Optimization of Modal and Material Dispersions in High-Bandwidth

Chapter 5

Optimization of Modal and Material Dispersions in High-Bandwidth Graded-index Polymer Optical Fibers Downloaded by UNIV OF GUELPH LIBRARY on October 7, 2012 | http://pubs.acs.org Publication Date: September 1, 1997 | doi: 10.1021/bk-1997-0672.ch005

1

2

1,2

Eisuke Nihei , T. Ishigure , and Yasuhiro Koike 1

Department of Material Science, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223, Japan Kanagawa Academy of Science and Technology, Yokohama, Kanagawa 236, Japan 2

The optimum refractive-index distribution of the high bandwidth graded-index polymer optical fiber (GI POF) was clarified by consideration of both modal and material dispersions. The ultimate bandwidth achieved by the POF is investigated by a quantitative estimation of the material dispersion as well as the modal dispersion. The results indicated that even if the refractive-index distribution is tightly controlled, the bandwidth of the poly (methyl methacrylate) (PMMA)-base GI POF was dominated by the material dispersion when the required bit rate becomes larger than 4 Gb/s for 100-m transmission. It was also confirmed that the material dispersion strongly depends on the matrix polymer and that the fluorinated polymer whose material dispersion (-0.078 ns/nm∙km) is lower than that of poly methyl methacrylate (-0.305 ns/nm∙km) allows for a 10 Gb/s transmission rate in 100 m link. Recent developments in optical fiber technology brings new life to the prospect of optical telecommunications and has triggered broad efforts to develop the science and technology essential to realize new communication concepts such as information super highway. Single mode glass fiber is widely used in the trunk area of the telecommunication system and the optical fiber system is expected to extend to the subscriber area and the network in building, offices, and homes. However, use of the single mode glass fiber system in short distance network is not necessarily suitable because it requires the precise handling and connection due to the small core size (5-10 μιη) and thus it would be expensive in broadband residential area network, ATM-LAN, interconnection, etc. In contrast, polymer optical fiber (POF) which has more than 500 pm of core is promising candidate to solve such problems. 58

© 1997 American Chemical Society

In Photonic and Optoelectronic Polymers; Jenekhe, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1997.

Downloaded by UNIV OF GUELPH LIBRARY on October 7, 2012 | http://pubs.acs.org Publication Date: September 1, 1997 | doi: 10.1021/bk-1997-0672.ch005

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Optimization of High-Bandwidth GI POF

59

Since all commercially available POF have been of the step-index (SI) type, the modal dispersion limits the possible bit rate of POF links to less than 100 megabit per second (Mb/s). Because of this, it has been thought that POF cannot be utilized for high speed transmission medium. Recently, however, we proposed a large core, low loss, and high bandwidth graded-index polymer optical fiber (GI POF) (1,2) for the first time and we confirmed that 2.5 Gb/s signal transmission for 100 m distance was possible in the GI POF (2,3). It is well known that the dispersion in the optical fibers is divided into three parts, modal dispersion, material dispersion, and waveguide dispersion. In the case of the SI POF, the modal dispersion is so large that the other two dispersions can be approximated to be almost zero. However, the quadratic refractive-index distribution in the GI POF can dramatically decrease the modal dispersion. We have succeeded in controlling the refractive-index profile of the GI POF to be almost a quadratic distribution by the interfacial-gel polymerization technique (2). Therefore, in order to analyze the ultimate bandwidth characteristics of the GI POF in this paper the optimum refractive index profile is investigated by taking into account not only the modal dispersion but also the material dispersion. Experimental Section In order to investigate the material dispersion of the optical fiber, we use several measurements methods that have already been reported (4,5). The material dispersion of glass fibers can usually be measured directly by measurement of the delay time of light pulse of several wavelengths through the fiber. However, this method cannot be applied to POF because the higher attenuation of POF than glass optical fiber limits the transmission distance of light pulses and much higher accuracy is required to detect the pulse delay time. Therefore, dispersion measurement in the bulk samples of the polymer used to prepare the GI POF was adopted. Sample Preparation. The material dispersion which is caused by the wavelength dependence of the refractive index was approximated by the direct measurement of the refractive indices of the polymer at several wavelengths. The PMMA samples were prepared by bulk polymerization of their monomers. We also succeeded in preparing low loss fluorinated polymer-base GI POF (6). For a comparison of the material dispersion between PMMA and the fluorinated polymer, poly (hexafluoroisopropyl 2-fluoroacrylate) (PHFIP 2-FA) sample was prepared. The PHFIP 2-FA is the partially fluorinated polymers whose monomer unit contains only three carbon-hydrogen bonds. As dopants to form the graded-index profile in the GI POF (2), benzyl benzoate (BEN) for PMMA and dibutyl phthalate (DBP) for PHFIP-2-FA were selected. The dopant feed ratio to the monomer (monomer / dopant) was 5/1 (wt./wt.). The monomer and dopant mixture with initiator and chain transfer agent were placed in a glass ampule with an inner diameter of 18 mm and was polymerized at 90 °C for 24 hours. The method of polymerization of the polymer rod has been described in detail elsewhere (7,8).


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PHOTONIC AND OPTOELECTRONIC POLYMERS


Refractive Index. The refractive indices of the bulk polymers were measured by using an Abbe's refractometer at room temperature. In order to measure the refractive indices at several wavelengths, an interference filter was inserted in the refractometer. Two or three measurements were made at each wavelength and averaged. Usually, the refractive-index data were fit to a three-term Sellmeier dispersion equation of the form (9)\

where η is the refractive index of polymer sample, Aj is the oscillator strength, λί is the oscillator wavelength, and λ is the wavelength of light. Results and Discussion Refractive Index. Average refractive indices of the PMMA, BEN doped PMMA, PHFIP-2-FA, and DBP doped PHFIP 2-FA are summarized in Figure 1 for different wavelengths. The solid lines are the best fitted curves computed by a least-square method for Equation (1). The coefficients resulting from the Sellmeier fitting of the data are given in Table I. It should be noted that the slopes of the refractive index versus wavelength curves indicate that the PHFIP 2-FA has the smaller dispersion of the refractive-index with respect to wavelength than PMMA. Table I.

Coefficients of the Sellmeier Equation Fit Ai λι A PMMA 0.4963 71.80 0.6965 PMMA-BEN 0.4855 104.3 0.7555 PHFIP 2-FA 0.4200 58.74 0.0461 PHFIP 2-FA-DBP 0.2680 79.13 0.3513 2

of Data λ 117.4 114.7 87.85 83.81 2

A λ 0.3223 9237 0.4252 49340 0.3484 92.71 0.2498 106.2 3

3

Material Dispersion. The material delay distortion D for propagation of a pulse in the step-index (SI) type and single-mode type optical fiber can be obtained from the following equation(P): m a t

where δλ is the root mean square spectral width of the light source, λ is the wavelength of transmitted light, c is the velocity of light, cfn/dA is the secondorder dispersion, and L is length of the fiber. The material dispersions of the PMMA, BEN doped PMMA, PHFIP 2-FA, 2



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NIHEI ET AL.


and DBP doped PHFIP 2-FA are shown in Figure 2. The material dispersion in Figure 2 were calculated from the results of Sellmeier fitting of Equations (1) and (2). The materia] dispersion of silica taken from Ref. 9 is also shown in Figure 2. The material dispersion of PMMA is larger than that of the silicafromthe visible to the near infra-red region. On the other hand, it was confirmed that the substitution of the hydrogen atoms in the polymer with fluorine decreases the material dispersion. In the case of the fluorinated polymer matrix, a little amount of additives such as DBP or BEN which has a large material dispersion increases the material dispersion of the doped polymer. Therefore, a fluorinated dopant should be used forfluorinatedpolymer in order to keep the material dispersion low. Refractive-Index Profile. The refractive-index profile was approximated by the conventional power law. The output pulse width from the GI POF was calculated by the Wentzel-Kramers-Brillouin (WKB) method (70) in which both modal and material dispersions were taken into account as shown in Equations (3), (4), and (5). Here, ointermodai, ointramodab and signify the root mean square pulse width due to the modal dispersion, intramodal (material) dispersion, and both dispersions, respectively. CTtotal

0"i

Intermodal

LN,A g ( g+2V 2c g + 1 \3g + 2J 1 2

Λ 1

2

+

2

(3)

2

4C,C A(g + l) 4A C (2g + 2) Ρ 2g + l ( 5 g + 2X3g + 2) 2

+

( Intramodal

άλ J

dk (4)

where,

C,=

g-2-g g+2 3g-2-2g 2(g + 2)


62



1.54 ι

• • ι • • • ι •

ι

1.34 I ι 400

•

ι

ι 600

I

800 1000 Wavelength (nm)

ι • 1200

ι

•

I

1400

Figure 1. Refractive-index dependence of the polymers on wavelength. • : benzyl benzoate doped PMMA; · : PMMA; • : dibutyl phthalate doped partially fluorinated polymer; A: partially fluorinated polymer. Reproduced with permissionfromreference 13. Copyright 1996 Optical Society of America.

.15 l 400

ι

' • 600

» • ' • 800 1000 Wavelength (nm)

ι ι I 1200 1400

Figure 2. Comparison of the material dispersion among PMMA, PHFIP 2-FA, and silica. (A): PMMA; (B): Silica; (C):PHFIP 2-FA.


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NIHEI ET AL.

63

Optimization of High-Bandwidth GI POF -2n λ dA N 'A' dk x

x

Here, σ is root mean square spectral width of the light source (in nanometer) and L is the fiber length. δ


(5)

Calculated results in PMMA-base and PHFIP 2-FA-base GI POFs are shown in Figures 3 and 4, respectively. Here, it was assumed that the fiber length and the spectral width of the light source (laser diode) were 100 m and 2 nm, respectively. When only modal dispersion was taken into account, the pulse width was minimized when g equaled 1.97 in both PMMA-base and PHFIP 2-FA-base GI POFs. On the other hand, when the material dispersion at 650-nm wavelength was taken into account in Figure 3, the total pulse width (atotai) becomes 45 times broader, and the index exponent giving the smallest pulse width ( a t a i ) shifted to 2.33. It is quite noteworthy that the effect of the material dispersion on the pulse width in PHFIP 2-FA-base GI POF in Figure 4 is much smaller that that in PMMA-base GI POF in Figure 3. Based on the results shown in Figures 3 and 4, we estimated the possible bit rate in the GI POF link when the rms spectral width of the light source was assumed to be 2 nm. It has been reported by Personick (77) that the power penalty of the receiver reaches 1 dB when the pulse width exceeds one fourth of the bit period (1/B [in second] where Β is the bit rate [in bit per second]). Therefore, the possible bit rate B was defined by Equation (6) w

a

s

to

p

~

P

4o

total

Calculated possible bit rate in PMMA-base and PHFIP 2-FA-base GI POF links is shown in Figures 5 and 6, respectively. The results indicate that maximum bit rates of 25.7 Gb/s and 5.48 Gb/s can be achieved at 780-nm wavelength in PHFIP 2-FA-base GI POF and PMMA-base GI POF links, respectively. Also, the maximum bit rates at 780-nm wavelength are higher than those at 650-nm wavelength in both PHFIP 2-FA-base and PMMA-base GI POF links, because the material dispersion becomes small with increase in wavelength of light as shown in Figure 2. The attenuation spectra of light transmission for both PMMA-base and


64

PHOTONIC AND OPTOELECTRONIC POLYMERS 1000

—ι—•—'—»—«—:

J


2

ψ

100

"(C)

I (A)

1.5

1

ι

ι

ι

ι

2 2.5 Index Exponent

3

Figure 3. Pulse width (a tai) versus index exponent of PMMA-base GI POF assuming equal power in all modes and light source having rms spectral width of 2 nm. (A) : Only modal dispersion is considered at 650-nm wavelength. (B) : Both modal and material dispersions at 780-nm wavelength are considered. (C) : Both modal and material dispersions at 650-nm wavelength are considered. Reproduced with permissionfromreference 14. Copyright 1996 The Society of Polymer Science, Japan. to

1000 L •

1' 1.5

I

I

' ι

I

I

•

I

ι •


•

I

I

J

ι 3

Figure 4. Pulse width (atotai) versus index exponent of PHFIP 2-FA-base GI POF assuming equal power in all modes and light source having rms spectral width of 2 nm. (A): Only modal dispersion is considered at 780-nm wavelength. (B) : Both modal and material dispersions at 780-nm wavelength are considered. (C) : Both modal and material dispersions at 650-nm wavelength are considered. Reproduced with permissionfromreference 14. Copyright 1996 The Society of Polymer Science, Japan. In Photonic and Optoelectronic Polymers; Jenekhe, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1997.


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NIHEI E T A L .


100 1 • • • • 1.5

ι • • • • » • • • • 2 2.5 Index Exponent

I 3

Figure 5. Relationship between index exponent g and possible bit rate in 100-m length PMMA-base GI POF link. Source width was assumed to be 2 nm. (A) : Only modal dispersion is considered at 650-nm wavelength. (B) : Both modal and material dispersions at 780-nm wavelength are considered. (C) : Both modal and material dispersions at 650-nm wavelength are considered.

100 1.5

ι , . . . ι . . . . 2 2.5 Index Exponent

ι 3

Figure 6. Relationship between index exponent g and possible bit rate in 100-m length PHFIP 2-FA-base GI POF link. Source width was assumed to be 2 nm. (A) : Only modal dispersion is considered at 780^nm wavelength. (B) : Both modal and material dispersions at 780-nm wavelength are considered. (C) : Both modal and material dispersions at 650-nm wavelength are considered.


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PHFIP 2-FA-base GI POFs are shown in Figure 7. As most carbon-hydrogen bondings in the PMMA-base GI POF are substituted with carbon-fluorine bondings in the PHFIP 2-FA-base POF, the absorption loss in the near infrared to infrared region due to carbon-hydrogen stretching vibration can be eliminated. Consequently, the total attenuation at the near infrared region of the PHFIP 2-FAbase GI POF is lower than that of PMMA-base GI POF as shown in Figure 7. For instance, the attenuation of PHFIP 2-FA-base GI POF at 780-nm wavelength is 135 dB/km, while 840.5 dB/km in PMMA-base GI POF. This low attenuation at near infrared region of PHFIP 2-FA-base GI POF enables the use of inexpensive laser diode (LD) for compact disc as the light source in PHFIP 2-FA-base POF link. Therefore, the fluorinated polymer base GI POF is advantageous because of the low attenuation at near infra-red region and of the low material dispersion (6). In the POF link, it has been proposed that inexpensive LED can be utilized as the light source (72). However, since the LED has large spectral width (15-20 nm) than the laser diode (1-3 nm) the effect of the spectral width on the GI POF link by the LED should be investigated. The possible bit rate in 100 m PMMA-base and PHFIP 2-FA-base GI POF links is shown in Figures 8 and 9, respectively when the spectral widths of the light source are assumed to be 0, 1, 2, 5, and 20 nm. The wavelengths of light sources in Figures 8 and 9 are 650 nm and 780 nm, respectively. In the case of the PMMA-base GI POF, the maximum bit rate dramatically decreases with an increase in the source spectral width increases as shown in Figure 8. When the source width is 20 nm, the bit rate becomes almost independent of the index exponent as shown in Figure 8E. Therefore, the GI POF with almost the quadratic refractive index distribution is more effective for high speed transmission when a light source with narrow spectral width such as laser diode (LD). It was confirmed that it is impossible to cover more than 1 Gbit/s of bit rate unless a light source with less than 5 nm spectral width can be used and the refractive-index profile can be controlled in the order of 2 to 3 of the index exponent g. On the other hand, in the case of the PHFIP 2-FA-base GI POF, the low material dispersion enables to transmit more the transmission of more than 1 Gb/s even if the spectral width of the light source is 10 to 20 nm. The relationship between the possible bit rate versus wavelength when the index exponent g is fixed in both PMMA and PHFIP 2-FA-base GI POF links is shown in Figures 10 and 11, respectively. In the case of PMMA-base GI POF, when the index exponent g is 2.33, the possible bit rate in 100 m link increases with increasing wavelength. When the index exponent is larger than 3, there is no wavelength dependence of the possible bit rate. In this case, as the index profile becomes close to step-index, the modal dispersion is dominant and the effect of the material dispersion is negligible even if the wavelength changes. On the other hand, in the case of PHFIP 2-FA-base GI POF, it is noteworthy that by changing the index exponent, the possible bit rate can be maximized at desired wavelength in the range of 500 nm to 1000 nm.


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3000

Λ

2500


CQ

2000

5 1000 < 500

;...J>

0 500

ι

/r

A 1 1 A A Jb 1 A A.J. A. 1-l-A.l 1 1 I.I 1 1

550

600

650 700 750 Wavelength (nm)

800

850

Figure 7. Total attenuation spectra of the GI POF. (A): PMMA-base; (B): PHFIP 2 FA-base.

100000 t


3

Figure 8. Relationship between bit rate in 100-m PMMA-base GI POF link and index exponent at 650-nm wavelength when the light source has a finite spectral width as follows: (A): 0 nm; (B):l nm; (C): 2 nm; (D): 5 nm; (E): 20 nm.


67

68



100000

100 1.5


3

Figure 9. Relationship between bit rate in 100-m PHFIP 2-FA-base GI POF link and index exponent at 780-nm wavelength when the light source has a finite spectral width as follows: (A):0 nm; (B):l nm; (C): 2 nm; (D): 5 nm; (E): 20 nm.

100000

,

0 0

I

400

ι

ι ι ι I ι ι ι I ι ι ι I ι ι ι I 600

800 1000 1200 Wavelength (nm)

1400

1600

Figure 10. Wavelength and index exponent g dependencies of possible bit rate in 100-m PMMA-base GI POF link at 650-nm wavelength. (A): g= 1.9; (B): g=2.0; (C): g=2.15; (D): g=2.33; (E): g=2.5; (F): g=3.0.



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100 I • • • ι • • • ι . • • ι • • • ι • • • ι • > • ' 400 600 800 1000 1200 1400 1600 Wavelength (nm)

Figure 11 Wavelength and index exponent g dependencies of possible bit rate in 100-m PHFIP 2-FA-base GI POF link at 780-nm wavelength. (A): g= 1.95; (B): g=2.0; (C): g=2.05; (D): g=2.1; (E): g=2.25.


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70



Conclusion The optimum refractive-index profile of GI POF was investigated by taking both modal and material dispersions into account. The material dispersion seriously affects the bit rate performance of GI POF link when the signal spectral width is larger than the order of 1 nm. In order to achieve bit rates of more than 1 Gb/s in 100-m POF link, the source width should be less than 5 nm and the index profile of the PMMA-base GI POF should be controlled in the range from 2 to 3 of the index exponent g. The PHFIP 2-FA-base GI POF can transmit higher bit rates than PMMA-base GI POF even if the source width is as broad as 20 nm because the fluorinated polymer has a low material dispersion. Furthermore, the low absorption loss of PHFIP 2-FA-base GI POF at the near infra-red region enables to use the longer wavelength in the POF link. It is concluded that fluorinated polymer-base GI POF is superior to the PMMA-base GI POF in both attenuation of light transmission and total bit rate at near infrared region where several inexpensive LEDs and LDs exist. Literature Cited (1) Ishigure, T.; Nihei, E.; Koike, Y.Appl. Opt. 1994, 33,4261. (2) Koike, Y.; Ishigure, T.; Nihei, E. IEEE J. LightwaveTechnol.1995, 13, 1475. (3) Ishigure, T.; Nihei, E.; Yamazaki, S.; Kobayashi, K.; Koike, Y. Electron. Lett. 1995, 31, 467. (4) Horiguchi, M.; Ohmori, Y.; Miya, T. Appl. Opt. 1979, 18, 2223. (5) Heckert, M. J. IEEE Photon. Technol Lett. 1992, 4, 198. (6) Ishigure, T.; Nihei, E.; Koike, Y.; Forbes, C. E.; LaNieve, L.; Straff, R.; Deckers, H. A. IEEE Photon. Technol. Lett. 1995, 7, 403. (7) Koike, Y.; Tanio, N.; Ohtsuka, Y. Macromolecules. 1989, 22, 1367. (8) Koike, Y.; Matsuoka, S.; Bair, H. E. Macromolecules. 1992, 25, 4809. (9) Fleming, J. W. J. Am. Ceram. Soc. 1976, 59, 503. (10) Olshansky, R.; Keck, D. B. Appl. Opt. 1976, 15, 483. (11) Personick, S. D. Bell Syst. Technol. J. 1973, 52, 875. (12) Yoshimura, T.; Nakamura, K.; Okita, Α.; Nyu, T.; Yamazaki, S.; Dutta A. K. Conference Proceeding of Plastic Optical Fibers & Applications, Boston, October 1995, 119 (13) Ishigure, T.; Nihei, E.; Koike, Y. Polymer J. 1996, 28, 272. (14) Ishigure, T.; Nihei, E.; Koike, Y.Appl. Opt. 1996, 35, 2048.


Optimization of Modal and Material Dispersions in High-Bandwidth

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