time window with a given power threshold, pTH. If a given pulse (bit) starts as a pinitial(t) pnoise optical power, p(t) optical power, p(t) Whereas edge-emitting lasers couple few longitudinal modes into single-mode fiber (SMF) and LED’s couple large numbers of modes uniformly across the core of the MMF, VCSEL’s couple a few transverse modes into a large core MMF in an under-filled launch condition. These pfinal(t) p1 t OMAinitial In general width of distribution is reduced. p1 pTH OLfinal OMAfinal OLinitial p0 initial pulses p0 final pulses No. of readings No. of readings Fig. 1. Explanation of bit error rate (BER). Digital pulses are launched into the multimode fiber (MMF) under test and undergo distortions that result in bit errors. See the text for an explanation of these symbols. OFC/NFOEC Conference 2 2005 Technical Proceedings 0 and falls above pTH, that bit will be erroneously recorded as a 1. A similar error occurs for a starting 1 bit which falls below pTH. Those bit errors are presented as the gray overlap areas, OLinital and OLfinal. the pulse maximum of the leading edge of the fastest pulse and 25% of the pulse maximum of the trailing edge of the slowest pulse in this sequence (see Fig. 2). If all the pulses in the DMD sequence are temporally aligned; then we expect that arrival time of each pulse, propagated by a distribution of mode groups, will be nearly the same from pulse to pulse. This condition translates into lower noise (lower temporal jitter) and a smaller BER (improves). See Fig. 1. Conversely, as the temporal misalignment increases in the DMD sequence, the temporal jitter increases, and the BER increases (becomes worse). The final bit error rate is then the ratio of the final overlap area, OLfinal, to the total area of the bimodal distribution on the right side of Fig. 1. To reduce the final BER it can be seen that OMAfinal must be increased and/or pnoise must be decreased. If the data sequence contains consecutive identical digits (case A), then the BER may change compared to alternating digits (0’s and 1’s, case B). This is because case A may contain significant low-frequency components compared to case B. To measure DMD consider the difference between tfast and tslow, which is comprised of DMD (due only to the fiber), the launch optical pulse, and the chromatic dispersion [in ps/(m*km)]. See ref. [1]. 3. DIFFERENTIAL MODE DELAY (DMD) 4. MEASUREMENTS OF DMD AND MMF PERFORMANCE In addition to BER another way to characterize MMF is to measure DMD. A spatially small (compared to the MMF core) and temporally short optical pulse is launched in the core of the MMF end face that is under test. At the output end face the resulting signal is measured [3 - 5]. This measurement is repeated, starting at the axis of the MMF core and moving outward to the core/cladding interface [1]. See Fig. 2 (not scaled and illustrates only the principle). Due to the cylindrical symmetry of the fiber this linear scan responds to many of the MMF modal structures. The launching spot can originate from a single mode fiber (or equivalent). There are additional requirements for the detection system and methods [1]. 4.1 Materials and methods for DMD measurements The layout of Fig. 3 was used to make DMD measurements. A VCSEL source is embedded in a commercially available XFP transceiver, powered by an evaluation board. Voltage pulses from the pulse generator are differentially supplied to the evaluation board and in response the VCSEL generates optical pulses. The pulse width, period, delay, amplitude, and voltage offsets are all controlled from the pulse generator. Optical pulses at 850nm are launched into SMF from the VCSEL, resulting in an approximately 18dB signal attenuation, compared to MMF. The launch SMF is positioned to better than 0.5µm accuracy and repeatability by the x-y-z precision location control and the bare fiber For a given offset launch only a weighted subset of all the possible mode groups is excited in the MMF. At the next offset launch location in the DMD measurement sequence a different weighted subset of mode groups is excited. In the full sequence of a DMD measurement all the mode groups are excited, according to the weights for each offset location. The different mode groups will, in general, have different propagation times as discussed in Section 2.1, illustrated in Fig. 2 (right-hand plot). Two times are measured, tfast and tslow, determined by the time of 25% of Fiber core Fiber cladding Evaluation PC board x-y-z precision location control Pulse generator Trace due to launching spot 1 Trace due to launching spot 2 Trace due to launching spot 3 Optical table MMF under test + + + stationar y fiber holder trigger input High frequency scope + SMF = single mode fiber MMF = multimode fiber optical input + tfast + tslow primary path alternate path time Optical power meter Fig. 2. End face of a MMF, showing three idealized launching spots into the core and an idealized and resulting DMD plot. Leading and trailing edge times (25%) threshold are identified with a “+”. OFC/NFOEC Conference bare fiber holders gap VCSEL source MMF end face Launching spot 2 Launching spot 3 optical power with offsets Launching spot 1 launch SMF Fig. 3. Summary of the experimental layout. 3 2005 Technical Proceedings the elements in this array (based on optical power, µW) to determine an accurate measurement of x = 0 and y = 0. The raw signal from the optical input of the high frequency scope was noisy. Mainly this was due to the low coupling efficiency of the VCSEL into the SMF as mentioned above. Digital filtering was used to reduce much of this noise. An example is shown in Fig. 4. For each interior point of 4096 raw points the optical power was averaged over a window of 200 consecutive points, centered on the raw point. Near the boundaries the averaging was asymmetric and included only those points within the overall time range. For that portion of the filtered optical power that was beyond the range of each pulse, the background structure was deleted and set to zero. The results were thus uncontaminated by background. Fig. 4. An example of the digital filtering used for the DMD measurements. holder. The MMF under test is located with a bare fiber holder mounted on a stationary fiber holder. The gap (less than 10µm) between the two fiber end faces is where the DMD offset distances are defined. The axis of the SMF output beam is perpendicular to the end face of the MMF to within 1.0°. Methods from ref. [1] were used to determine DMD in the time domain and are summarized here. The launch SMF was positioned at offset launch locations of x = 0, 2, …, 24µm and y = 0µm. At each location raw optical pulses from the MMF under test were captured by the scope (see Fig. 3). After digital filtering (Fig. 4) the time locations of 25% of the maximum optical power of each pulse were determined, marked by +’s in Fig. 5. From the complete set of +’s the left most “+” and the right-most “+” were determined and are indicated by thicker dashed lines in Fig. 5. This difference defines the time between the leading edge of the fastest resultant pulse and the training edge of the slowest resultant pulse. The pulse width due only to the Fiber type 2 Fiber type 3 24 26 26 22 24 24 20 22 22 20 20 8 6 4 2 12 10 8 6 14 12 10 8 6 4 4 2 2 time, ps time, ps 1000 800 600 400 200 1000 800 600 400 0 -2 200 0 -2 0 0 -2 time, ps 1000 10 14 16 800 12 16 18 600 14 18 0 16 0 offset launch distance, µ m 18 offset launch distance, µ m 28 offset launch distance, µ m 28 400 Fiber type 1 26 200 Positioning the axis of the SMF congruently with the axis of the MMF requires a detailed procedure (see “Launching spot 1” in Fig. 2). A coarse location is first determined by finding the (horizontal, vertical) edges (x, y) using the optical power meter and the x-y-z precision location control. Based on this estimate of x = 0 and y = 0, a matrix of measurements is taken with a step size of 5.0µm for both x and y directions. Numerical methods are used to weight Fig. 5. DMD measurements for the three types of fiber. See the text for details. OFC/NFOEC Conference 4 2005 Technical Proceedings fiber can be determined by subtracting the width of the launch pulse from this resultant difference. The pulse width due only to the fiber per unit length, DMD in units of ps/m, is given as follows: [(time distance between these two dashed lines) – (time between corresponding launch pulse points)] / (fiber length). For example, for Fiber type 1 (left-most “+”) – (right-most “+”) = 525ps. The time between the 25% maximum points of the launch pulse is 229ps. The fiber length is 2438m so that DMD = (525ps229ps)/2438m = 0.121ps/m. Here discrete p0(fk) values are the N Fourier transform elements of the P0 values, given in Eq. (2), where k = 1, 2, …, N and where fk are the N frequencies. The Fourier transform function, FT{…}, can be computed in Microsoft® Excel with the Fourier Analysis tool, for example. In Eq. (3) the subscript k was deleted from the time, t, dependency to indicate that all the P0(t) values are used to calculate each p0(fk) value. The magnitude of each complex element within the array of N Fourier transform values is squared to give each p0(fk) value to convert from electrical to optical power (e.g., squaring the IMABS(…) function in Excel where the arguments are the elements of the FT{…} array). Longer fiber lengths are typically used for these types of DMD measurements. The lengths used in this study were chosen to balance our requirements for sensitivity to the various DMD pulse delays and our corresponding BER measurements. The relationship between time and frequency is ∆f = 1 ( N ⋅ ∆t ) 4.2 Methods for MMF bandwidth measurements where ∆t is the time step size (in sec) between the successive N times, tk, and ∆f is the corresponding frequency step size (in Hz) between the successive N frequencies, fk. Following the notation of ref. [1] (Sections 6.2.1 and 6.2.2), let U(rj,tk) be the digitally filtered output pulse where U is optical power (in units of Watts), rj (j = 1, 2, …, M) are the M offset distances (µm) between the axis of the launch SMF and the axis of the MMF under test (see Fig. 3), and tk (k = 1, 2, …, N) are the N discrete times (sec). Note that U(rj,tk) is in the time domain. For simplicity here let W(rj) be the mean of the 10 VCSEL weighting factors, given in Annex D of ref. [1], simulating a typical VCSEL. This method can be readily expanded to include the full set of weighting factors. Similarly the reference pulse in the time domain is converted to the frequency domain as given in Eq. (5). r ( f k ) = FT {R ( t )} M p0 ( f k ) = r ( f k ) ⋅ h ( f k ) (2) From Eqs. (2) and (3) and the associated measurements the p0(fk) values are determined. Using Eq. (5) and its associated measurements the r(fk) values are determined so that the h(fk) values can found from Eq. (6): h( f k ) = p0 ( f k ) r ( f k ) To represent our VCSEL we took the mean of these matrix elements at each offset distance to weight our results, using W(rj), (j = 1, 2, …, M). Summing over all M offsets as described in Eq. 2, gave a resultant pulse in the time domain (N = 4096 values in units of Watts vs. ps) for each of the three MMF types. Convert P0(tk) in the time domain to the frequency domain using Eq. (3): OFC/NFOEC Conference (6) where h(fk) is the fiber frequency response, also called the fiber transfer function. This implies that the resultant function, p0, is comprised only of the reference pulse, r, and the fiber frequency response, h. The effects due to the connectors and other sources that may affect p0 are ignored here. Also in the time domain let R(tk) be the reference pulse that is launched into the MMF under test. This is measured and filtered in the same manner as the U(rj,tk) values. In Fig. 3 note the alternate path directly from the VCSEL source to the optical input of the scope to allow an unfiltered measurement of R(tk). p0 ( f k ) = FT {P0 (t )} (5) From the Convolution theorem [6, 7] we have A resultant output temporal response function, P0(tk), simulates all significant mode groups that are simulated by the typical VCSEL (through the W values) and the MMF under test (through the U values). P0 (tk ) = ∑ j =1W (rj ) ⋅ U (rj , t k ) (4) (7) The normalized functions for p0(fk), r(fk), and h(fk) [p0(fk)/p0(f1), r(fk)/r(f1), and h(fk)/h(f1)] are plotted in Fig. 6. The effective modal bandwidth (EMBc) is found by locating that frequency, fb, where h(fk) is 1.5 dB down from the zero frequency, f1. The EMBc frequency, fc, is given by fc = 1.414. fb. In practice fb must be found by interpolation within the h(fk) array, e.g., a linear interpolation. EMBc typically has units of MHz.km. This means that fc, in Hz, is to be multiplied by the length of the MMF under test in km and divided by 106 Hz/MHz. (3) 5 2005 Technical Proceedings specified BER for a minimum receiver power. We characterize the performance of the fiber under test by measuring the BER as a function of receiver average power. The input power to the optical receiver is incrementally reduced by means of an external variable optical attenuator (VOA). For compliance we have confirmed that our 50/125µm MMF under test performs to a maximum operating range. For reference, a baseline BER curve is routinely generated for a reference MMF. 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 r(fk) p0(fk) For the reference MMF we achieve a specified BER for an average optical receiver power that exceeds the minimum system requirement. It is important to note that performance is highly dependant on the characteristics of the transmitter output pulse, which has been adjusted to meet the requirements. It was observed that seemingly small changes in output launch conditions have large measurable effects on BER performance. 4.5E+09 4.0E+09 3.5E+09 3.0E+09 2.5E+09 2.0E+09 1.5E+09 1.0E+09 5.0E+08 h(fk) 0.0E+00 Normalized power, W Fibe r type 3 frequency, Hz Fig. 6. An example of the three kinds of frequency responses, described in Section 4.2 4.3 Materials and methods for BER measurements 4.4 Results To characterize the optical fibers under test for 10Gb/s Ethernet performance we configured a test and procedure to emulate a 10GBASE-S Ethernet link. The method employs a Bit Error Rate Test (BERT) system to simulate the optical transmitter and receiver and to measure the link performance in terms of bit error rate. The BERT is programmed to take repetitive measurements over extended periods of time. Modal interference effects in the optical link are minimized by eliminating unnecessary modal losses. Using these methods to determine DMD in the time domain, bandwidth, and BER; three distinct fiber types were evaluated. All had core diameters of 50µm. Type 1 was laser optimized for 10GbE data rates. An optical time domain reflectometer (OTDR) measurement of fiber length yielded 2438.4m for the DMD measurements. Type 2 was not laser optimized for 10GbE. Its OTDR length was 1019.1m. And Type 3 was laser optimized for 10GbE and had an OTDR length of 1016.1m. A summary of those measurements, including digital filtering, is shown in Fig. 5. The fiber under test is connected to the BERT using two patch cords with their cladding modes suppressed. The Bit Error Rate Test configuration is shown in Fig. 7 where TP refers to test point and (Tx, Rx) refer to optical (transmit, receive) functions. A pattern generator drives the VCSEL transmitter. The output power levels of the transmitted signal were compliant to IEEE 802.3ae [8]. 5. DISCUSSION AND CONCLUSIONS From Fig. 4 it is clear that digital filtering is required to significantly reduce the high frequency component of the noise in the raw measurements. Smooth curves are required to measure DMD where the leading and trailing edges of the slowest and fastest points are analyzed to determine tfast and tslow. The required performance for a 10GbE system is a Pattern Generator VCSEL Tx In Fig. 5 we see that the noise is greater for Fiber type 1 than for either type 2 or type 3. This is due to the length of type 1, 2438.4m for the DMD measurements while type 2 was 1019.1m and type 3 was 1016.1m. Comparing Fiber type 2 with Fiber type 3 in Fig. 5, we see that the pulses for Patch Cord TP1 Patch Cord Fiber type 3 line-up nearly perfectly, corresponding to a small DMD for Fiber type 3. The pulses for Fiber type 2 are clearly displaced from each other as a function of offset launch distance, corresponding to clearly not having 10GbE performance at 300m as shown in Fig. 8 (discussed below). Variable Optical Attenuator TP2 Each of the three fiber types was terminated with connectors such that the total fiber length was 300m. BER measurements were made on all three fiber types and on control and baseline samples. Under automatic control all Optical Rx `Fig. 7. Bit Error Rate Test Configuration. OFC/NFOEC Conference 6 2005 Technical Proceedings Average BER for 3 fiber types which satisfy the 10GbE requirements, we see that the correlation with measured DMD and measured bandwidth is not perfect. From our experience BER results are sensitive to connector types and blemishes at the connector interfaces, which translate into mode selective losses within the fiber link. We suspect this cause for this type of disagreement. 1.0E+00 1.0E-01 1.0E-02 1.0E-03 1.0E-04 Fiber type 1 BER 1.0E-05 1.0E-06 Fiber type 2 1.0E-07 Fiber type 3 1.0E-08 Generally, we can conclude that there is a less than perfect correlation between BER and measured DMD and bandwidth. DMD measurements mostly depend on modal dispersion but are not so responsive to other causes that limit bandwidth (e.g., inter-symbol interferences). On the other hand, BER is a realistic measurement of bandwidth that includes most, if not all, causes of bandwidth limitations. For the end customer the performance of the fiber link is most importantly determined by BER and data rate. 1.0E-09 1.0E-10 1.0E-11 1.0E-12 -7.0 -7.5 -8.0 -8.5 -9.0 -9.5 -10.0 -10.5 -11.0 -11.5 -12.0 -12.5 -13.0 -13.5 -14.0 -14.5 1.0E-13 Received power, dBm Fig. 8. BER measurements for 3 fiber types. The two curves with solid markers meet the requirements for 10GbE. 6. ACKNOWLEDGMENTS results were acquired and subsequently analyzed and plotted (see Fig. 8). The contributions of Bo Wang are acknowledged who prepared many of the samples and took the BER measurements. Manho Chung also is acknowledged for preparing other samples for the DMD measurements. Ken Reeder arranged for the availability of several of the samples. A discussion with John S. Abbott, Corning Inc., was very helpful. The results are summarized in Table 1 where it is seen that for smaller DMD results (ps/m) we have higher bandwidths (MHz.km). Within the MMF under test if the pulses that propagate within the available modal groups all arrive at the scope at nearly the same time are indicated by small DMD values which translate into higher bandwidth capacity. Our results are consistent with this interpretation. The last column compares our measured results with the standard [6] which requires that the MMF transmit data at 10Gbits/s with BER ≤ 10-12 and received power ≤ -9.9dBm. Fiber types 1 and 3 pass this requirement but Fiber type 2 does not. 7. REFERENCES [1] “FOTP-220: Differential Mode Delay Measurement of Multimode Fiber in the Time Domain,” TIA/EIA Standards Document, TIA/EIA 455220-A, (January 2003). [2] M. Webster, L. Raddatz, I. H. White, and D. G. Cunningham, “A statistical Analysis of Conditioned Launch for Gigabit Ethernet Links Using Multimode Fiber”, J. Lightwave Technol., 17, 1532 – 1541 (1999). For Fiber type 2 the BER measurement was much different that the BER measurement for the other two fiber types (see Fig. 8). This is consistent with the measured DMD result for Fiber type 2 that is larger than the other two fiber types and the measured bandwidth for Fiber type 2 that is smaller than the other two fiber types. [3] L. Raddatz, I. H. White, D. G. Cunningham, M. C. Nowell, “An experimental and theoretical study of the offset launch technique for the enhancement of the bandwidth of multimode fiber links”, J. Lightwave Technol., 16, 324 – 331 (1998). [4] S. E. Golowich, W. A. Reed, “Technique for measuring modal power distribution between an optical source and a multimode fiber”, U.S. Pat. 6,788,397, (2004). Comparing the BER results for Fiber types 1 and 3, both of [5] J. B. Schlager and D. L. Franzen, NIST Symposium on Optical Fiber Measurements, PP. 127 – 130, (1998). Table 1. Comparisons of measured DMD, measured bandwidth, and BER for three types of MMF’s. [6] J. B. Thomas, “An Introduction to Statistical Communication Theory,” New York: Wiley, 1969, p. 143. At BER = DMD meas. meas. 10-12, received MMF length, DMD bandwidth BER . MHz km type m ps/m length, m power, dBm 1 2438 0.121 2830 300 -10.2 2 1019 0.254 1404 300 No signal detected. 3 1619 0.114 2451 300 -11.3 OFC/NFOEC Conference [7] W. H. Press, et al., “Numerical Recipes: The Art of Scientific Computing,” Cambridge, UK: Cambridge University Press, 1986, p. 383. [8] IEEE 802.3ae – 2002, Part 3: Carrier Sense Multiple Access with Collision Detection (CSMA/CD) Access Method and Physical Layer Specifications (2002). 7 2005 Technical Proceedings

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