Spatial division multiplexing has been proposed as an option for further capacity increase of transmission fibers. Application of this concept is attractive only, if cost and energy efficient implementations can be found. In this work, optical amplification and optical filter based signal processing concepts are investigated. Deployment of multi mode fibers as the waveguide type for erbium doped fiber amplifiers potentially offers cost and energy efficiency advantages compared to using multi core fibers in preamplifier as well as booster stages. Additional advantages can be gained from optimization of the amplifier module design. Together with transponder design optimizations, they can increase the attractiveness of inverse spatial multiplexing, which is proposed as an intermediate step. Signal processing based on adaptive passive optical filters offers an alternative approach for the separation of channels at the receiver which have experienced mode coupling along the link. With this optical filter based approach, fiber capacity can potentially be increased faster and more energy efficiently than with solutions relying solely on electronic signal processing.
©2011 Optical Society of America
The traffic volume in optical metro and core networks has grown exponentially in the past over multiple decades [1–4]. This growth was enabled by advances in optical transmission technology, especially higher bit rate transponders and wavelength division multiplexing (WDM) with increasing channel numbers per installed fiber. However, the technological advances did not just provide more capacity but also an economically viable solution due to cost savings. A new technology was considered cost efficient, if it provides 4 times the capacity at 2 to 2.5 times the cost.
Traffic demand will most likely continue to grow exponentially in the coming years fueled by stronger utilization of existing services or emergence of new services such as cloud computing, web based personal data storage, and higher definition video streams. From an economical perspective, a network capacity increase following the demand can only be realized, if new technologies provide solutions for capacity growth with less than proportional capital expenditures (CAPEX).
In addition to the CAPEX constraints, even stronger than in the past, attention has to be paid to energy efficiency. The energy consumption of the internet has already reached a considerable fraction of the overall energy consumption, at least in developed countries . An increase of the energy required for data transport proportional to the exponential traffic growth cannot be sustained for many coming years. Moreover, the expenses carriers have to spend for electrical energy supply has reached a significant fraction of the overall operational expenditures (OPEX). Technologies deployed for future capacity increase have to feature enhanced energy efficiency - from an environmental as well as from a cost perspective.
Spatial division multiplexing (SDM) based on multi core or multi-mode fibers has been proposed to increase the transmission capacity per fiber [6–8]. It has a potential to enable capacity increase well beyond the limits foreseen for enhanced bandwidth efficiency by higher order modulation or more WDM channels by additional wavelength bands. Several promising demonstrations concerning the feasibility of SDM have been published recently [9–13]. However, the potential for fiber capacity increase can only be transformed into commercially viable solutions, if cost and energy efficient implementations are found. In case the realization is available in time, further capacity increase by SDM can be more attractive than capacity increase by enhanced bandwidth efficiency or additional wavelength bands.
In this contribution, several approaches are proposed for a cost and energy efficient realization of spatial division multiplexing. They encompass novel concepts for optical amplification, integration of optical components, and optical filter based signal processing.
2. Optical amplifier concepts
The tremendous success of the application of optical amplification to long haul high capacity data transport resulted from the capability of optical amplifiers to process multiple channels simultaneously. Combined with WDM, a single inline optical amplifier module can replace 100 optoelectronic regenerators (OEO) or even more. As such an amplifier module usually features less cost and power consumption than a single regenerator for bitrates of 10 Gbit/s and above, inline optical amplification provides a much more cost and energy efficient approach than optoelectronic regeneration.
It is challenging to repeat this success, if SDM is combined with WDM for even more capacity per fiber, as the benchmark is set quite high. Single mode WDM amplifiers have been optimized at least over a decade and reached a decent cost position and energy efficiency. In order to enable less than proportional cost and power consumption scaling, an amplifier module capable of both SDM and WDM operation (SWAM) has to cost less and has to consume less power than the respective number of single mode WDM amplifiers for the same number of WDM channel groups. The potential to achieve this goal differs for the preamplifier stage and the booster stage of an inline amplifier.
2.1. Preamplifier stage
The main purpose of the preamplifier stage is to provide low noise amplification of the signals at the output of a transmission fiber span. In case of lumped amplification, this requirement can only be met with a high level of inversion of the microsystems providing the stimulated emission. For the purpose of lumped single mode WDM amplification, erbium doped fiber amplifiers (EDFA) are most widely deployed due to their decent noise performance, superior pump efficiency, low cost and good compatibility with fiber based transmission. They also offer the most promising option for the realization of lumped amplification being capable of combining SDM with WDM operation.
The pump power density Sp in W/m2 which is required for a high level of inversion or excitation ratio η can be estimated from a simplified rate equation model :
In Eq. (1), N2 denotes the population density in 1/m3 of the Er3+ ions in the upper laser level 4I13/2, Nt the total ion concentration in 1/m3, h Planck's constant, ν the frequency of the pump radiation in Hz, A21 the spontaneous emission rate in 1/s from the upper laser level to the ground level 4I15/2, and σ13 the absorption cross section in m2 for the pump radiation with a wavelength around 980 nm. Decent noise performance with noise figures close to the quantum limit can be achieved with an excitation ratio η of approx. 0.95. For a typical spontaneous emission rate A21 = 83 1/s, corresponding to a lifetime of the upper laser level of 12 ms and an absorption cross section for the pump radiation of σ13 = 2.3 x 10−25 m2, a pump power density Sp = 1.6 GW/m2 is required for this level of inversion.
The total pump power required to achieve an appropriate level of inversion depends on the active fiber type and design. Multi single mode core (MSC) fibers and fibers with a single multi-mode core (SMC) have been proposed as transmission fiber types for the realization of spatial multiplexing. It is not clear yet, which fiber type will provide better performance for long haul transmission. For good compatibility of components along the link, the active fiber type of the amplifier modules should coincide with the transmission fiber type. Consequently, MSC as well as SMC fiber types should be considered as active fibers for SWAM.
A suitable design of the individual cores of the MSC active fiber should exhibit a small effective mode area Aeff,c for good pump power efficiency. An Aeff,c = 20 µm2, similar to the value of typical active fibers for single mode amplifiers, is proposed here. With this effective mode area, each core of the multi core fiber requires an individual pump power of Pi = Sp x Aeff,c = 32 mW for the above mentioned excitation ratio η = 0.95. The total pump power scales proportionally to the number of cores Mc. For example, an MSC fiber with Mc = 7 cores requires a total pump power of Mc x Pi = 224 mW.
The small effective mode area of the individual cores of the multi core active fiber can only be achieved with a numerical aperture NA which is higher than typical values for transmission fibers. In the latter fibers, numerical apertures are kept small in order to achieve low fiber attenuation. The resulting larger effective mode field area helps to reduce the impact of nonlinear effects.
Active fibers in amplifier modules for wavelengths of approx. 1530 nm to 1565 nm, the C-band, exhibit a typical length in the order of a few 10 m. As such fibers are much shorter than transmission fiber spans, neither the requirement for low attenuation nor the one for reduced nonlinear effects does apply with the same strength. Numerical apertures of active fibers can feature increased NA values compared to transmission fibers, resulting in smaller effective mode field areas and higher spatial pump power densities for a given pump power.
The same optimization can be applied to the design of the active fiber type with a single multi-mode core. For example, with a numerical aperture of NA = 0.23 and an effective mode field area of Aeff = 85 µm2, the proposed SMC active fiber is capable of guiding Mm = 6 modes with a high spatial power density for a given pump power. Each of these modes can propagate in two orthogonal polarizations, resulting in the same transmission capacity as a multi core fiber with 6 cores. In such a multi-mode fiber, a total pump power of Pt = Sp x Aeff = 136 mW is required to achieve the above mentioned excitation ratio η = 0.95. A multi core fiber with the core design specified above would need a total power of Pt = 6 x 32 mW = 192 mW.
The smaller pump power required for the multi-mode fiber results from the denser packing of modes compared to the multi core single mode fiber. This trend can also be observed in Fig. 1 , which plots the required total pump power versus the number of modes or capacity for both fiber types. In case of the multi core fiber, geometrical considerations suggest suitable core numbers of 1, 7, 19, and 37, with respective total pump powers of 32 mW, 224 mW, 608 mW, and 1,184 mW, proportional to the number of cores.
For the multi-mode fiber, determination of the required total pump power for a given number of modes Mm is less straight forward. The values plotted in the figure were determined using the following algorithm. The number of modes guided by a fiber with a given core radius a in m can be estimated using the fiber parameter V and the phase parameter B with the following definitions:15,16].
For the assessment of the number of modes Mm plotted on the horizontal axis in Fig. 1, a mode was counted as guided, if the phase parameter B of the mode exceeds a value of 0.2. The core radius a was determined from the respective V parameter. The effective mode field area, which is usually slightly larger than the core area for the specified phase parameter, was calculated from the mode field distribution for the respective core radius and numerical aperture.
For step index fibers which are guiding many modes, the number of modes guided by the core Kc can be estimated from the V parameter using the equation: Kc = V 2/2 . In this equation, each of the two orthogonal polarizations of a given mode is counted as an individual mode. As mentioned above, each single mode core in a multi core fiber is capable of guiding a mode in two orthogonal polarizations. Hence, the number of modes Kc guided by the core of the multi-mode fiber has to be divided by a factor of two for compatibility of the mode count numbers of MSC and SMC fibers with respect to total fiber capacity:
With the definition of the fiber parameter V, the number of modes can be expressed as a function of the core radius, the vacuum wavelength and the numerical aperture:
The effective mode area Aeff can be calculated from the effective mode radius aeff with the equation Aeff = π aeff 2. The effective mode field radius aeff is usually slightly different from the core radius: aeff = (1 + ε) a with |ε|<<1. These expressions together with Eq. (4) solved for a2 enable to calculate the total power required for the excitation ratio η = 0.95 of the erbium ions:
Equation (5) provides an approximation for the total power required for pumping a multi-mode fiber active fiber as a function of the number of modes with the goal to achieve a high level of inversion. According to Eq. (5), the necessary total pump power is proportional to the number of modes, as in case of the multi core fiber.
The respective proportionality factor between the total pump power and the number of modes for the multi core fiber can be estimated as follows. The total pump power equals the product of the number of cores Mc, the effective mode field area of a single core Aeff,c and the power density Sp required for strong inversion:
In the chosen notation, an index “c” is added to all variables describing the multi core fiber that differ from the multi-mode fiber case. With the relation between the core radius ac and the effective mode field radius aeff,c = (1+εc) ac, the effective mode field area can be formulated as:
By replacing the core radius ac by the definition of the fiber parameter Vc for a single core solved for ac and inserting (7) into (6), the equation for the total pump power follows as:
The major difference between the proportionality factor of the multi-mode fiber and the multi core fiber is the term Vc2/4. For decent guiding of the fundamental mode, the fiber parameter of a single mode fiber is usually selected in the range from 1.8 to 2.2. This range applies to the signal radiation with a wavelength in the C-band. According to its definition, the fiber parameter V depends on wavelength. Consequently, the shorter wavelength around 980 nm of the pump radiation results in a higher value of the Vc parameter for the pump radiation in the active fiber. For example, a fiber with a V parameter of 2.0 at the signal wavelength of 1550 nm exhibits a Vc = 3.16 at the pump wavelength of 980 nm, if material dispersion is neglected.
In consequence, the term Vc2/4 will usually contribute a factor larger than one. As a result, the same amount of inversion in the multi core fiber requires more total pump power than in the multi-mode fiber for the same number of modes. Another advantage for the multi-mode fiber may be gained from an ε smaller than εc due to stronger guiding of the modes by the large core. The overall difference in total pump power for the two fiber types can be influenced by fiber design, but it will probably not exceed 50%. With these observations, the multi-mode active fiber qualifies as the better fiber type for SDM amplification from a pump power efficiency perspective, but not by far.
2.2. Booster stage
As shown in the previous section, deploying multi-mode fibers as the active fiber in a preamplifier stage offers the potential for better energy efficiency than using multi core fibers. The overall cost and energy efficiency of the amplifier module will also depend on the realization of the booster stage. The main purpose of the booster stage is to provide sufficient output power for the following elements. In this amplifier stage, power conversion efficiency (PCE) plays a more important role than the level of inversion.
The importance of PCE for booster stages capable of combining SDM with WDM is aggravated compared to single mode amplifiers due to the increase of total output power. Terrestrial long haul systems are operating with typical channel powers launched into the following span of 0 dBm. With a channel number of 100, the total output power of the amplifier card amounts to 20 dBm. Due to insertion losses between the output of the active fiber and the amplifier card of approx. 2 dB introduced by the pump signal combiner for backward pumping, an isolator, and a tap coupler for output power monitoring found in many designs, the power level relevant for the power conversion efficiency is rather 22 dBm or 158 mW.
Assuming that multi core and multi-mode transmission fibers will tolerate at least the same launch power levels per channel as currently deployed fibers, amplifier modules capable of combining SDM with WDM have to provide total output powers equal to the power of a WDM channel group times the number of modes. For example, an amplifier module for 7 modes has to achieve a total output power in excess of 1,100 mW assuming a power of 158 mW of a single WDM channel group. Good PCE is indispensible with such high total output power levels.
Several design choices for the booster stage such as the pump wavelength or direct versus cladding pumping have an impact on the optical power conversion efficiency. Pumping the core of the erbium doped fiber directly with a wavelength of 1480 nm provides better efficiency compared to pumping at 980 nm due to the smaller amount of energy wasted in the conversion process from a pump to a signal photon. A PCE of 80% could be achieved experimentally by pumping at 1480 nm , while pumping at 980 nm resulted in a PCE of 56% . However, the better optical power conversion efficiency of 1480 nm pumping can be offset by a better electrical to optical power conversion efficiency of 980 nm pump laser modules.
The inferior optical power conversion efficiency of typically less than 20% achieved when using cladding pumping of a single doped core can also be compensated by a better electrical to optical power conversion efficiency of laser diode modules. Broad stripe laterally multi-mode laser modules used for cladding pumping in many cases do not require a thermo electric cooler (TEC). Omitting the electrical power for TEC cooling helps to improve the power conversion efficiency of cladding pumping. Together with the higher output power of broad stripe laser modules compared to single mode laser modules and the capability to combine the output power of multiple pump modules by using a multi-mode coupler, cladding pumping is well suited for EDFAs with very high output powers. Single mode amplifier modules with output power in excess of 1 W typically use cladding pumping for the booster stage.
In the SDM case, multi-mode active fibers are potentially better suited for pumping with multi-mode laser modules than multi core active fibers. A large spacing is required between the individual cores of a multi core fiber to avoid excessive coupling between cores. Due to this spacing and the additional spacing needed between the outer cores and the interface between the inner and the outer cladding, very large diameters of the inner cladding are required for cladding pumping. The large diameter can lead to excess loss and problems to distribute the pump power density equally across all doped cores.
The cores of multi-mode active fibers can potentially be pumped directly using laterally multi-mode laser modules. But even if cladding pumping is required, the smaller diameter of the inner cladding and the single core around the fiber axis will help to avoid excess loss and equalize the pump power density in the core.
One additional aspect has to be considered. Cladding pumped amplifier modules are usually equipped with pump lasers emitting at wavelengths shorter than 1000 nm. In this wavelength range, the gain spectrum of the erbium ions is sensitive to the pump spectral power distribution due to pump induced inhomogeneity [20,21]. A flat gain spectrum required for good WDM performance may be difficult to achieve over a wide module operating temperature range without wavelength stabilization, which in turn may require temperature stabilization. Either heating can be applied to keep the pump laser chips at a stable maximum temperature or TEC cooling for stabilization at a medium temperature. In any case, additional electrical energy is required. This would significantly deteriorate the energy efficiency of cladding pumping for amplifier modules capable of combining SDM with WDM operation.
An option to circumvent the pump wavelength sensitivity issue would be to use broad stripe lasers emitting at 1480 nm. However, such lasers are not available and it is not clear, whether they can be realized without cooling. With these constraints, the best way to pump multi core active fibers may be direct pumping of the core with single mode pump lasers emitting at 1480 nm. This approach takes advantage of the better PCE achieved with the longer pump wavelength and avoids issues with pump wavelength sensitivity. The core of multi-mode active fibers can be pumped directly with laterally multi-mode pump lasers emitting at 1480 nm, if they become available. It is difficult to predict, which active fiber type will achieve a better energy efficiency in the booster stage. Given the fact that multi-mode pumping is better suited for high power applications, the fiber type with a single multi-mode core potentially has advantages.
2.3. Amplifier module design considerations
The previous two sections were mainly focusing on a comparison between the multi core and the multi-mode active fibers types with respect to the realization of preamplifier and booster stages. As mentioned in the introduction, an amplifier module capable of combining SDM with WDM operation has to be more cost and energy effective than multiple single mode WDM amplifiers for the same number of WDM channel groups. The requirement to process multiple WDM channel groups in a single amplifier module offers opportunities for module design optimization.
In recent years, single mode WDM amplifier module designers were confronted with the fact that 980 nm TEC cooled pump laser modules provided more maximum output power than required for pumping a single active fiber section. As the pump lasers contribute a large share of the amplifier module cost and power consumption, solutions were developed to deploy the output signal of a single pump laser for pumping multiple active fiber sections by splitting the output power. This path can be followed further to optimize the cost and power consumption of amplifier modules.
Figure 2 shows a block diagram of an amplifier module using pump laser sharing between SDM modes. The chosen example features multi core input and output fibers with 7 cores each. Amplification is provided by Er3+-doped multi core fibers with the same number of cores. Each core is pumped directly by pump radiation delivered to the WDM coupler in 7 single core fibers. The preamplifier stage is pumped codirectionally at the wavelength of 980 nm for good noise performance, whereas the booster stage is pumped counterdirectionally at 1480 nm for good power conversion efficiency.
Pumping at 1480 nm stimulates transitions of the Er3+-ions between the ground state 4I15/2, which coincides with the lower laser energy level, and the upper laser level 4I13/2. For very high spatial pump power densities in this wavelength range, the ratio of the population densities of the upper laser level and the lower laser level approaches the ratio of the absorption and the emission cross section at the pump wavelength. As this ratio is not much larger than one, pumping the first stage of an amplifier at wavelengths around 1480 nm cannot deplete the lower laser level completely, resulting in incomplete inversion and higher noise figures than in the quantum limited case.
Pumping at 980 nm excites the upper laser level via a transition from the ground state to the level 4I11/2, followed by a fast nonradiative, phonon assisted decay from this level to the upper laser level. As pump radiation in the wavelength range around 980 nm cannot stimulate transitions from the upper laser level to the ground state, the latter can be depleted nearly completely by high spatial pump power densities. In consequence, pumping amplifier input stages in this wavelength range can achieve very high levels of inversion and noise figures very close to the quantum limit.
However, the better noise performance achievable by pumping at 980 nm compared to pumping at 1480 nm comes with the drawback of less optical power conversion efficiency. During the fast nonradiative decay from the level 4I11/2 to the upper laser level, phonons are excited and the corresponding energy is no longer available for the amplification of signal radiation. The energy difference lost when a pump photon at the wavelength 980 nm is converted into a signal photon at 1550 nm is significantly larger than in case of pumping at 1480 nm. Due to the smaller photon energy difference, pumping at 1480 nm achieves better optical power conversion efficiency and is potentially better suited for amplifier stages with high signal output power requirements.
The pump radiation for the preamplifier stage in Fig. 2 is generated by two pump laser modules emitting at a wavelength of 980 nm. The output signals of the two modules are combined and split into 7 equal parts with equal power by a power combiner. The latter is connected to the WDM coupler by 7 single core fibers. Due to the higher output power requirements of the booster stage, three 1480 nm pump laser modules are necessary to generate the pump radiation for this stage. It is also combined by a power combiner and delivered to the WDM coupler in individual single core fibers.
The advantage of the approach to share pump laser module is given by the ability to supply a given number of cores with pump power generated by a smaller number of pump laser modules. A smaller number of modules with high output power can be more cost and energy efficient than an individual pump laser for each core. For further optimization of energy efficiency, the chips of the pump lasers can be mounted on a common TEC cooler. Alternatively, multiple pump lasers can be integrated on a single chip together with the power combiner and splitter.
One major drawback of the pump sharing approach consists of the loss of individual pump power control. The cores of the doped multi core fiber potentially have to process unequal numbers of WDM channels. If the amplifier stage is operated in saturation, different pump powers are required for the individual cores to equalize the channel powers at the output of the stage. This drawback applies more to the booster stage than to the preamplifier stage. The preamplifier stage can be operated in the linear regime for good noise performance without too much impact on power efficiency.
For the booster stage, the capability to control the pump powers of the individual cores is more desirable. Even if the pump power for each core is generated by a separate pump laser to enable individual power control, the pump lasers can still be integrated on a common chip and utilize a common TEC for cost and energy efficiency optimization.
3. Inverse spatial multiplexing
An important factor contributing to the success of WDM was the ability to use already installed transmission fibers to transport multiple channels instead of a single one. SDM using multi core or multi-mode transmission fibers does not provide the same advantage. So far, there are no multi-mode or multi core fibers installed in cables for long haul links. In submarine networks, it is common practice to install the transmission fiber together with the other network elements along the link. So installation of new fiber types for the implementation of SDM in submarine links would not contribute a major issue.
In terrestrial networks, new links are usually deployed using already installed fibers for cost reasons. The budget carriers have to allocate for the installation of new cables is usually much higher than the cost of the network elements for a given link. If SDM cannot be deployed without the installation of new cables for the entire link, it will be very difficult to find cost efficient ways for capacity increase by SDM compared to adding another WDM system of the same type using already installed dark fibers.
The discussions on amplifier module design options in the previous section have shown that adding the capability to process multiple WDM channel groups in a single module can lead to cost reductions and improved energy efficiency compared to a solution with individual amplifier modules for each WDM channel group. A similar optimization can be applied to transponder cards. Current transponder cards usually provide a single transmitter and a single receiver for the line side. Infinera has demonstrated the option to combine multiple transmitters and multiple receivers for different WDM wavelengths on a single card by using monolithic integration [22,23]. The same concept could be used to realize transponders for multiple SDM channels with the same wavelength.
The approach to use the same wavelength in all transmitters on the transponder card has the advantage that the optical signal for the transmitter can be generated by a single laser source. The output signal from this source can be split by a power splitter and coupled into an array of modulators for the individual SDM channels. If the laser itself does not provide sufficient output power for the modulators, a semiconductor optical amplifier (SOA) can be inserted between the laser and the power splitter. All these functions can potentially be integrated on a single InP chip. If the line side receivers in the SDM transponder use coherent detection, a single laser can be deployed to generate the local oscillator signals for all receivers again by power splitting.
Such module optimizations potentially enable the realization of transponder cards for multiple SDM channels with the same wavelength with lower cost and better energy efficiency than individual transponders for the same number of channels. Together with the amplifier modules capable of processing multiple WDM channel groups, they can be deployed to realize a concept which may be called inverse spatial multiplexing. A block diagram of a system implementing this concept is depicted in Fig. 3 .
The main idea of inverse spatial multiplexing is to benefit from amplifier and transponder optimization targeting at SDM without the need to install multi-mode or multi core transmission fibers. The SDM transponders in Fig. 3 and the amplifiers capable of combining SDM and WDM operation are equipped with single core and single mode interface fibers. These fibers carry a single channel in case of the transponders and a single WDM channel group in case of the amplifiers. Wavelength multiplexing and demultiplexing can be performed with single mode components already available today. Even more importantly, the output signals of the amplifier modules can be coupled into single mode and single core transmission fibers already installed in the ground.
The concept of inverse multiplexing is proposed as an intermediate step before installed multi-mode or multi core transmission fibers become available in sufficient quantity to realize entire links. The immense cost of installing new fibers for an entire core network can be shared by adding at least a few multi-mode or multi core fiber in any cable that has to be installed for other reasons. Examples are the intention of carriers to replace older fibers with undesirable characteristics for high bit rates or to provide more capacity in hot spots of the network where all installed fibers are already in use.
With a decent amount of MSC or SMC fibers already in place due to other installation activities, closing the gaps for an entire SDM link may require the installation of a few additional spans only. Once an entire network is equipped with sufficient fibers capable of carrying multiple modes in a single cladding, adoption of the concept of SDM can be extended from the transponders and amplifiers to the transmission fiber spans to leverage the full benefit of the SDM approach.
4. Optical filter based signal processing
An important factor leading to the success of WDM was the capability to increase fiber capacity without relying on progress of electronic or optoelectronic components. Before the deployment of WDM, transmission capacity per fiber was increased by using faster electrical time division multiplexing (ETDM) of a single wavelength carrier. Progressing to higher bit rates required optoelectronic and electronic components with more bandwidth. By using this approach, fiber capacity could be increased on average by a factor of 4 every 4 years.
In contrast, the adoption of WDM resulted in fiber capacity increase by approx. a factor of 10 every 4 years. The speed up in capacity increase was enabled by transmitting additional channels with different wavelengths instead of relying on higher channel bit rates. As a key factor, the multiplexing and demultiplexing of wavelength channels did not depend on progress of electronic components, because it was performed using passive optical filters.
The multiplexing and demultiplexing of modes for spatial division multiplexing can also be performed using passive optical components. In case of multi core fibers, taper structures have been proposed and demonstrated providing the transition between single core fibers and multi core fibers . The transformation between field distributions in single mode and multi-mode fibers can be performed by using spatial light modulators [12,25] or holographic elements . However, there is a noteworthy difference between WDM and SDM. In case of WDM, coupling between wavelength channels can be neglected. Some linear coupling can occur due to insufficient isolation of filter elements and nonlinear coupling due to four wave mixing. Both effects can be suppressed below acceptable limits by appropriate system design.
In case of SDM, linear coupling between channels propagating in different modes at the same wavelength can probably not be neglected. The coupling originates from several sources. Most of them will be present in both transmission fiber types, MSC as well as SMC. For example, both fiber types will exhibit coupling due to bending or fiber axis misalignment in fiber junctions such as splices or optical connectors.
In case of the multi core fiber, a compromise has to be found between fiber capacity and coupling strength. With a given cladding diameter, large fiber capacity requires dense packing of cores. A lot of equipment and components had to be changed or replaced, if diameters of multi core transmission fibers were deviating from the well-established value of 125 µm. Denser packing of the cores increases the coupling due to stronger overlap of the evanescent fields around the cores. Options to implement a faster decay of these fields exist by adaptation of the refractive index profile [26,27]. However, flexibility is limited due to a potential deterioration of dispersion characteristics and sensitivity to nonlinear effects compared to standard single mode fibers. Accepting some linear coupling along the link and separation of the channels at the output of the link probably provides a better solution than implementing demanding measures for sufficient suppression of coupling.
Coupling of modes along the link exhibits similar characteristics as coupling of polarization channels in case of polarization multiplexing (PolMUX). Concepts based on multiple input / multiple output (MIMO) processing are deployed successfully in digital coherent receivers to separate the channels. In these receivers, the required signal processing functions are performed digitally in the electrical domain. Figure 4 shows a block diagram of the so called butterfly equalizer structure consisting of four couplers and four filters, which are capable of decoupling the channels transmitted in two orthogonal polarizations.
Behind the receiver input, the incoming signal is split into two signals with orthogonal polarizations using a polarization beam splitter (PBS). Due to the random polarization rotations and coupling along the link, the signals in each output arm of the PBS are typically containing spectral components from both PolMUX channels. These signals are coherently detected and transformed into the digital domain by analog to digital converters (ADC), preserving amplitude and phase information.
After some initial processing for other functions, the signal originating from one output arm of the PBS is fed to the input of the upper coupler on the left hand side in Fig. 4, the signal from the other arm to the lower coupler. Each coupler splits the signal into two equal parts. One part is delivered to the upper coupler on the right hand side, the other to the lower one. The main purpose of the filters is to enable separation of the PolMUX channels by constructive and destructive interference of spectral components in the couplers on the right hand side. For example, amplitude and phase responses H1 and H3 of filters 1 and 3 will be adjusted to achieve constructive interference in coupler 3 of spectral components belonging to PolMUX channel 1 and destructive interference of spectral components from channel 2. Vice versa, PolMUX channel 2 is recovered in coupler 4 by constructive interference of its own spectral components and destructive interference of spectral components from the unwanted channel 1.
The concept to separate signal spectra transmitted over multiple paths by constructive interference of spectral components belonging to the wanted signal and destructive interference of all other spectral components forms an integral part of MIMO processing. It can also be applied to spatial division multiplexed signals which have experienced mode coupling along a transmission link which is equipped with multi mode or multi core fibers. For this purpose, the equalizer structure has to be extended as shown in Fig. 5 .
In the chosen example, two modes with two orthogonal polarizations in each mode are transmitted over a link carrying a total of four space division and polarization division multiplexed channels. Modes and polarizations of the signals received at the output of the link are split and the resulting signals are fed to the inputs of the four couplers on the left hand side in Fig. 5. Each coupler splits the signals into four equal parts and sends them via filters to the four couplers on the right hand side. Filter transfer functions are adjusted to recover one transmitted channel in each coupler by constructive and destructive interference of wanted and unwanted spectral components, respectively. Compared to the butterfly equalizer in Fig. 4, the number of couplers has increased proportionally to the number of channels as has the number of ports of the individual couplers. In contrast, the number of filters experiences a quadratic growth with channel number.
In a digital coherent receiver for bit rates of 100 Gbit/s, finite impulse response (FIR) filters are implemented to provide the filter functions between couplers. Due to the maximum possible clock speeds of available application specific integrated circuits (ASIC) below 1 GHz, signal processing has to be parallelized in order to enable the line speed of 100 Gbit/s. In such parallelized and time discrete digital circuits, loops or backward coupling of signals are very difficult to implement. In consequence, lattice filters of the FIR type are easier to implement than infinite impulse response (IIR) filters, which would provide better performance for the required filter function in the butterfly equalizer .
Implementation of digital coherent receivers for bit rates of 100 Gbit/s stretches the capabilities of currently available ASIC technologies. Additional processing power would be desirable for enhanced processing functions such as nonlinearity compensation or enhanced forward error correction (FEC). Deploying digital signal processing in ASICs for separation of SDM channels would tie the speed of capacity increase enabled by SDM to the progress of ASIC technology. As in the case of WDM, having the capability to add channels without relying on advances in processing speed of electronic circuits would be more desirable.
In addition, the digital signal processing in the receivers of 100 Gbit/s transponders contributes a significant fraction of several 10 W to the overall electrical power consumption. If signal processing effort grows more than proportionally with the number of channels, as in case of the butterfly equalizer filter structures, it will be difficult to increase fiber capacity with less energy required per bit.
Couplers and adaptive transversal filters are also realizable using passive optical components . With this approach, the separation of channels can be shifted from the electrical domain into the optical domain in front of the receivers. Monolithically integrated components offer an option to realize the entire structure of the butterfly equalizer on a single chip. Figure 6 shows an example block diagram of a butterfly equalizer suitable for the separation of polarization and mode multiplexed channels implemented using passive optical components.
The coupling function is provided by multi-mode interference (MMI) couplers, whereas the filtering is performed using adaptive optical transversal filters. Such an equalizer structure would be inserted between the mode demultiplexers and polarization splitters on one side and an array of single polarization receivers for the individual channels on the other side. The filter coefficients of the transversal filters have to be controlled adaptively to follow temporal changes of coupling and polarization rotations along the link. Feedback signals for the filter control can be derived from the receivers using similar algorithms as in case of the equalizer implementation in the digital domain.
The higher flexibility enabled by using optical filters offers the option to deploy IIR filters instead of FIR filters as in the digital case. A block diagram of a potential implementation of an adaptive IIR filter stage is shown in Fig. 7 . The structure consists of a Mach-Zehnder interferometer and a loop resonator. The two phase shifters offer the two degrees of freedom required to adjust the amplitude and the phase response of the filter.
As the required number of filters increases quadratically with the number of polarization and mode multiplexed channels, planar integration of the filters will lead to large chip sizes. Including an additional dimension offers an option for a more compact arrangement of the components in the butterfly equalizer as shown in Fig. 8 . In this example, the couplers on the left hand side are oriented vertically, whereas the couplers on the right hand side are oriented horizontally. With such an arrangement, it is easy to connect each output of a coupler on the left hand side to an input of a different coupler on the right hand side as required for the butterfly equalizer structure.
Moreover, the two dimensional arrangement of filters offers an option to take better advantage of the parallel processing capabilities of optical components. An example for the implementation of the butterfly equalizer structure using parallel optics is shown in Fig. 9 . The coupler functions are provided using planar waveguide devices with MMI couplers. At the coupler outputs and inputs, graded index (GRIN) lenses perform the transformation between signals guided in the waveguides and collimated beams. The beams emitted from the coupler outputs are propagating through arrays of amplitude and phase modulators as known from spatial light modulators.
The resonators required for the IIR filter stages are realized by reflective coating of the modulator array surfaces. The resulting Fabry-Perot filter structures enable realizing a similar filter response as the loop resonators in the planar example. If the amplitude and phase modulators are based on an electrooptic effect, total power consumption for the adaptive filter control can potentially be kept very low.
The proposed concept offers an energy efficient approach for the realization of the butterfly equalizer. The filter structure is capable of providing the MIMO processing functions required for the separation of the mode and polarization multiplexed SDM channels which have experienced coupling during propagation along the link. The proposed signal processing based on adaptive passive optical components does not rely on advances in electronic processing capabilities. Therefore, it potentially enables faster capacity increase than digital signal processing in the electrical domain. Last but not least, signal processing based on passive optical filters can deploy the more powerful IIR filter type.
5. Summary and conclusions
Concepts were investigated for a cost and energy efficient realization of spatial division multiplexing with a focus on optical amplification and optical filter based signal processing. With respect to the active fiber type deployed for erbium doped amplification, fibers with a single multi-mode core were found to require less total pump power than multi core fibers for low noise preamplification of the same number of modes. The multi-mode fiber type also has a higher potential for pump power efficiency in the booster stage due to its better compatibility with multi-mode pumping.
Further potential for improving the energy efficiency of amplifier modules for spatial multiplexing was identified in the module design. Sharing of available output power from high power pump laser modules by power splitting and integration of multiple pump lasers on a single thermo electric cooler can help to reduce cost and total electrical power consumption compared to separate amplifier modules for the same number of modes. These optimizations of amplifier modules together with optimization of transponders such as integration of components as well as sharing of lasers for the generation of the signal radiation increase the attractiveness of deploying spatial division multiplexing. It can even be advantageous to deploy SDM amplifiers and transponders with non-SDM fibers. This concept called inverse spatial multiplexing is proposed as an intermediate step, before installed multi core or multi-mode transmission fibers become available in sufficient quantities for the realization of entire terrestrial long haul links.
In transmission systems based on spans equipped with multi core or multi-mode fiber, the issue of coupling between modes has to be addressed. Suppressing the coupling below acceptable limits offers one option. Another option is given by the separation of channels at the output of the link by MIMO processing. A signal processing approach based on adaptive passive optical filters is proposed for this function. This approach leverages the parallel processing capabilities of optical components. It has a potential to enable a faster and more energy efficient capacity increase by spatial division multiplexing than MIMO processing in the electronic domain.
Spatial division multiplexing can be combined with higher channel bit rates enabled by the progress of electronic and optoelectronic components the same way as wavelength division multiplexing was combined with faster ETDM for higher fiber capacity. If cost and energy efficient implementations of SDM such as the ones proposed in this work can be realized, they will open a path for a faster and more efficient increase of fiber capacity than a solution based on the progress of electronic components alone.
The author would like to thank Klaus Petermann and Stefan Warm from Technische Universitaet Berlin as well as Stephan Pachnicke from Technische Universitaet Dortmund for fruitful discussions.
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