Dispersion compensation using apodized Bragg fiber ... - IEEE Xplore

0 downloads 0 Views 346KB Size Report
Abstract—The use of apodized Bragg fiber gratings for disper- sion compensation, when operated in transmission, is discussed. Using a system simulation, it is ...
2336

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 16, NO. 12, DECEMBER 1998

Dispersion Compensation Using Apodized Bragg Fiber Gratings in Transmission Kerry Hinton

Abstract—The use of apodized Bragg fiber gratings for dispersion compensation, when operated in transmission, is discussed. Using a system simulation, it is shown that these devices have several intrinsic limitations. If these limitations can be overcome, apodized Bragg fiber gratings can be used to compensate a 10Gb/s system over 200 km of standard fiber with an eye-closure penalty of less than 2 dB.

II. FIBER FIRST-ORDER AND HIGHER ORDER DISPERSION The dispersion properties of an optical fiber in the 1550 nm window can be described in the following manner. The of a pulse with spectral width dispersed pulse width around wavelength can be expressed by a Taylor series (1)

Index Terms—Dispersion compensation, gratings.

I. INTRODUCTION

A

PODIZED chirped fiber gratings have become one of the preferred approaches to dispersion compensation in optical systems [1], [2]. Alternative approaches for using Bragg fiber gratings (BFG’s) for dispersion compensation have also been researched including the use of unchirped ramped gratings operated in reflection [3], [4] and in transmission [4]–[6]. The use of apodized BFG’s (ABFG’s) in transmission for dispersion compensation has several advantages over using them in reflection. To operate the grating in reflection requires the use of a circulator which introduces losses into the system. The circulator also increases the complexity and cost of the dispersion compensation unit. In contrast, if an ABFG is used in transmission, the device can be spliced directly into the transmission link. This will avoid the losses due to bulk optical devices such as the circulator. Another problem with using ABFG’s in reflection is that the signal optical field must interact strongly with the grating. That is, it must reflect from the grating. This means that any imperfection in the fabrication of the ABFG will have a detrimental impact on its properties as a dispersion compensator. In particular, delay ripple (due to noise in the UV writing process) and polarization mode dispersion introduced into the signal by the grating can severely degrade system performance. In contrast, if the grating is operated in transmission, the interaction between the signal optical field and the grating is much weaker, and hence imperfections in the grating do not become impressed upon the signal field. This paper discusses the use of ABFG’s, operated in transmission, as dispersion compensators. It considers a range of limitations these devices have and gives several design guidelines for the use of such ABFG’s.

Manuscript received February 4, 1998; revised August 12, 1998. The author is with Telstra Research Laboratories, Clayton, Victoria 3168 Australia. Publisher Item Identifier S 0733-8724(98)09108-7.

where fiber link length and We have group velocity of light at wavelength This gives for (1) (2) and disperWhere the (first-order) fiber dispersion sion slope (also referred to as second-order dispersion) are given by

(3) In the 1550-nm window, standard fiber has ps/nm/km and ps/nm/nm/km. A convenient and useful “rule of thumb” for the impact of dispersion on an intensity-modulated optical system is that Hence, the pulse spread must be less than the bit period the effect of dispersion and higher order dispersion is often measured by this rule. Applying this rule in the context of dispersion compensation gives three cases. Case 1: No dispersion compensation required. This corresponds to link lengths with (4) For a 10-Gb/s system at 1550 nm, this gives the well known km. limit of Case 2: Only first-order dispersion must be compensated. This corresponds to link lengths with (5) That is, the dispersion compensating technique need not compensate higher order dispersion because these terms do not result in a pulse spread of order . For a single-channel 10-Gb/s system at 1550 nm, this gives 60 km km. For a WDM system which has channels spanning 10 nm, km. In this case, dispersion this distance reduces to

0733–8724/98$10.00  1998 IEEE

HINTON: DISPERSION COMPENSATION USING BRAGG FIBER GRATINGS

2337

compensation must be done either channel by channel or include dispersion slope compensation. Case 3: Second-order dispersion must also be compensated. There are two situations that can lead to this. 1) Ultralong link lengths where both first-order and secondorder dispersion cause significant pulse spreading. This corresponds to link lengths with

and effective local impedance as

Defining the local detuning (9)

and where number of the incident light, gives

the free space wave (10)

(6) This situation becomes important when an ultralong link is compensated only for first-order dispersion. In this case, second-order dispersion effects will degrade system performance. The limits for this were given immediately above. In this case, 2) Wide bandwidth systems with fiber dispersion must be compensated over a bandwidth so wide that second-order dispersion is as significant as first-order dispersion. Therefore, even though firstorder dispersion has been compensated, the residual higher order dispersion still significantly degrades system performance. This bandwidth is given by (7) nm. In the 1550 nm window, this gives From (7), it can be seen that, in standard fiber, Case 3b) is extremely unlikely to eventuate. However, it is important to note that the above equations, particularly (7), apply equally to the dispersion compensator as to the fiber link. As it is shown below, this is an important issue when considering the design and application of BFG’s, operating in transmission, for dispersion compensation. III. ABFG’S

IN

TRANSMISSION

To model an ABFG in transmission, the “effective medium method” is used [7]. The refractive index variation of the ABFG, of length , is written in the form

(8) background refractive index, nominal Bragg where variations in the average refractive index, grating pitch, modulation amplitude , and grating phase. It is and are slowly varying quantities. It is assumed that assumed that the signal is incident into the grating from the end. Using (8) in Maxwell’s equations and applying perturbation techniques, the grating can be represented as an “effective , effective medium” with an effective refractive index dielectric permittivity , effective magnetic permeability ,

(11) In the rest of this paper, the depenwhere on is indicated only when needed for clarity. dence of When operating in transmission, the transmission coefficient can be written in the form found in (12) shown at the bottom of the page, where (13) The group delay is derived from the phase of the transmission coefficient and dispersion slope of the The dispersion grating are given by (respectively) ps/nm ps ps/nm ps

(14)

When operating in transmission, well away from the reflecis real, hence for all tion band edge, This allows some simplification of the calculation of argument giving to lowest order of the transmission coefficient (15) for and for This result where and is continuous for all is precise when That is, the grating modulation grows and decays continuously from and to a zero value. Gratings designed with are called apodized gratings. this form for Apodized gratings do not have any discontinuities in This removes the resonant cavity effects typical of uniform Bragg gratings. It has already been noted that these resonant cavity effects severely limit the applicability of uniform Bragg gratings for dispersion compensation [8]. Another advantage of apodization is that the transition between reflection and transmission is very abrupt. Fig. 1 displays the effect of apodization on the magnitude of a grating’s transmission coefficient. Fig. 1(a) has no apodization

(12)

2338

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 16, NO. 12, DECEMBER 1998

(a)

1 = () ()

0 Fig. 2. A comparison of the bandwidth  jd k =d k j given by (16) and (17) (solid line) for a BFG in transmission with the asymptotic form given by (21) (dashed line).

where The dispersion slope

and has the form (in

) (17) (b)

For the rest of this paper, we shall assume the grating is constant) and constant for the unchirped (i.e., length of the grating. This latter assumption allows us to set without loss of generality. These assumptions result , i.e., is a function of only. in In the asymptotic region with large detuning away from the which reduces Bragg wave number, we have (16) and (17) to the forms (18)

(c) Fig. 1. (a) End cavity effects in a uniform distributed Bragg grating, with no apodization. The oscillations are due to the cavity resonances arising from the discontinuities in h z at z and z L: The heavy line indicates the reflection band edge. (b) The impact of semi-apodization (i.e., apodization at one end of the grating) is to remove the resonant cavity oscillations. The transition between reflection and transmission is gradual. (c) Apodization at both ends removes the resonant cavity effects and also produces a very rapid transition between reflection and transmission. This allows operation of the device much closer to the reflection band edge.

()

=0

=

(i.e., is discontinuous at and is continuous and displays resonant cavity effects typical of for all other uniform distributed Bragg reflector (DBR). Fig. 1(b) shows the magnitude of the transmission coefficient for a semi-apodized is continuous for all except grating (i.e., Fig. 1(c) shows the magnitude of the transmission coefficient is continuous for all for an apodized grating (i.e., Assuming the grating is apodized, the dispersion has the form (in ps/nm)

(16)

(19) of the For a dispersion compensator, the dispersion compensator is set to negate the impact of fiber dispersion. However, as seen from (18) and (19), That is, is nonzero, then so is . With the net dispersion if zero, the impact of the dispersion slope must be considered. Although Section II discussed the relative impact of fiber dispersion slope, we must also consider the impact of the dispersion compensator’s dispersion slope. The inequality in (7) gives the bandwidth for which dispersion slope becomes important. As stated above, this constraint applies to both the fiber and the dispersion compensator. Hence, the bandwidth of a dispersion compensator is given by (20) For the compensator to properly compensate the fiber link (i.e., the compensator dispersion, we require either negates both fiber dispersion and dispersion slope) or the signal bandwidth must be less than the quotient given in (20). For an and ABFG in transmission, it will be seen that so the bandwidth given by (20) will be the key constraint.

HINTON: DISPERSION COMPENSATION USING BRAGG FIBER GRATINGS

Fig. 3. A comparison of the bandwidth

1 = d(k)=d (k) j

0

j

2339

for a triangular grating profile for grating lengths of 100 cm (dashed line) and 10 cm (solid line).

For a grating operating in transmission, the asymptotic form is given by (18) and (19) for this bandwidth

compensated. This gives the requirement (22)

(21) A variant of this ratio has been proposed as a “figure of merit (FoM)” [9]. As an FoM, for a given total fiber link dispersion, (20) gives the maximum bandwidth of a signal which can be compensated without the ABFG’s dispersion slope degrading the signal. Fig. 2 shows a plot of the quotient in (20) using (16) and (17) as well as the approximate form given in (21). It can be seen that the approximate form only becomes inaccurate close to the reflection band edge. Two immediate conclusions can be drawn from (20) and (21). First, the compensation bandwidth of the ABFG increases from the reflection band edge. with increasing detuning However, as seen from (16) and (17), this also decreases the ABFG’s ability to compensate fiber dispersion. Second, at a given wavelength, away from the reflection band edge, the actual details of the grating’s profile, i.e., , are relatively unimportant in regard to the ABFG’s , (21) compensation bandwidth. Also, for a given detuning shows that the bandwidth is independent of the grating length. This issue is discussed in greater detail below. The results (18)–(21) can also be used to address the need for wavelength stability of the transmitter when using these devices for dispersion compensation. Wavelength stability of the transmitter describes the gradual drift, over time, of the carrier wavelength. This is an issue of some importance in WDM systems. It is of crucial importance here because drift of the in the carrier wavelength will change the offset signal field and hence change the dispersion and dispersion slope experienced by the signal. To calculate the sensitivity of the dispersion compensating properties of these devices, in (18), to a very good approxTaking a derivative of (18) imation, we can set with respect to the dependence of the detuning allows the calculation of the impact of wavelength drift of the carrier. We due to wavelength drift require the change in dispersion to be much less than the dispersion being of the carrier

From this it can be seen that the bandwidth constraint on these devices is identical to the wavelength stability constraint. Further, the closer the carrier is to the reflection band edge ), the more sensitive the compensator to (i.e., the smaller wavelength drift. This issue is further discussed in Section IV. IV. NUMERICAL RESULTS As shown in Fig. 2, the asymptotic form given in (21) loses accuracy close to the reflection band edge. To attain an understanding of the dispersion properties of an apodized grating in this region, a series of numerical calculations based upon (16) and (17) were undertaken for a range of profiles One consideration is the impact changing the length of the grating. Fig. 3 shows the impact of the grating length on the relationship between the compensator’s bandwidth and the dispersion of the device. The length of the grating was set at 10 cm (solid line) and 100 cm (dashed line), both with a triangular profile. This shows that, for a given profile , to compensate larger amounts of dispersion over a fixed bandwidth will require a longer grating. Another way of improving the bandwidth of the compensator, for a given amount of dispersion, is to change the profile To consider the impact of the grating profile, numerical simulation for seven different profiles was undertaken. These with all continuous and profiles all had in a 10-cm grating and attaining a maximum of 1000 m were symmetric about the midpoint of the grating. The profiles were: raised cosine; super Gaussian (order 5); sine; square root; semicircular; trapezium; and saw tooth (with a lower limit of the saw tooth of 900 m ). These profiles are depicted in Fig. 4. Fig. 5 shows the dispersion properties of these profiles. It can be seen that at a given wavelength some profiles have a larger dispersion, but this is accompanied by a larger dispersion slope at that wavelength.

2340

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 16, NO. 12, DECEMBER 1998

Fig. 4. Grating profiles studied in the numerical simulations.

square root; semicircular; super Gaussian; saw tooth; and trapezium. V. THE TRAPEZOIDAL ABFG DISPERSION COMPENSATOR Focusing on the trapezoidal-profiled ABFG, operating in transmission as a dispersion compensator, the key parameters which determine its limitations as a dispersion compensator ], the length are the strength of the grating [maximum of , and degree of apodization. The degree of of the grating apodization can be represented as the fraction Frc of the length from zero to its maximum of the grating used to increase value. These parameters are displayed in Fig. 7. To investigate the impact of these parameters on the dispersion compensation abilities a trapezoidal ABFG, an optical system simulation including fiber dispersion and an ABFG was implemented. The impact of fiber dispersion and dispersion slope can be represented by expressing the propagation as a Taylor series in frequency Expressing constant and the propagation constant in terms of fiber dispersion gives dispersion slope Fig. 5. Dispersion of the various grating profiles studied in the numerical simulation. All these gratings have the same Bragg wavelength and reflection band edge wavelength.

(23) Fig. 6 shows the relationship between the compensator’s bandwidth [as given in (20)] and the amount of dispersion it can compensate. This figure shows that some profiles provide dispersion compensation over a wider bandwidth than others. The trapezium provides the widest bandwidth, for a given dispersion value. The triangular profile has the narrowest bandwidth for a given dispersion value. In order of increasing bandwidth, the profiles are: triangular; raised cosine; sine;

carrier frequency, carrier wavelength, where group velocity, and With no dispersion compensation, the dispersed electric field has the form at the receiver (24) is the transmit field and represents the net where fiber losses, including any optical amplification.

HINTON: DISPERSION COMPENSATION USING BRAGG FIBER GRATINGS

2341

1 = () ()

0 Fig. 6. The bandwidth  jd k =d k j for the various grating profiles shown in Fig. 4. It can be seen that, for a given value of dispersion, some profiles have a wider bandwidth than others. The profile with widest bandwidth is the trapezium profile (the uppermost trace). The profile with the narrowest bandwidth it the triangular profile (the lowermost trace).

the ABFG would be designed such that (26)

Fig. 7. The key parameters describing a trapezoidal ABFG. These paramefh z g, the length of the ters are the maximum strength of the grating grating L, and fraction of grating length used for the apodization at each end L 1 Frc:

max ( )

To model the impact of the dispersion compensator, the dispersive properties of the ABFG are added to (23), giving for the net propagation delay

(25) and are the dispersion and dispersion slope where and , respectively. of the ABFG expressed in The goal of dispersion compensation is cancel all terms in of order and higher. Ideally the compensator would reduce all these terms to zero. The dominant dispersive , hence the dispersion term, in fiber, is the term of order compensator is usually designed to cancel this term. Therefore,

, For an ABFG, this condition then sets the value of term. Fig. 8 shows which is unlikely to cancel the that the relationship between dispersion and dispersion slope term is for a trapezoidal ABFG. Hence, although the canceled, the remaining higher order dispersion terms may distort the signal. Although the higher order dispersion terms for the fiber may be negligible, except in the cases listed above in Section II, Fig. 8 shows this may not be the case for the higher order ABFG terms. The system simulation was a 10-Gb/s system with an unbalanced Mach–Zehnder external modulator with a pass bandwidth of 13 GHz. (Hence, the transmit signal is chirped.) The fiber was standard fiber with 17-ps/nm/km dispersion and 0.06-ps/nm/nm/km dispersion slope. The receiver filter was a low pass filter with a pass bandwidth of 7.5 GHz. The trapezoidal ABFG dispersion compensator was tuned to exactly cancel the first-order dispersion, and the impact of higher order dispersion was measured by filtered detector current eye closure relative to the transmit signal. No fiber losses were included in the model, so that the impact of higher order ABFG dispersion could be singled out in the eye-closure calculations. Fig. 9 shows the eye-closure penalty, as a function of grating length and apodization, arising from dispersion slope terms in an ABFG, when used as a dispersion compensator in transmission. From this it can be seen that the longer the grating and the smaller apodization region, the better the compensator. However, fabrication of very long gratings poses a range of technical problems. Also, reducing the length of the apodization region (i.e., reducing Frc) will result ultimately

2342

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 16, NO. 12, DECEMBER 1998

Fig. 8. The relationship between dispersion and dispersion slope of a trapezoidal ABFG. This grating has L 50 cm, max () = 1000 m01 , and Frc = 0.1.

=

Fig. 9. The impact of grating length (L) and apodization (Frc) on the eye-closure penalty for a 100-km length link with max = 1000 m01 :

in resonant cavity effects arising. As shown in Fig. 1, these effects severely reduce the applicability of the grating as a dispersion compensator. Fig. 10 shows the bandwidth of the device (in GHz) as a function of grating length and apodization. This figure, along with Fig. 9, displays the general relationship between the bandwidth of the grating, defined via (20) and the system performance of the device. That is (typically), the wider the bandwidth, the better the compensated system performance. Using (22), Fig. 10 also displays the sensitivity of the device to wavelength drift. From this figure, it can be seen that these devices are highly sensitive to carrier wavelength drift. Even the least sensitive grating displayed in Fig. 10 requires stability of the carrier frequency to fluctuations less than 70 GHz in magnitude. This constraint is currently at the limit of commercial laser wavelength stabilization technology. The relationship between grating bandwidth and compensated system performance becomes weaker for a longer span lengths. This is because, with the fiber dispersion exactly canceled, the significance of the ABFG dispersion slope becomes greater for longer lengths. A metric for the significance of

Fig. 10. Bandwidth of a trapezoidal ABFG [defined in (20)] as a function of grating length and apodization. This grating has max = 1000 m01 :

Fig. 11. The significance of ABFG dispersion slope as a function of grating length and apodization. This grating has max = 1000 m01 :

ABFG dispersion slope is the product Bit Rate

(27)

is expressed in sec3 . The larger the greater where the impact of the residual ABFG dispersion slope and the greater the eye-closure penalty. This can be seen in Fig. 11. Fig. 12 displays the dependence of the eye-closure penalty on the link length (which is proportional to the link dispersion) for a given ABFG. This figure shows that the ability of the ABFG to compensate longer link lengths becomes increasingly limited by its dispersion slope. The longer the length, the closer the ABFG must be operated to its reflection band edge and hence the larger its dispersion slope. This is shown in Fig. 13, where the metric defined in (26) has been plotted as a function of link length for which the dispersion is compensated by the ABFG. Therefore, to compensate longer links with a small system penalty, longer gratings must be used. , Turning to the dependence on the grating strength Fig. 14 shows the dependence of the eye-closure penalty on for a given link length of compensated fiber. This figure shows that a diminishing improvement is attained beyond a certain grating strength. This is fortunate because writing very strong gratings presents several problems. In

HINTON: DISPERSION COMPENSATION USING BRAGG FIBER GRATINGS

Fig. 12. The eye-closure penalty as a function of link length for a trapezoidal ABFG with L 50 cm, max () = 1000 m01 ; and Frc = 0:1.

=

2343

Fig. 14. The eye-closure penalty as a function of grating strength (max (z ) ); for gratings of length 50 cm (solid line) and 40 cm (dashed line), both with apodization, Frc = 0:1.

f

g

where total grating length, Frc fraction of the grating speed of allocated to apodization at each end (see Fig. 7), chirp parameter given by [cf. (8)] light, and (29) (signal bandIn (28) we require, among other things, width) for the grating to provide good system performance [10]. The amount of dispersion compensated by the grating is (30) Fig. 13. The metric d0 (!0 ) (Bit Rate)3 which results from operating the ABFG closer to the reflection band edge to dispersion compensate longer link lengths.

2

particular, saturation in the writing process will result in distortion of the grating fringe profile. VI. COMPARISON WITH OPERATION IN REFLECTION The design of chirped Bragg fiber gratings for dispersion compensation while operating in reflection has been the subject of some consideration [10], [11]. Of particular interest is the relationship between apodization profile, length of fiber compensated, and grating length. For gratings operating in reflection, the key properties of the device are the grating length, apodization profile, the grating strength, and the grating chirp. The relationship between these properties can be understood using the effective medium method [7] which gives, as an of a chirped BFG estimate for the useful bandwidth, Frc

(28)

These equations can be used to understand some of the numerical results presented in [10]. In particular, it can be , bandwidth , and seen that for a given grating length reflectivity , different apodization profiles (Frc) will and hence different amounts of require different values of or length of fiber compensated dispersion compensation [10]. For a given apodization profile, reflectivity, and bandwidth, the dispersion increases with grating length. To attain a certain bandwidth, shorter gratings require larger chirp. Also, for a given bandwidth, apodization profile and reflectivity, using a longer grating allows compensation of a longer link length To make a comparison between dispersion compensation in reflection and transmission, it can be seen that the dependence of the bandwidth and grating dispersion on the grating parameters is more direct for operation in reflection than transmission. This is seen by comparing (30) with (16) and noting that constant, Also, for a given operational for is independent wavelength, (21) shows that the bandwidth of grating length for operation in transmission. This is in contrast to (28) for operation in reflection.

2344

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 16, NO. 12, DECEMBER 1998

1

Fig. 15. Plot of eye-closure penalty against bandwidth  as defined in (20) for a 10-Gb/s system for a range of trapezoidal grating lengths and (signal bandwidth). A more appropriate requirement on signal apodization lengths. The trend shows that low eye-closure penalties require  bandwidth  is given in (22).

For a trapezoidal ABFG, the bandwidth can be calculated in a closed form for detunings from the reflection band edge out. In (31), shown on the bottom of the page, It can be seen that this form is also independent of grating length. Although the length of the grating does not influence the grating bandwidth, it does impact the grating dispersion required to directly. This, in turn, determines the offset compensate a given length of fiber. From (31), it can be seen that the bandwidth is dependent upon To compare a trapezoidal grating operating in transmission with a chirped grating operating in reflection, it must be noted that the definition of bandwidth given in (28) is somewhat given in (28) gives different to that given in (20). The a direct indication of the signal bandwidth over which the chirped grating will give good system performance [10]. In given in (20) corresponds to the bandwidth contrast, the at which the magnitude of the dispersion slope term in (23) is approximately equal to that of dispersion. Of course, since the dispersion is canceled, the dispersion slope may still have a major impact on the signal. This is shown in Fig. 15, in which the eye-closure penalty is plotted against bandwidth using the data plotted in Figs. 9 and 10. This plot is for a 10-Gb/s signal, and it can be seen that the eye closure Ghz (signal is approximately 1 dB only for bandwidth). For a direct comparison of bandwidths between operating in (22) is a more appropriate in reflection and transmission, definition of bandwidth for operation in transmission. The nature of this inequality makes direct comparison of band-

1



widths between the two types of compensators difficult. A more meaningful comparison is the eye-closure penalty as a function of length for a given grating. Fig. 16 is a plot of eye-closure penalty against fiber link length for a range of system bit rates for a given grating (trapezoidal profile with cm, Frc m It can be seen that operation in transmission is quite effective at 2.5 Gb/s, however at higher bit rates, operation in reflection can attain much longer distances for a given grating length [10]. These results indicate that operation in transmission is more Gb/s rather than suited to WDM systems based on TDM higher rate systems.

VII. OPERATIONAL ISSUES There are several key advantages of using ABFG’s in transmission rather than in reflection. First, operation in transmission removes the need for a circulator to inject the signal into the compensator. The circulator introduces extra losses, complexity, and cost into the system. In contrast, a grating in transmission is simply spliced into the link without the need for any extra optics. An ABFG compensator operating in transmission can be inserted into the system in either orientation. A chirped, or ramped, BFG must be inserted into the system in a specific orientation, otherwise it will not operate as required. Because operation in transmission means the optical field does not interact with the grating as strongly as operation in

Frc Frc

Frc Frc

Frc

(31)

HINTON: DISPERSION COMPENSATION USING BRAGG FIBER GRATINGS

Fig. 16.

2345

Impact of bit rate system on eye-closure penalty for an ABFG dispersion compensator operating in transmission over a range of fiber link lengths.

reflection, imperfections in the grating have a reduced impact on the dispersion-compensating properties of the grating. This can be seen from the asymptotic forms (18) and (19). The imperfections in gratings which operate in reflection feed directly through to its dispersion compensation properties [4]. Despite these advantages, the above results also indicate some of the constraints ABFG’s pose if they are to be used for dispersion compensation, while operating in transmission. One is the high sensitivity of these devices to wavelength drift. Another is the length of the grating required to compensate long haul, high bit-rate systems. The simulations presented above indicate that a 50-cm grating is required to compensate 100 km of standard fiber. Such a grating must be housed in a suitable environment. The grating must be temperature controlled and cannot be bent or spooled. Temperature stability is essential to keep the at the required value. detuning Another issue which must be considered is the ability to fabricate these gratings. Although gratings have been fabricated and utilized for dispersion compensation in transmission [5], rather than being smooth as displayed in Fig. 5, the fabricated device displayed some ripple in its dispersion profile. It is most likely that this ripple arose from noise in the grating writing process producing small resonant structures within the grating. These structures will cause resonant cavity effects in transmission near the reflection band edge. It is yet to be seen whether all of these technological issues can be resolved. However, it is worth noting that several of these issues must also be resolved before chirped BFG’s, operating in reflection, can be deployed commercially to compensate high-speed, high-dispersion optical systems. From the above results, it can be seen that an appropriately designed and fabricated 50 cm ABFG, operating in transmission, can compensate 100 km of standard fiber with a power penalty 1 dB. Gratings of lengths up to 1 m have been fabricated [12], therefore 50-cm length devices are already feasible. VIII. CONCLUSIONS The dispersion compensation properties of ABFG’s, operating in transmission, have been analyzed using a numerical

system simulation. The results of this simulation have shown that these devices have several intrinsic limitations. In particular, bandwidth and sensitivity to carrier frequency drift and environmental conditions. For long-haul systems, ABFG’s operating in transmission are more suited to -Gb/s systems rather than higher rate TDM systems. However, provided long gratings can be fabricated, these devices have several key advantages over chirped Bragg gratings which operate in reflection. ACKNOWLEDGMENT The author would like to acknowledge the helpful discussions with T. Stephens, J. Arkwright, G. Dhosi, and F. Ruhl. Permission to publish this material was granted by the Director of Research, Telstra Research Laboratories. REFERENCES [1] I. Bennion, J. Williams, L. Zhang, K. Sugden, and N. Doran, “UVwritten in-fiber Bragg gratings,” Optic. Quantum Electron., vol. 28, p. 93, 1996. [2] R. Laming, W. Loh, M. Cole, M. Zervas, K. Enner, and V. Gusmeroli, “Fiber gratings for dispersion compensation,” in Tech. Dig. OFC’97, 1997, p. 234. [3] T. Stephens, P. Krug, Z. Brodzeli, G. Dhosi, and F. Ouellette, “257 km transmission at 10 Gbit/s in nondispersion shifted fiber using an unchirped 81 mm long fiber Bragg dispersion compensator,” Electron. Lett., vol. 31, p. 1091, 1995. [4] K. Hinton, “Ramped un-chirped fiber gratings for dispersion compensation,” J. Lightwave Technol., vol. 15, p. 1411, Aug. , 1997. [5] B. Eggleton, T. Stephens, P. Krug, G. Dhosi, Z. Brodzeli, and F. Ouellette, “Dispersion compensation over 100 km at 10 Gbit/s using a Bragg grating in transmission,” Electron. Lett., vol. 32, p. 1610, 1996. [6] K. Hinton, “Dispersion compensation using Bragg fiber gratings in transmission,” in Proc. 21st Australian Conf. Optical Fiber Technology, ACOFT ’96, p. 41. [7] L. Polladian, “Graphical and WKM analysis on nonuniform Bragg gratings,” Phys. Rev. E, vol. 48, p. 4758, no. 6, 1993. [8] F. Ouellette, “Limits of chirped pulse compression with an unchirped Bragg grating filter,” Appl. Opt., vol. 29, p. 4826, 1990. [9] N. Litchinitser, B. Eggleton, and D. Patterson, “Fiber Bragg gratings for dispersion compensation in ttrnsmission: Theoretical model and design criteria for nearly ideal pulse recompression,” J. Lightwave Technol., vol. 15, p. 1303, Aug. 1997. [10] K. Ennser, M. Zervas, and R. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron., vol. 34, p. 770, May 1998.

2346

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 16, NO. 12, DECEMBER 1998

[11] D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol., vol. 14, p. 2581, Nov. 1996. [12] R. Kayshyap, A. Ellis, D. Malyon, H. Froehich, A. Swanton, and 10 Gb/s simultaneous dispersion D. Armes, “Eight wavelength compensation over 100 km singlemode fiber using a single 10 nm bandwidth 1.3 m long super-step-chirped fiber Bragg grating with a continuous delay of 13.5 ns,” submitted for publication.

2

Kerry Hinton was born in Adelaide, Australia, in 1955. He received the Honors degree in electrical engineering and Masters degree in mathematical sciences from the University of Adelaide, Australia, in 1977 and 1981, respectively. He received the Ph.D. degree in theoretical physics (in the field of quantum field theory in curved spacetimes) from the University of NewcastleUpon-Tyne, U.K., and the Diploma degree in industrial relations from the Newcastle-Upon-Tyne Polytechnic, U.K., in 1984. He joined the Telstra Research Laboratories, Victoria, Australia, in September 1984 and is currently working upon analytical and numerical modeling of optical systems and components.