Wavelength Dependence of Modal Bandwidth of Multimode Fibers for High Data Rate Transmission and Its Implications

: Vertical-cavity surface-emitting laser (VCSEL)-based transmission over multimode fiber (MMF) has achieved data rates of 100G per lane and is progressing towards 200G per lane. Recently, high-data-rate MMFs derived from OM3 and OM4 have been proposed. These fibers exhibit higher effective modal bandwidths at 910 nm, leading to a different wavelength dependence compared to conventional OM3 and OM4 MMFs. Understanding the wavelength dependence of these fibers is crucial to address their utilization in a broader range of applications. Through Monte Carlo simulations, we have obtained the low-end boundary of the effective modal bandwidths (EMBs) for these fibers, revealing capability improvements over the existing OM3 and OM4. The high-data-rate OM4 performs the same as or better than OM5 from 840 nm to 920 nm, while also showing a high bandwidth for the 850–870 nm wavelength window, favoring VCSELs with center wavelengths shifted toward 860 nm. We also obtained the link bandwidth, which includes both modal bandwidth and chromatic dispersion contributions, and the transmission reaches for various types of transceivers. We find that for both high-data-rate OM3 and high-data-rate OM4, the link bandwidth stays above the value at 850 nm until around 910 nm, delivering a similar transmission performance from 850 to 910 nm without declining towards longer wavelengths, unlike the standard OM3 and OM4. This characteristic favors a wider range of wavelength choices for VCSELs and enables optimal deployments for various applications.


Introduction
Multimode fibers (MMFs) have been extensively employed for short-reach communications, such as within buildings, campuses, or data centers [1,2].MMFs, used with vertical-cavity surface-emitting lasers (VCSELs), form a system suitable for short-reach applications spanning distances up to 100 m or more.VCSELs offer cost-effective manufacturing and a lower power consumption when compared to traditional single-mode lasers, making them an economical and energy-efficient choice for short-range communications.In contrast to single-mode fibers, MMFs boast a large core diameter and high numerical aperture, enabling the use of lower-cost VCSEL light sources and connectors between fibers.
The past decade has witnessed a rapid advancement in optical transmission technology, fueled by the explosive growth in data traffic and the soaring demand for cloud computing services in data centers [3].The single-lane data rates have undergone a remarkable evolution, transitioning from 10G to 25G and further to 100G.The rise of artificial intelligence (AI) and graphics processing unit (GPU)-based computing has indeed catalyzed this acceleration in data rate increases, and the latest GPU architectures are now paving the way towards 200G speeds [4].has a higher EMB of 4700 MHz•km at 850 nm.They were standardized in 2002 and 2009, respectively.OM5 is a sub-category of OM4, sharing the same EMB at 850 nm but with an additional EMB requirement of 2470 MHz•km at 953 nm, which is the longest wavelength supported by shortwave-wavelength division multiplexing (SWDM) technology [8].OM5 was first specified by Telecommunications Industry Association(TIA) in 2016 as TIA-492AAAE [15], followed by International Electrotechnical Commission(IEC) in 2017 [16].
As mentioned in the Introduction, to address the needs of high data rate transmission, we have proposed the concept of 'HDR MMFs' for future-ready 100G-per-lane multimode applications.Essentially, 'HDR MMFs' are defined by re-categorizing a subset of OM3 or OM4 fibers.The EMB values of 'HDR MMF' are specified in Table 1 and are defined at two wavelengths of interest: 850 nm and 910 nm for 100G-per-lane transmission.Therefore, these fibers can support VCSEL transceivers involving either an 850 nm wavelength only or both 850 nm and 910 nm wavelengths, with targeted transmission reaches of 80 m and 100 m, respectively.

Generation of Refractive Index Profiles for Monte Carlo Simulation
The relative refractive index profile, or delta profile of an MMF with a graded-index profile, is often referred to as the alpha profile.It takes the following form: where ∆ 0 is the relative refractive index in the center of the core defined as ∆ 0 = n 2 0 − n 2 1 / 2n 2 0 , wherein n 0 is the refractive index in the center of the core, n 1 is the refractive index of the cladding, a is the core radius, and α is the profile shape parameter, also called the alpha parameter or the alpha shape parameter.As illustrated in Figure 1, the fiber has a 1% core delta, and a ~50 µm core diameter.Note that when the alpha value is two, the profile takes a parabolic shape.The MMF is most optimized when the alpha parameter has a value of around 2.1, at which point the MMF's modal bandwidth peaks at a wavelength near 850 nm.A trench with a negative delta value is placed outside the core to enhance the bending performance of the fiber [23].The cladding is typically pure silica and is used as a reference with zero delta value.
Due to the nature of MMF fabrication, each individual MMF differs from another.The idea behind the current work is to generate an ensemble of MMFs with a range of variation types that can occur in real fibers.Figure 2 schematically shows the wavelength dependence of modal bandwidth for an individual MMF.The MMF follows a curve that can reach a peak or maximal modal bandwidth at a wavelength called the peak wavelength.Each MMF can have its own maximum modal bandwidth value and peak wavelength value.Therefore, they can have different modal bandwidth values at a given wavelength of interest, such as 850 nm.An MMF with an ideal refractive index profile can have a higher maximum bandwidth than other MMFs, but its peak wavelength can vary over a range, resulting in different wavelength dependence for each individual MMF.Below, we describe several types of variations that can affect the fiber modal bandwidth and its wavelength dependence.Due to the nature of MMF fabrication, each individual MMF differs from another The idea behind the current work is to generate an ensemble of MMFs with a range o variation types that can occur in real fibers.Figure 2 schematically shows the wavelength dependence of modal bandwidth for an individual MMF.The MMF follows a curve tha can reach a peak or maximal modal bandwidth at a wavelength called the peak wave length.Each MMF can have its own maximum modal bandwidth value and peak wave length value.Therefore, they can have different modal bandwidth values at a given wave length of interest, such as 850 nm.An MMF with an ideal refractive index profile can have a higher maximum bandwidth than other MMFs, but its peak wavelength can vary ove a range, resulting in different wavelength dependence for each individual MMF.Below we describe several types of variations that can affect the fiber modal bandwidth and it wavelength dependence.One of the most important parameters to consider is the alpha parameter, as it deter mines where the fiber modal bandwidth peaks, as illustrated in Figure 2. When the alpha parameter is altered, the wavelength at which the modal bandwidth peaks also changes Therefore, to emulate actual fiber, we would alter the alpha value within a range of ove  Due to the nature of MMF fabrication, each individual MMF differs from another The idea behind the current work is to generate an ensemble of MMFs with a range o variation types that can occur in real fibers.Figure 2 schematically shows the wavelength dependence of modal bandwidth for an individual MMF.The MMF follows a curve tha can reach a peak or maximal modal bandwidth at a wavelength called the peak wave length.Each MMF can have its own maximum modal bandwidth value and peak wave length value.Therefore, they can have different modal bandwidth values at a given wave length of interest, such as 850 nm.An MMF with an ideal refractive index profile can have a higher maximum bandwidth than other MMFs, but its peak wavelength can vary over a range, resulting in different wavelength dependence for each individual MMF.Below we describe several types of variations that can affect the fiber modal bandwidth and its wavelength dependence.One of the most important parameters to consider is the alpha parameter, as it deter mines where the fiber modal bandwidth peaks, as illustrated in Figure 2. When the alpha parameter is altered, the wavelength at which the modal bandwidth peaks also changes Therefore, to emulate actual fiber, we would alter the alpha value within a range of over 200 nm. Figure 3 shows the relationship between alpha and peak wavelength.When the alpha value is decreased, the peak wavelength shifts to a higher value.One of the most important parameters to consider is the alpha parameter, as it determines where the fiber modal bandwidth peaks, as illustrated in Figure 2. When the alpha parameter is altered, the wavelength at which the modal bandwidth peaks also changes.Therefore, to emulate actual fiber, we would alter the alpha value within a range of over 200 nm. Figure 3 shows the relationship between alpha and peak wavelength.When the alpha value is decreased, the peak wavelength shifts to a higher value.

Radius (m)
The second type of variation is the fluctuation of the alpha profile itself on top of the perfect alpha profile, which is referred to as non-alpha error.In the modeling, we expand such errors using Fourier series, as follows: In our actual generation of the Monte Carlo data, N is chosen to be six.The second type of variation is the fluctuation of the alpha profile itself on top of the perfect alpha profile, which is referred to as non-alpha error.In the modeling, we expand such errors using Fourier series, as follows: In our actual generation of the Monte Carlo data, N is chosen to be six.Another type of error that can occur in the center portion of the core involves a small spike or dip in the refractive index, leading to split pulses, which can degrade system performance [24].In our modeling, we introduce such errors within the first several microns of the core radius.One last type of error to consider is the variation of the trench.In this case, we generate random offsets in the Monte Carlo data set.Alternatively, one can alter the depth of the trench to achieve similar performance variations.

Wavelength Dependence of EMB of MMFs
Using the refractive index profiles, the EMB of a particular fiber can be obtained from its differential mode delay (DMD) chart, which is the sequence of output pulses resulting from single-mode pulse launches at various radial offsets at the input.In reality, the DMD chart is measured using a DMD bench, while, in our case, it is calculated based on the refractive index profile [25].In the standard, 10 VCSEL launch conditions were used [26], as the modal bandwidth depends on the launch condition.The DMD weight functions associated with the 10 launch conditions are shown in Figure 4. Using the measured DMD chart, the output pulses over ten VCSEL launch conditions are assembled as weighted by alpha shape parameter Another type of error that can occur in the center portion of the core involves a small spike or dip in the refractive index, leading to split pulses, which can degrade system performance [24].In our modeling, we introduce such errors within the first several microns of the core radius.One last type of error to consider is the variation of the trench.In this case, we generate random offsets in the Monte Carlo data set.Alternatively, one can alter the depth of the trench to achieve similar performance variations.

Wavelength Dependence of EMB of MMFs
Using the refractive index profiles, the EMB of a particular fiber can be obtained from its differential mode delay (DMD) chart, which is the sequence of output pulses resulting from single-mode pulse launches at various radial offsets at the input.In reality, the DMD chart is measured using a DMD bench, while, in our case, it is calculated based on the refractive index profile [25].In the standard, 10 VCSEL launch conditions were used [26], as the modal bandwidth depends on the launch condition.The DMD weight functions associated with the 10 launch conditions are shown in Figure 4. Using the measured DMD chart, the output pulses over ten VCSEL launch conditions are assembled as weighted by the ten DMD weight functions.The modal bandwidth associated with each weight or launch condition can be calculated from the 3 dB drop of the frequency response, S 21 , and is referred to as calculated effective modal bandwidth (EMBc).The frequency response of a particular launch condition is calculated from the Fourier transform of the input pulse (P in (t)) and output pulses P out,i (t) as follows: where F (P out,i (t) ) and F (P in (t) )denote the Fourier transform operations of the output pulse and input pulse respectively.The range of launch conditions ensures that essentially all conditions are covered, so the EMB reflects not just the outcome of one launch condition but the modal bandwidth capability of the specific fiber.With the 10 EMBcs obtained, the EMB can be further obtained.We also note that the integration of the DMD weight function over radius, which represents integrated power over radius, is referred to as encircled flux.
The standard requires that, at the 4.5 µm radius, the integrated power is less than 30% of the total power and, at the 19 µm radius, the integrated power is over 86% of the total power.
the EMB can be further obtained.We also note that the integration of the DMD weigh function over radius, which represents integrated power over radius, is referred to as en circled flux.The standard requires that, at the 4.5 m radius, the integrated power is les than 30% of the total power and, at the 19 m radius, the integrated power is over 86% o the total power.In the Monte Carlo study, we generated 10,000 cases of refractive index profiles to cover a wide range of profile variabilities, as described in Section 3.1, with a mixture of al types of profile errors.The magnitude of each type of error was also randomized within a range to yield MMFs with EMB spread over a range of interest.The purpose of the Monte Carlo set is to generate refractive index profiles with various possibilities that can affec the modal bandwidth under different launch conditions.For each wavelength, we calcu lated the EMB from the profiles as described above.By combining all the wavelengths, we can generate the wavelength dependence curve of one individual MMF.However, MMF are primarily categorized as OM3 and OM4, so the interest lies in the low-end values o each type of MMF.IEC 60793-2-10 [16] published the low-end EMB values for OM3 and OM4 over the range of 840 nm to 953 nm.In the simulation presented in the current paper we have repeated the work to ensure that the methodology yields consistent results.Ou main objective, as described in Section 1, is to study the EMB wavelength dependence fo 'HDR MMFs', which are further broken down into 'HDR OM4' and 'HDR OM3'.For mos of the calculations, the low-end EMB values were obtained at the 99.9th percentile, mean ing there is a 0.1% chance that the values can fall below the threshold.We believe this is a reasonable practice, as the truly worst case or lowest value can be overly pessimistic and therefore, not a good representation of the product's practical capability.Later in the  In the Monte Carlo study, we generated 10,000 cases of refractive index profiles to cover a wide range of profile variabilities, as described in Section 3.1, with a mixture of all types of profile errors.The magnitude of each type of error was also randomized within a range to yield MMFs with EMB spread over a range of interest.The purpose of the Monte Carlo set is to generate refractive index profiles with various possibilities that can affect the modal bandwidth under different launch conditions.For each wavelength, we calculated the EMB from the profiles as described above.By combining all the wavelengths, we can generate the wavelength dependence curve of one individual MMF.However, MMFs are primarily categorized as OM3 and OM4, so the interest lies in the low-end values of each type of MMF.IEC 60793-2-10 [16] published the low-end EMB values for OM3 and OM4 over the range of 840 nm to 953 nm.In the simulation presented in the current paper, we have repeated the work to ensure that the methodology yields consistent results.Our main objective, as described in Section 1, is to study the EMB wavelength dependence for 'HDR MMFs', which are further broken down into 'HDR OM4' and 'HDR OM3'.For most of the calculations, the low-end EMB values were obtained at the 99.9th percentile, meaning there is a 0.1% chance that the values can fall below the threshold.We believe this is a reasonable practice, as the truly worst case or lowest value can be overly pessimistic and, therefore, not a good representation of the product's practical capability.Later in the paper, we will discuss the impact of choosing such a percentile to put the results in perspective.In some cases, we will refer to the EMB of a particular type of MMF at its low-end value or 'worst' value without explicitly stating that these are the low-end values.
We first show the EMB of OM4 and OM3 in Figure 5a,b, referring to them as 'IEC OM4' and 'IEC OM3', respectively, as they are based on IEC guidance.The curves with discrete dots were obtained from Monte Carlo simulations for OM4 and OM3.They were labeled as 'Monte Carlo OM4' and 'Monte Carlo OM3' to differentiate them from the IEC-guided OM4 and OM3 EMBs.As the wavelength moves away from 850 nm, the EMB values for both OM4 and OM3 decrease, because the EMB value at 850 nm can be achieved by MMFs with peak wavelengths higher or lower than 850 nm.The agreement between the IEC guidance and the current Monte Carlo simulations is excellent.Note that the low-end EMB values in the simulation were obtained from the 99.9th percentile instead of using the 100th percentile or absolute lowest value, in order to be more realistically aligned with real-world situations.The agreement also gives us confidence that the methodology used in the current work would be valid when applied to 'HDR OM4' and 'HDR OM3'.
by MMFs with peak wavelengths higher or lower than 850 nm.The agreement between the IEC guidance and the current Monte Carlo simulations is excellent.Note that the lowend EMB values in the simulation were obtained from the 99.9th percentile instead of using the 100th percentile or absolute lowest value, in order to be more realistically aligned with real-world situations.The agreement also gives us confidence that the methodology used in the current work would be valid when applied to 'HDR OM4' and 'HDR OM3'.In Figure 6, we show the wavelength dependence of EMB for 'HDR OM4' obtained from the Monte Carlo simulation with a comparison to two related types of MMFs, namely OM4 and OM5.The EMB values for OM4 and OM5 are based on IEC guidance.As mentioned in Section 1, OM5 was established for supporting SWDM-based VCSEL transceivers with the highest wavelength at 953 nm.SWDM is a type of WDM that includes more wavelengths and, therefore, more data traffic within one transceiver, which is in contrast to BiDi transceivers, which use 850 nm and 910 nm.However, in the past decade, BiDi transceivers have seen more widespread use and have now reached the In Figure 6, we show the wavelength dependence of EMB for 'HDR OM4' obtained from the Monte Carlo simulation with a comparison to two related types of MMFs, namely OM4 and OM5.The EMB values for OM4 and OM5 are based on IEC guidance.As mentioned in Section 1, OM5 was established for supporting SWDM-based VCSEL transceivers with the highest wavelength at 953 nm.SWDM is a type of WDM that includes more wavelengths and, therefore, more data traffic within one transceiver, which is in contrast to BiDi transceivers, which use 850 nm and 910 nm.However, in the past decade, BiDi transceivers have seen more widespread use and have now reached the Terabit age [6].MMFs that can align with the underlying transceivers would allow for more economical deployments of such applications in larger volumes.It can be found that the EMB values of 'HDR OM4' are roughly equal to or above those of OM5 from 840 nm to 920 nm.Therefore, it has the same capability as OM5 for the wavelengths of interest for BiDi transceivers.Even for wavelengths from 920 to 953 nm, where the EMB of 'HDR OM4' falls below that of OM5, the EMB values are still significantly better than those of OM4, enabling better transmission reach when SWDM wavelengths are used.On the other hand, OM4's EMB decreases rapidly as the wavelength increases from 850 nm, which explains the limitations encountered for transmission at longer wavelengths, such as those used in BiDi transmission.
BiDi transceivers.Even for wavelengths from 920 to 953 nm, where the EMB of 'HDR OM4' falls below that of OM5, the EMB values are still significantly better than those of OM4, enabling better transmission reach when SWDM wavelengths are used.On the other hand, OM4's EMB decreases rapidly as the wavelength increases from 850 nm, which explains the limitations encountered for transmission at longer wavelengths, such as those used in BiDi transmission.In Figure 7, we show the wavelength dependence of EMB for 'HDR OM3' obtained from the Monte Carlo simulation, as compared to those of OM3 and OM4 based on IEC guidance.The EMBs of 'HDR OM3' over the whole wavelength range are higher than those of OM3, since the EMB at 850 nm is chosen to support an 80 m reach for 100G-perlane transmission.Coupled with the corresponding EMB at 910 nm, the EMB over the entire wavelength range has been increased, not just for the 850 nm and 910 nm wavelengths where the fiber EMBs are defined.Also, when compared to OM4, the EMB of 'HDR OM3' becomes higher, starting at 883 nm.The overall higher EMB over the wavelength range can enable 'HDR OM3' to achieve a system reach of 80 m for 800G BiDi applications, even exceeding the specified reach for OM4 at 70 m, as will be shown in the next section.In Figure 7, we show the wavelength dependence of EMB for 'HDR OM3' obtained from the Monte Carlo simulation, as compared to those of OM3 and OM4 based on IEC guidance.The EMBs of 'HDR OM3' over the whole wavelength range are higher than those of OM3, since the EMB at 850 nm is chosen to support an 80 m reach for 100G-per-lane transmission.Coupled with the corresponding EMB at 910 nm, the EMB over the entire wavelength range has been increased, not just for the 850 nm and 910 nm wavelengths where the fiber EMBs are defined.Also, when compared to OM4, the EMB of 'HDR OM3' becomes higher, starting at 883 nm.The overall higher EMB over the wavelength range can enable 'HDR OM3' to achieve a system reach of 80 m for 800G BiDi applications, even exceeding the specified reach for OM4 at 70 m, as will be shown in the next section.

Wavelength (nm)
In the Monte Carlo simulation presented above in Figures 6 and 7, we have used the 99.9th percentile for obtaining the low-end EMB.We would note that the low-end boundary can be affected by how EMB is distributed.To illustrate how the change in percentile can affect the EMB, we show the results obtained from two thresholds in Figure 8.Some differences are shown for wavelengths between 850 and 900 nm, but smaller differences are observed at higher wavelengths.In particular, in the 99.6th percentile, the EMB of 'HDR OM4' exceeds 4700 MHz•km over the range of 850 nm to 870 nm.The actual low-end EMB values can be fine-tuned to align with realistic situations with the support of actual measurement results.In the Monte Carlo simulation presented above in Figures 6 and 7, we have used the 99.9th percentile for obtaining the low-end EMB.We would note that the low-end boundary can be affected by how EMB is distributed.To illustrate how the change in percentile can affect the EMB, we show the results obtained from two thresholds in Figure 8.Some can affect the EMB, we show the results obtained from two thresholds in Figure 8.Some differences are shown for wavelengths between 850 and 900 nm, but smaller differences are observed at higher wavelengths.In particular, in the 99.6th percentile, the EMB of 'HDR OM4' exceeds 4700 MHz•km over the range of 850 nm to 870 nm.The actual lowend EMB values can be fine-tuned to align with realistic situations with the support of actual measurement results.

The Role of Chromatic Dispersion (CD) and Link Bandwidth
EMB is one important gauge of MMF quality.However, at the link level, the fibercontributed bandwidth also includes chromatic dispersion and laser linewidth-contributed bandwidth [13,24],   .Therefore, the bandwidth at the link level,   , is given by the following equation:

The Role of Chromatic Dispersion (CD) and Link Bandwidth
EMB is one important gauge of MMF quality.However, at the link level, the fibercontributed bandwidth also includes chromatic dispersion and laser linewidth-contributed bandwidth [13,24], BW CD .Therefore, the bandwidth at the link level, BW link , is given by the following equation: BW CD is related to both the chromatic dispersion value and the root mean square (RMS) linewidth [16,27].For most of the VCSEL transmission applications, the RMS linewidth is primarily specified at 0.6 nm, with some specified at different values, such as 0.58 nm and 0.65 nm.Since, currently, the commercially deployed VCSELs are multimoded, the existence of several modes results in a laser linewidth of around 0.6 nm.One future direction of sustaining the VCSEL transmission reach is to reduce the laser linewidth by adopting SM VCSEL [9,28,29], which can reduce the laser linewidth to around 0.1-0.2nm.In Figure 9, we show the CD as a function of wavelength and the corresponding BW CD in the same wavelength range as a standard-based 50 µm-core MMF.It can be observed that, as the wavelength increases, the CD drops, resulting in a higher BW CD .This means that, as the wavelength increases, a lower EMB value is sufficient to achieve the same link bandwidth.Since link bandwidth is the measure that affects the transmission performance, one would resort to its value, not solely to the EMB value, to judge the link performance.The effect of EMB varies depending on the wavelength.

Link Bandwidths of Various MMFs at Lengths of Interest
The standardization of 100G-per-lane VCSEL transmission started with the IEEE 802.3db standard [14], which specifies the required link bandwidth for MMFs.The transmission is broken into two sub-categories, 'SR' and 'VR', wherein the 'SR' type has a longer reach than the 'VR' type.In this paper, unless otherwise specified, we refer to the 'SR' type by default for 100G-per-lane transmission.For 100G-per-lane transmission, the required link bandwidth, taking into account both EMB and CD, is 18 GHz, defined at a 3 dBe drop of the frequency response from zero frequency level.The VCSEL transmission defined by IEEE 802.3db is an 850 nm-only transmission, where the 850 nm window for the 'SR' type is specified to be 844-863 nm.Within this wavelength window, the link bandwidth is required to stay at 18 GHz or above.The same requirement is inherited by Terabit BiDi MSA for its 'SR' type of applications, which further includes the 910 nm wavelength, in addition to an 850 nm wavelength window.'HDR OM3' and 'HDR OM4' were defined to meet 18 GHz in both 850 nm and 910 nm windows.The Monte Carlo study in Section 3 allows us to show the link bandwidth over the entire wavelength range, relative to the 18 GHz requirements for 100G-per-lane applications at a given transmission reach.
moded, the existence of several modes results in a laser linewidth of around 0.6 nm.One future direction of sustaining the VCSEL transmission reach is to reduce the laser linewidth by adopting SM VCSEL [9,28,29], which can reduce the laser linewidth to around 0.1-0.2nm.In Figure 9, we show the CD as a function of wavelength and the correspond ing   in the same wavelength range as a standard-based 50 m-core MMF.It can be observed that, as the wavelength increases, the CD drops, resulting in a higher   .This means that, as the wavelength increases, a lower EMB value is sufficient to achieve the same link bandwidth.Since link bandwidth is the measure that affects the transmission performance, one would resort to its value, not solely to the EMB value, to judge the link performance.The effect of EMB varies depending on the wavelength.

Link Bandwidths of Various MMFs at Lengths of Interest
The standardization of 100G-per-lane VCSEL transmission started with the IEEE 802.3db standard [14], which specifies the required link bandwidth for MMFs.The trans mission is broken into two sub-categories, 'SR' and 'VR', wherein the 'SR' type has a longer reach than the 'VR' type.In this paper, unless otherwise specified, we refer to the 'SR' type by default for 100G-per-lane transmission.For 100G-per-lane transmission, the required link bandwidth, taking into account both EMB and CD, is 18 GHz, defined at a 3 dBe drop of the frequency response from zero frequency level.The VCSEL transmission defined by IEEE 802.3db is an 850 nm-only transmission, where the 850 nm window for the 'SR' type is specified to be 844-863 nm.Within this wavelength window, the link band width is required to stay at 18 GHz or above.The same requirement is inherited by Terabi BiDi MSA for its 'SR' type of applications, which further includes the 910 nm wavelength in addition to an 850 nm wavelength window.'HDR OM3' and 'HDR OM4' were defined to meet 18 GHz in both 850 nm and 910 nm windows.The Monte Carlo study in Section 3 allows us to show the link bandwidth over the entire wavelength range, relative to the 18 GHz requirements for 100G-per-lane applications at a given transmission reach.In Figure 10, we show the link bandwidth for 100 m 'HDR OM4', 100 m OM4, 100 m OM5, and 70 m OM4.The 18 GHz threshold is shown as a dashed line.For both 'HDR OM4' and OM5, the EMB stays above 18 GHz from 844 nm to 910 nm, ensuring that they both meet the link bandwidth requirements for the corresponding transmission reach for different types of transceivers.The drawback of OM4 is that its EMB drops rapidly once the wavelength exceeds 850 nm, and it has insufficient EMB at 910 nm for 100 m transmission.One has to substantially shorten the fiber length to restore the link bandwidth at 910 nm, as shown in the case of 70 m OM4.OM5 also meets the 18 GHz threshold between 844 nm and 910 nm.However, we note that the link bandwidth of 100 m OM5 drops below the critical 18 GHz threshold at wavelength above 910 nm, even though such fiber is specified for holding higher modal bandwidth up to 953 nm.The link bandwidth of 100 m OM5 is insufficient to support 100 m transmission once the wavelength is above 910 nm.Since OM5 was standardized around 2016-2017, predating the IEEE standard 802.3db for 100G per lane, it is not aligned with the 100G-per-lane transmission requirements.This highlights one limitation of OM5.

Wavelength (nm)
In Figure 11, we show the link bandwidth for 80 m 'HDR OM3', 70 m OM3, 45 m OM3, and 70 m OM4.For 80 m 'HDR OM3', the link bandwidth stays above the 18 GHz line from 850 nm to 910 nm, similar to 100 m 'HDR OM4' and 100 m OM5.To bring the link bandwidth back to 18 GHz for OM3 and OM4, their lengths would need to be reduced to 45 m and 70 m, respectively.We also observed that, for 70 m OM3, which has been used for 25 Gbaud transmission, the link bandwidth does not meet the 18 GHz threshold at any wavelength.This highlights the need to define 'HDR OM3' to restore transmission capabilities above 70 m.
the critical 18 GHz threshold at wavelength above 910 nm, even though such fiber is spec ified for holding higher modal bandwidth up to 953 nm.The link bandwidth of 100 m OM5 is insufficient to support 100 m transmission once the wavelength is above 910 nm Since OM5 was standardized around 2016-2017, predating the IEEE standard 802.3dbfo 100G per lane, it is not aligned with the 100G-per-lane transmission requirements.Thi highlights one limitation of OM5.In Figure 11, we show the link bandwidth for 80 m 'HDR OM3', 70 m OM3, 45 m OM3, and 70 m OM4.For 80 m 'HDR OM3', the link bandwidth stays above the 18 GHz line from 850 nm to 910 nm, similar to 100 m 'HDR OM4' and 100 m OM5.To bring the link bandwidth back to 18 GHz for OM3 and OM4, their lengths would need to be reduced to 45 m and 70 m, respectively.We also observed that, for 70 m OM3, which has been used for 25 Gbaud transmission, the link bandwidth does not meet the 18 GHz threshold at any wavelength.This highlights the need to define 'HDR OM3' to restore transmission capa bilities above 70 m.

Transmission Reaches for Various Types of Transceivers
The transmission reach is essentially the maximum length of an MMF that can mee the link bandwidth requirements.Table 2 lists the transmission reach of the transceivers with 100G-per-lane data rates at either the 850 nm or both 850/910 nm wavelength win dows.Note that the focus here is on the 'SR' type of transmission.For the 850 nm window the wavelength range is 844-863 nm, based on both IEEE 802.3db standard and Terabi BiDi MSA, while, for the 910 nm window, the wavelength range is 900-916 nm, based on Terabit BiDi MSA.One can see a notable limitation for OM3 in 400G SR4 and 800G SR8 transmission, as the reach has dropped to 60 m from the 70 m that people have grown accustomed to.The reaches of OM3 and OM4 for 800G SR4.2 or 800G BiDi are 45 m and 70 m, respectively, in contrast to the 70 m and 100 m people are accustomed to.The issue is alleviated with 'HDR OM3' and 'HDR OM4', which reach 80 m and 100 m distances respectively.One subtle detail to note is that using a 0.6 nm RMS linewidth at a 910 nm window would result in the link bandwidth dropping below 18 GHz above 910 nm.This issue has been addressed in the MSA [6] by using a 0.58 nm laser linewidth for the wave length window of 900-916 nm.The calculations in Figures 9 and 10 use 0.6 nm for sim plicity when showing results.When a 0.58 nm laser linewidth is used, the link bandwidth over 900-916 nm would stay above 18 GHz for 100 m 'HDR OM4', 100 m OM5, and 80 m 'HDR OM3'.The fact that 'HDR OM3' can transmit over 80 m at 100G per lane is very

Transmission Reaches for Various Types of Transceivers
The transmission reach is essentially the maximum length of an MMF that can meet the link bandwidth requirements.Table 2 lists the transmission reach of the transceivers with 100G-per-lane data rates at either the 850 nm or both 850/910 nm wavelength windows.Note that the focus here is on the 'SR' type of transmission.For the 850 nm window, the wavelength range is 844-863 nm, based on both IEEE 802.3db standard and Terabit BiDi MSA, while, for the 910 nm window, the wavelength range is 900-916 nm, based on Terabit BiDi MSA.One can see a notable limitation for OM3 in 400G SR4 and 800G SR8 transmission, as the reach has dropped to 60 m from the 70 m that people have grown accustomed to.The reaches of OM3 and OM4 for 800G SR4.2 or 800G BiDi are 45 m and 70 m, respectively, in contrast to the 70 m and 100 m people are accustomed to.The issue is alleviated with 'HDR OM3' and 'HDR OM4', which reach 80 m and 100 m distances, respectively.One subtle detail to note is that using a 0.6 nm RMS linewidth at a 910 nm window would result in the link bandwidth dropping below 18 GHz above 910 nm.This issue has been addressed in the MSA [6] by using a 0.58 nm laser linewidth for the wavelength window of 900-916 nm.The calculations in Figures 9 and 10 use 0.6 nm for simplicity when showing results.When a 0.58 nm laser linewidth is used, the link bandwidth over 900-916 nm would stay above 18 GHz for 100 m 'HDR OM4', 100 m OM5, and 80 m 'HDR OM3'.The fact that 'HDR OM3' can transmit over 80 m at 100G per lane is very attractive, as it not only carries over the benefit of OM3 from the 25 Gbaud age but also exceeds OM4 reach for 800G BiDi.It is especially beneficial for customers requiring 70-80 m distances for the majority of their links.Experimental testing using an 800G BiDi transceiver has also been conducted in [19,20], using 100 m 'HDR OM4' and 80 m 'HDR OM3', respectively, with good transmission performance demonstrated.The 'HDR MMFs' can also serve well for 25 Gbaud-based VCSEL transmission.We list the calculated transmission reaches for various transceivers in Table 3.For 850 nm-based 25G SR, 100G SR4, and 400G SR8 transceivers, 'HDR OM3' can transmit up to 87 m, longer than OM3 at 70 m.For 100G BiDi and 100G SWDM4, 'HDR OM3' can transmit 120 m and 112 m, respectively, even exceeding OM4.For 'HDR OM4', it matches the reach of OM4 and OM5 for 25G SR, 100G SR4, 400G SR8, and 100G BiDi.For 100G SWDM4, 'HDR OM4' has a shorter reach than OM5 at 130 m, but its value is still significantly greater than that of OM4.Since commercially available SWDM-type transceivers are capped at 100G so far, with the underlying data rate at 25G NRZ per wavelength, while other types of transceivers have reached a 100G-per-lane data rate, the value of OM5, with its key strength aligned with a 953 nm EMB, is put in doubt [30,31].VCSEL transmission data rates have increased from 10G to 25G and now reach 100G per wavelength.To fabricate VCSELs with higher bandwidth, indium has been added to the quantum well to improve the differential gain, resulting in the operating wavelength shifting higher [32].This situation has occurred since the adoption of 25 Gbaud VCSEL transceivers.In Figure 12, we show the optical spectrum, as measured from one 850 nm channel of a 400G SR4.2 transceiver (LMQ8811B-PC+ from Hisense, Qingdao, China).Additionally, 400G SR4.2 transceivers adopt two wavelengths around 850 nm and 910 nm, with each channel operating with 50G PAM4 modulation.The center wavelength is 859.5 nm in this case.Although the nominal wavelength for the 850 nm window is defined as 844-863 nm in IEEE 802.3db for 100G per lane, it is known in the industry that, for much of the 850 nm window, 100G VCSELs have center wavelengths around 860 nm, with the range between 850 and 870 nm.The higher range is outside the current 850 nm window defined by the IEEE standard.While accepting this de facto situation, we show that 'HDR MMFs' are ideally positioned for such wavelength shifts of 850 nm VCSELs to maintain desired transmission reaches.In Figure 13, we zoom in on several curves from Figure 10 between 845 and 875 nm.As seen, for OM4, the link bandwidth drops below 18 GHz at 863 nm and beyond.Therefore, for the wavelength range between 863 nm and 870 nm, the transmission reach is below 100 m, with the lowest reach at 870 nm being 96 m.On the other hand, both 100 m 'HDR OM4' and 100 m OM5 retain a link bandwidth above 19 GHz, exceeding the 18 GHz threshold.In addition to the benefits of 'HDR MMFs' for wavelength-shifted VCSELs toward 860 nm, we observe that the link bandwidth for such fibers would stay above the value at 850 nm, ensuring that VCSEL transmission at higher wavelengths would not suffe from lower bandwidth, as is the case for OM3 and OM4.This brings flexibility to VCSEL manufacturing and opens the door to using 'HDR MMFs' for broader benefits over the whole wavelength range from 850 nm to 910 nm, thereby not limited to the two wave lengths at which they are defined.Even at wavelengths above 910 nm, they still have bette bandwidth than OM3 and OM4 while trailing OM5, which can be seen in Figures 9 and  10.Using 'HDR MMFs', transceivers can be implemented at any wavelength between 850 nm and 910 nm, with the benefits of achieving higher data rates for VCSEL transceivers similar to what can be achieved at 850 nm.

Discussion
In this paper, we have studied the wavelength dependence of modal bandwidth fo In addition to the benefits of 'HDR MMFs' for wavelength-shifted VCSELs toward 860 nm, we observe that the link bandwidth for such fibers would stay above the values at 850 nm, ensuring that VCSEL transmission at higher wavelengths would not suffer from lower bandwidth, as is the case for OM3 and OM4.This brings flexibility to VCSEL manufacturing and opens the door to using 'HDR MMFs' for broader benefits over the whole wavelength range from 850 nm to 910 nm, thereby not limited to the two wavelengths at which they are defined.Even at wavelengths above 910 nm, they still have better bandwidth than OM3 and OM4 while trailing OM5, which can be seen in Figures 9 and 10.Using 'HDR MMFs', transceivers can be implemented at any wavelength between 850 nm and 910 nm, with the benefits of achieving higher data rates for VCSEL transceivers, similar to what can be achieved at 850 nm.In addition to the benefits of 'HDR MMFs' for wavelength-shifted VCSELs toward 860 nm, we observe that the link bandwidth for such fibers would stay above the value at 850 nm, ensuring that VCSEL transmission at higher wavelengths would not suffe

Discussion
In this paper, we have studied the wavelength dependence of modal bandwidth for the 'HDR MMFs' we have recently proposed [17][18][19][20][21].We have shown detailed results in terms of EMB and link bandwidth, which are directly tied to transmission performance.The 'HDR MMFs' were proposed to address the needs for VCSEL-based 100G-per-lane transmission over a wide wavelength range, with the highest performance from 850 nm to 910 nm.To better understand the benefits as they relate to wavelength, we discuss and highlight the capabilities from the following perspectives.

•
Benefit for the 850 nm wavelength window: By definition, 'HDR OM3' and 'HDR OM4' are defined at 850 nm and 910 nm wavelengths.However, since we have taken into consideration the limitation of OM3 for 100G-per-lane transmission with a reach of 60 m, we have chosen the 850 nm EMB for 'HDR OM3' to support an 80 m reach.This ensures that 'HDR OM3' can also benefit 850 nm-only applications.It alleviates the issue of OM3's reach dropping below 70 m, a distance that many customers have grown accustomed to and around which many data centers have been designed.• Addressing the wavelength shifting toward 860 nm in 850 nm window: As the VCSEL data rate increases to 100G per lane and will reach 200G per lane very soon, some implementations of VCSELs have shown a shift in the wavelength, more centered around 860 nm instead of 850 nm.The 'HDR MMFs' offer the benefit of having enhanced performance for the entire 850-870 nm wavelength window.Taking into account the CD contribution, the link bandwidth over this wavelength range stays above the level at 850 nm, meeting the high bandwidth demands despite the wavelength shift.

•
Comparison to OM3 and OM4: One major limitation of OM3 and OM4 is that their EMBs decrease rapidly as the wavelength moves away from 850 nm, particularly when moving toward higher wavelengths up to 910 nm.Even though the 850 nm EMBs of these fibers remain adequate in many cases, the limitation at 910 nm restricts their applications for longer wavelength use, including 860 nm-centered applications and BiDi applications involving 850/910 nm dual wavelengths.

•
Enabling VCSELs with more wavelengths: Currently, most VCSELs are implemented at 850 nm and 910 nm, with the exception of SWDM VCSELs, which work up to 953 nm but are so far limited to 100G data rates at the transceiver level.The current study shows that 'HDR MMFs' can have uniform link bandwidths from 850 nm to 910 nm.This opens up the feasibility of implementing VCSELs at any wavelength from 850 nm to 910 nm to achieve similar performance.

•
Benefits for SWDM applications: even though SWDM applications have not been deployed in large volumes like other types of VCSEL transceivers and have not reached higher data rates, 'HDR MMFs' still demonstrate their advantages over OM3 and OM4 by delivering significantly better transmission reaches, although they trail somewhat behind OM5.

•
Comparison to OM5: Unlike OM5, which was defined based on EMBs at 850 nm and 953 nm, 'HDR MMFs' were defined based on EMBs at 850 nm and 910 nm.'HDR OM4' has the same EMBs as OM5 at both 850 nm and 910 nm.The wavelength dependence study in Section 3 shows that 'HDR OM4' has an EMB, from 850 nm to 910 nm, equal to or higher than that of OM5 guided by IEC.This implies that 'HDR OM4' can cover all the needs of OM5 from 850 nm to 910 nm and can be a more cost-effective and higher-volume solution for a wide range of applications using the relevant wavelengths.

Conclusions
VCSEL-based transmission over MMFs has been widely deployed.When the data rate for VCSEL-based transmission reaches 100G per lane, the modal bandwidth of OM3 and OM4 becomes limiting for certain wavelengths.In light of such limitations, we have proposed sub-categories of OM3 and OM4 fibers to address the needs of HDR transmission [17][18][19][20][21].These fibers exhibit a higher EMBs at 910 nm, leading to a different wavelength dependence compared to conventional OM3 and OM4 MMFs.Understanding the wavelength dependence of these fibers is crucial to address their utilization in a broader range of applications.We adopted Monte Carlo simulations as the primary approach for the current study.We have generated refractive index profiles of 10,000 MMFs.By calculating EMB of each fiber over a range of wavelengths of interest, from 840 nm to 953 nm, we obtained the low-end boundary of the EMB at each wavelength.These values were compared with known cases of OM3 and OM4, revealing the capability differences.
We observe that both 'HDR OM4' and 'HDR OM3' offer higher EMBs than OM4 and OM3 for wavelengths longer than 850 nm.In particular, our findings indicate that the 'HDR OM4' performs the same or better than OM5 from 840 nm to 920 nm.Due to their higher bandwidth capability at longer wavelengths, these fibers are more suitable for high-data-rate transmission.We also obtained the link bandwidth that includes both the modal bandwidth contribution and the CD-contributed bandwidth, which is directly tied to the system level performance.We find that, for both 'HDR OM3' and 'HDR OM4', the link bandwidth stays above the value at 850 nm until around 910 nm.This means these fibers deliver similar transmission performances from 850 to 910 nm without declining towards longer wavelengths, unlike standard OM3 and OM4.In the application space, we further list the transmission reaches for various transceiver applications, both for 100Gper-lane-based and older 25 Gbaud-based transceivers.To better illustrate various aspects of 'HDR MMFs', in the discussion section, Section 5, we presented several comparisons.We believe the current study provides insights about the benefits of high-data-rate MMFs, enabling more VCSEL wavelength choices and optimal deployment in diverse scenarios.

Figure 1 .
Figure 1.Delta profile of an MMF with 50 m-diameter core.

Figure 2 .
Figure 2. The schematic of wavelength dependency of modal bandwidth of an individual MMF.

Figure 1 .
Figure 1.Delta profile of an MMF with 50 µm-diameter core.

Figure 1 .
Figure 1.Delta profile of an MMF with 50 m-diameter core.

Figure 2 .
Figure 2. The schematic of wavelength dependency of modal bandwidth of an individual MMF.

Figure 2 .
Figure 2. The schematic of wavelength dependency of modal bandwidth of an individual MMF.

Figure 3 .
Figure 3.The peak wavelength as a function of alpha for MMF with 1% delta and 50 m core diameter.

Figure 4 .
Figure 4.Ten weight functions associated with ten VCSEL launch conditions.

Figure 4 .
Figure 4.Ten weight functions associated with ten VCSEL launch conditions.

Figure 6 .
Figure 6.The EMB as a function of wavelength for 'HDR OM4' as compared to those for OM4 and OM5 defined by IEC.

Figure 6 .
Figure 6.The EMB as a function of wavelength for 'HDR OM4' as compared to those for OM4 and OM5 defined by IEC.

Figure 7 .
Figure 7.The EMB as a function of wavelength for 'HDR OM3' as compared to those for OM3 and OM4 defined by IEC.

Figure 8 .
Figure 8.The EMB as a function of wavelength for 'HDR OM4' with two different percentiles.

Figure 8 .
Figure 8.The EMB as a function of wavelength for 'HDR OM4' with two different percentiles.

Figure 9 .
Figure9.CD as a function of wavelength for MMF from 840 to 953 nm, shown as a black curve using left side axis scale pointed by the black arrow, and   as a function of wavelength for MMF from 840 to 953 nm, assuming 0.6 nm VCSEL RMS linewidth, shown as a blue curve using right side axis scale pointed by the blue arrow.

Figure 9 .
Figure9.CD as a function of wavelength for MMF from 840 to 953 nm, shown as a black curve using left side axis scale pointed by the black arrow, and BW CD as a function of wavelength for MMF from 840 to 953 nm, assuming 0.6 nm VCSEL RMS linewidth, shown as a blue curve using right side axis scale pointed by the blue arrow.

Figure 13 .
Figure 13.The link bandwidth as a function of wavelength for 100 m 'HDR OM4', 100 m OM4, and 100 m OM5.

Figure 13 .
Figure 13.The link bandwidth as a function of wavelength for 100 m 'HDR OM4', 100 m OM4, and 100 m OM5.

Figure 13 .
Figure 13.The link bandwidth as a function of wavelength for 100 m 'HDR OM4', 100 m OM4, and 100 m OM5.
The peak wavelength as a function of alpha for MMF with 1% delta and 50 µm core diameter.

Table 3 .
The transmission reaches for 25Gbaud-based transceivers.