## Abstract

This work focuses on the design and engineering of metropolitan area optical networks for multicast session provisioning. Specifically, the impact of polarization-dependent gain/loss of optical components in coordination with other physical layer impairments is investigated for the first time for several optical multicast algorithms and switch designs. Performance results indicate that the conventional probabilistic handling of PDG/PDL is not practical in this case, requiring a more refined and computationally efficient interaction between physical and control layers.

© 2014 Optical Society of America

## 1. Introduction

Optical multicasting is receiving considerable attention from the service providers because of emerging applications that can potentially utilize this feature, such as interactive distance learning, video-teleconferencing, movie broadcasts, and others. Such bandwidth-intensive multicast applications can be supported in the optical domain by utilizing the inherent light-splitting capability of multicast-capable optical switches that use optical splitters to split the signal to multiple destinations. Recent work on optical multicasting with quality-of-transmission (QoT) considerations included light-tree routing approaches for multicasting that used physical layer constraints (PLIs) through the Q-factor [1]. Specifically, in [1] it was shown that by taking into account the noise contributions, budgeting for other physical layer effects, and calculating the Q-factor as opposed to just the optical power, which was previously performed in [2], it significantly improved blocking probability for multicast connections. Along these lines, in [3], a more detailed optical node engineering was investigated, and in [4] the effect of transmitter/receiver (TX/RX) availability and type (fixed/tunable) was added to the above methodology.

In this work, the aforementioned research is expanded to include modeling of polarization-dependent gain/loss (PDG/PDL) for the optical components. This model is then implemented on a number of optical multicast routing algorithms for three specific case studies; two that provide the boundaries and one realistic scenario in terms of the polarization alignment of the various components in the multicast sessions. Several works exist in the literature relevant to the PDG/PDL effect, dealing with quantifying the PDG/PDL induced penalties through statistical methods [5–9] and with developing new techniques aiming at compensating the PDG/PDL effect [10, 11]. However, this is the first time that the effect of PDG/PDL is investigated in conjunction with other physical layer impairments for optical multicasting. Performance results indicate a significant performance variation in terms of blocking probability for the multicast connections utilizing typical component values of PDL/PDG, for several optical multicast algorithms and optical node designs. Previous approaches at optical multicasting while considering the PLIs [2] that did not take into account the PDG/PDL effect would result in the provisioning of a significant number of paths that would not be provisioned when these new constraints are accounted for. This fact clearly signifies that another level of refined and, more importantly, computationally-efficient interaction between the physical and control layers is crucial for multicast connection provisioning.

## 2. PDL/PDG model and physical layer system simulation

PDL and PDG are defined as the maximum variation of power (in dB) among all possible polarizations. In the case of an amplifier this translates into gain variation (PDG) whereas for any other component (excluding fiber) this manifests itself as variation of insertion loss (PDL). A statistical Monte Carlo model was used in [9] to calculate the PDL/PDG-induced channel power divergence for different sections of a worst-case path in an optical network but that work did not include any computation for the control layer multicast provisioning aspect. The latter makes the aforementioned problem computationally intractable, if the statistical approach is used. The proposed approach in this work starts with a simple PDL/PDG model that is based on the work presented in [12]. For each amplifier/component, the PDL/PDG model assumes polarization beam splitters/combiners and two simple amplifier/component models, one for each max/min gain/loss polarization axis as shown in Figs. 1(a) and 1(b). As an example, if an amplifier has a specification for 17.5dB gain and 1dB PDG, this translates into the following: a gain of 17.5dB for the case when the signal enters aligned to the maximum gain polarization axis and 16.5dB for the case when the signal enters aligned to the minimum gain polarization axis. The same is true for other components, where typical specification values of insertion losses refer to the min-loss polarization axis.

The maximum gain and minimum loss of each amplifier/component are the values around which the multicast network is engineered, as described in [3, 4]. As a result, the induced PDG/PDL results in a system deviation from the target performance point.

Figures 2(a) and 2(b) present the basic optical node designs that are used in this work to obtain the performance results. These architectures, discussed in [3, 4], consist of passive splitters, variable optical attenuators (VOAs), optical switches, EDFAs, and semiconductor optical amplifiers (SOAs) that act as gates and are used to turn off the signal for the outputs that are not part of the multicast tree. At the add/drop ports, different designs are used, including one with a fixed number of TXs/RXs, with their total number equal to the number of working wavelengths *N* times the degree of the node *M* [shown in Fig. 2(a)], and one with tunable TXs/RXs where the total number of TXs/RXs is equal to the number of wavelengths in the system *N* [shown in Fig. 2(b)]. For the second design, a switch is also needed at both the receiver and transmitter sides with an add/drop capability of fifty percent on the total number of working wavelengths. This is a realistic percentage of wavelengths to be accessed in a system at each given node. As a result, the dimensions of such a switch are (*NXM*) × (0.5*NXM*). Thus, in the tunable TXs/RXs case, only 50% of the possible input ports can be dropped at the same time [4]. For both optical node designs, the network is engineered in a generic way as described in [3, 4], where +5dBm power is launched into each span of optical fiber, with the pre-amplifiers designed to increase power to +7dBm coming into the optical node, and post-amplifiers bring the power back to +7dBm (to further improve the overall node noise figure) as the signal is launched into the next fiber span.

Insertion losses for muxes/demuxes, switches, SOAs, and VOAs are based on commercially available components and noise figures for the pre- and post-EDFAs are calculated from a look-up table whose information is based on commercial amplifier designs and depend on the amplifier gain at each instance [4]. Typical commercial PDG and PDL values for the various components are shown in Table 1. The ASE noise being un-polarized is averaged over the two polarization axes of the model in Fig. 1. In order to determine the Q-value for each call, a baseline system Q-value is first calculated based on the signal and noise terms, assuming 10Gbps bit rate, a pre-amplified photodiode, a wavelength division multiplexing (WDM) system with 32 wavelengths spaced at 100GHz, and certain budgeting for the various physical layer effects [4]. In this work, a Q-threshold of 8.5dB is assumed for the system, corresponding to a BER of 10^{−12} which is a standard bit error rate currently used in the operation of optical networks. Insertion loss is calculated based on the maximum loss that a signal can experience passing through a given node. In particular, the determining factor is the node splitting loss which varies depending on the node fanout (e.g., in the network utilized, the maximum fanout of any node is 6, and by adding one more for add/drop purposes, the maximum power split used is 7). Based on this, VOAs are engineered to set the total power of each signal to a specific worst-case value so that power equalization is achieved at the input of the post-EDFA.

The introduction of PDG/PDL is done as a perturbation to the above engineering scenario for three case studies: (1) best-case PDG/PDL; the assumption here is that the max-gain/min-loss polarization axes of all components are aligned with the signal, (2) worst-case PDG/PDL; the assumption here is that the min-gain/max-loss polarization axes of all components are aligned with the signal, and (3) a random orientation of the signal and component PDG/PDL axes is assumed over a sample of 1, 000 possible polarizations (note that no significant result variability was obtained for up to 5, 000 samples of randomized polarizations). As the algorithm “runs” through each path to calculate the signal and noise powers, it has to make some assumption on the values of gain and insertion loss that it has to use for each component. Depending on the above case studies, it will assume the max gain/min loss or the min gain/max loss or a third (in-between) case based on the random polarization orientation. Since the nodes are assumed to have amplifiers that compensate exactly each fiber span loss, the introduction of PDG/PDL will slightly disturb that assumption, thus causing some variability in the performance on top of the ASE noise accumulation effect. In addition to the amplifier gain, the amplifier noise figure (NF) will also change. The calculation of the effective noise figure (NF) of an amplifier based on the model of Fig. 1 has a value half a dB higher than the usually quoted NF which always corresponds to the max-gain/min-loss polarization axes scenario. This is a direct result of the NF definition (SNR in/SNR out). Thus, for example, a typical industry amplifier that has a NF of 6dB and PDG of 1dB will produce an effective NF of 6.5dB (6dB for the max-gain/min loss polarization and 7dB for the min gain/max loss polarization).

The first two case studies are meant to provide the boundaries of the performance in the multicast network and although quite unlikely in large multicast group sizes, they have been shown to be realistic for cascades of up to five amplifiers [8] (note that the diameter of the network used in the simulations in this work consists of 13 EDFAs). Case study 3 assumes a more realistic randomized scenario which is computationally manageable as opposed to the methodology used in [9] which is intractable in the context of the physical/control layer interactions described here.

## 3. Heuristic algorithms for QoT multicasting

The well-known Steiner Tree (ST) heuristic is initially used as the basis to build a multicast tree. The cost used for each link is the physical distance of the link since the goal is to try and improve the Q-factor at the destination nodes. Several heuristics were also derived to take into account the physical layer effects described above. In our previous work in [1] the balanced light-tree Q heuristic (BLT Q) was developed that introduces the Q-factor figure in the power calculation of [2] (heuristic BLT) when constructing each multicast tree. In addition, the BLT Q tolerance heuristic algorithm was also introduced that considers a minimum acceptable Q-tolerance value, *q*, and tries to maximize the Q-factor only at the destination nodes where *Q* < *q*.

## 4. Performance results

To evaluate the performance of the three different case studies described above in the presence of PDL/PDG, a typical metro network is used consisting of 50 nodes and 98 bidirectional links with an average node degree of 3.9 and an average distance between the links of 60 km. A dynamic traffic model is used where multicast sessions arrive at each node according to a Poisson process and the holding time is exponentially distributed with a unit mean (with a load of 100 Erlangs used for all simulation runs). In each simulation 5, 000 requests are generated for each multicast group size for a total of 40, 000 multicast requests and the results are averaged over five simulation runs. For all simulation scenarios there was a very small variation between the maximum and the minimum values obtained between the five simulation runs, with this variation decreasing to infinitesimal values for large multicast group sizes. It should also be noted here that for all the simulations performed in this work a small number of wavelengths (32) is chosen so as to avoid extensive simulation running times. However, the usage of a small number of wavelengths tends to cause significant blocking due to the unavailability of resources (as shown below), something that in practice can be avoided as nowadays a much larger number of wavelengths per fiber is deployed by the network operators.

Figure 3(a) shows the blocking probability versus the multicast group size for the node design shown in Fig. 2(a) and covers case studies (1) – (2) above, i.e., best-case scenario when the signal/component polarizations are aligned to the maximum gain/minimum loss polarization axes (upper set of curves) and worst-case scenario when they are aligned to the minimum gain/maximum loss polarization axes (lower set of curves). The performance of the three routing heuristic algorithms (Steiner Tree (ST), BLT, and BLT Q tolerance, with the Q-tolerance value set at 8.5dB, corresponding to a BER of 10^{−12}) is similar for the best-case scenario simply because the blocking probability is quite low (< 1%). As expected, for the worst-case scenario the performance is a lot worse for all three heuristics compared to the best-case scenario, with BLT Q 8.5 performing significantly better than the rest. Clearly, our proposed BLT Q 8.5 heuristic is the only one in this case that produces acceptable blocking probability results for small multicast group sizes. Figure 3(b) shows case study (3) where the polarization axes are randomly varied as discussed before. The performance is now significantly improved compared to case study (2), with BLT Q 8.5 again significantly outperforming the rest of the heuristics.

Considering now only the best routing heuristic (BLT Q 8.5), a large variability in the blocking probability is observed [Fig. 4(a)] for the three case studies previously described as well as a fourth case where the PDG/PDL effect is not taken into consideration. For example, for a group size of 22, the best case, which is very close to the no PDG/PDL results of [3, 4], exhibits less than 1% blocking whereas the worst-case has an unacceptable 33% blocking. The more realistic random polarization scenario yields a blocking of about 7%, still a significant variation from the results of [3, 4].

In Fig. 4(a), it is interesting to note that the results for the case of no PDG/PDL (when the effect is not studied as was done in [3, 4]) are slightly worse in terms of blocking probability compared to the best-case with PDG/PDL. This is due to the un-polarized ASE noise which experiences less net gain than the signal in the best-case scenario (becoming partially polarized), and thus results in slightly higher OSNR and less blocked calls. This effect was also observed in [12]. Figure 4(b) shows performance results (again for BLT Q 8.5) for the case of the optical node architecture which includes tunable TXs/RXs in the network as shown in Fig. 2(b) (with the available number of TXs/RXs equal to the number of wavelengths in the system, *N*) [3]. These results again demonstrate a large blocking variability among the three cases.

Simulation results also show that the blocking probability in the case of fixed TXs/RXs [Fig. 4(a)] is less compared to the blocking probability in the case of tunable TXs/RXs [Fig. 4(b)], as in the first case the blocking probability caused due to a low Q-factor is not significant, compared to the latter case. Specifically, in the fixed TXs/RXs case the worst-case node loss is less compared to the case with tunable components, where switches are also used in the design of the add/drop ports. Additionally, in the case of fixed TXs/RXs there is more flexibility in the network to assign wavelengths to the multicast connections as there are more TXs/RXs available for wavelength assignment, whereas in the case of tunable TXs/RXs, only 50% of the possible input ports can be dropped at the same time.

It must be noted that in all scenarios investigated the VOAs in the optical node designs, as shown in Fig. 2, could not handle PDG/PDL as they were not engineered taking this effect into consideration. Clearly, the results indicate that the effect of PDL/PDG cannot be ignored when engineering an optical network for provisioning multicast connections, as for typical PDL/PDG component values a large performance variation is introduced. Provisioning for a worst-case scenario, which may be the easiest engineering solution will produce unacceptable results in terms of blocking. However, the worst-case approach is not always an obvious choice. Polarization mode dispersion (PMD) has been shown to be treated using a maxwellian distribution approach in system simulations in the past. This has an inherent averaging approach and is not a worst-case scenario. Thus, looking at the average and best-case scenarios and obtaining the variation in blocking that results utilizing different routing algorithms is a very interesting comparison. To our knowledge, this is the first time that the effect of PDG/PDL has been introduced to the study of control and transport layer interactions for multicast applications in optical networks.

Even in cases where worst-case is used and shown to fail, there is significant insight to be gained. The results of the work in [8] showed that for a small number of cascaded amplifiers in an access network (about 5 SOAs in that case), the system designer could not move away from the worst-case assumption, i.e., assume that the signal polarization is perfectly aligned with the min-gain polarizations of all amplifiers. However, for longer amplifier cascades it was shown that it was possible to use creative five-9s techniques to move away from the aforementioned assumption and ease on the performance requirements. This work is the first to show the impact of the two extreme assumptions (i.e., max gain/min loss and the worst-case min gain/max loss) on the performance of a multicast network. Utilizing the results obtained from this work, for metro networks with a large number of amplifier cascades, the range of such an effect is now known. These performance ranges can then be utilized by other techniques to treat such an effect, such as the use of wavelength selective switches (WSSs) as described below.

Current work involves providing an efficient solution to the above problem by utilizing multicast-capable WSSs. A WSS is a software-controlled optical component that selects specific wavelengths from either the Input or the Add ports and routes these to the Output port for transmission to the next network node. Even though WSSs utilize different switching technologies, in general, all available switching engines are able to control wavelength-separated beams using one or more of the following: angle, phase, polarization, and displacement. In conjunction with its switching capabilities, the WSS can also perform signal attenuation, thus providing channel equalization with no additional cost or complexity [13, 14]. A generic WSS implementation is shown in Fig. 5 [13]. The function of each module in this generic WSS implementation is as follows: (a) The input and output optics are used to steer the light beam in and out of the device. Typically, the input/output optics can be fiber and micro lens arrays; (b) The beam/polarization optics are used to shape the collimated beam and introduce polarization diversity, typically using prisms, cylinders, birefringent crystals and waveplates, if needed, at the input and output of the device. Polarization diversity is needed, for example, when the switching engine of the WSS is based on Liquid Crystals (LCs), where the input beam is separated into its orthogonal polarization states and then one of them is rotated so that they are both incident on the LC cell in identical fixed polarization states. The LC cell is then used in conjunction with a polarization splitter to convert a change in polarization state into a displacement or an angle; (c) The dispersion system (e.g., a common grating which is polarization sensitive and thus requires incident light to be of a specific polarization) is then used, as WSSs operate on light that has been dispersed in wavelength without the requirement that the dispersed light be physically demultiplexed into separate ports; (d) Finally, the switching engine manipulates wavelengths from one port to another by changing the phase, polarization, angle or position of a wavelength-dispersed optical beam. Some of the technologies that can be used to achieve this function are MEMS, liquid crystal, and PLZT. Note that the optical components needed for the implementation of the WSS (excluding the dispersion system) are dependent on the choice of the technology of the switching engine. For example, if MEMS technology is used for the switching engine then there is no need for polarization optics, as was the case discussed above, when LC-based technology is used [13, 14].

Therefore, the next step in our work will be to propose a solution using dynamic equalization based on WSSs placed at specific locations in the network. Looking at the average, best- and worst-case PDG/PDL scenarios described in this work will then be relevant in determining an efficient placement of the WSSs.

## 5. Conclusion

The introduction of PDG/PDL in the optical multicast routing heuristics using PLIs has demonstrated an increased complexity that renders its conventional probabilistic handling not practical. It also shows the need for more refined and computationally-efficient interaction between the physical and control layers. The randomized axes approach which is the most realistic in such a system shows significant rise in the blocking probability of multicast connections compared to the studies where no PDG/PDL effects were included. Nevertheless, our BLT Q tolerance multicast routing heuristic, which accounts for the PLIs, outperforms routing approaches that either do not consider them entirely or only account for the power budget. Clearly, another layer of interaction is needed between the physical and control layers, involving dynamic gain equalizers, that is the subject of ongoing work.

## Acknowledgments

This work was supported by the Cyprus Research Promotion Foundation’s Framework Programme for Research, Technological Development and Innovation (DESMI 2008), co-funded by the Republic of Cyprus and the European Regional Development Fund, and specifically under Grant Project New Infrastructure/Strategic/0308/26.

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