Standard Single-Mode Fiber with High Modal Bandwidth as Two-Mode Fiber around 1060 nm for High Data Rate Transmission

Abstract

A step-index standard single-mode fiber as a two-mode fiber at 1060 nm can have a high modal bandwidth. In the current work, we conducted a detailed study and found that the LP11 mode of such a fiber is bending-sensitive and that the light excited to LP11 mode can be stripped out due to bending. The transmission experiments were conducted using offset launch with both LP01 and LP11 modes excited and center launch with only LP01 mode excited to show transmission performance in different conditions. We demonstrated the feasibility of 25 Gb/s NRZ transmission over 1 km of the fiber when both LP01 and LP11 modes were excited. We further explored the feasibility of a trench-assisted bending-insensitive step-index standard single-mode fiber with good bending properties for both LP01 and LP11 modes for two-mode transmission at 1060 nm. We found a fiber that has high modal bandwidth at 1060 nm and can sustain bending down to at least a 20 mm diameter. The high-bandwidth two-mode fiber can be potentially useful for future 1060 nm-based VCSEL transmission.

1. Introduction

In the past decade, multimode fibers (MMF) and Vertical Cavity Surface Emitting Lasers (VCSELs) together have provided a cost-effective and energy-efficient system for short-distance communications. Ongoing research in this field seeks to push transmission data rates to ever higher levels. One area of particular interest is single-mode (SM) VCSELs [1,2,3,4,5]. These devices offer benefits such as a narrower linewidth, a lower numerical aperture, and a smaller spot size compared to multimode VCSELs. As a result, they are ideal for high-speed data transmission with reduced chromatic dispersion. SM VCSELs are also compatible with a wider range of optical fibers, including those with smaller core sizes such as few-mode fibers (FMF) and single-mode fibers, thanks to their smaller aperture. Note that traditionally there has been a preference for using larger core multimode fiber, either glass- or plastic-based, for ease of light coupling with a laser source for short-length transmission below a couple of hundred meters. However, for longer-length transmission the bandwidth becomes a limitation. Standard single-mode fiber as a two-mode fiber below a 1260 nm wavelength offers the possibility of using the same fiber for both short- and long-length transmission, thereby reducing system engineering costs and offering network operators greater flexibility in optical cable deployment and management. Moreover, VCSELs have been investigated at several wavelengths of interest, including 980 nm and 1060 nm [6,7], in addition to the dominant wavelength of 850 nm.

Few-mode fiber (FMF) is currently the focus of active research and shows potential in overcoming the inherent capacity limit of standard single-mode fiber through mode division multiplexing (MDM) [8,9,10,11,12,13,14]. To achieve this, it is important for FMF to satisfy various criteria, such as low attenuation, low crosstalk, and low differential mode delay (DMD). When the low-loss modes also exhibit low DMD, it simplifies the receiver design and reduces the need for equalization through digital signal processing (DSP) [9,15]. Furthermore, low DMD FMF can enable high-speed data transmission similar to a multi-mode fiber (MMF).

Standard single-mode fibers are commonly used for SM transmission in the wavelength range of 1260–1650 nm. Below the cable cutoff wavelength of 1260 nm, a standard single-mode fiber becomes an FMF. In the 850 nm to 1060 nm range, which is of particular interest for VCSEL transmission, the fiber operates as a two-mode fiber with LP01 and LP11 modes. Recent research has demonstrated that standard single-mode fibers with graded-index profiles can achieve a high bandwidth at around 850 nm, enabling data transmission at rates of 25 Gb/s over distances of up to 1500 m [16,17]. Similarly, standard single-mode fibers with step-index profiles also exhibit two modes within the 850 nm to 1060 nm range. However, a standard single-mode fiber with a step-index profile as a two-mode fiber has an extremely low modal bandwidth of about 0.18 GHz·km around 850 nm [17]. Recent work has shown that a step-index standard single-mode fiber can have a high modal bandwidth at a wavelength much higher than 850 nm, around 1060 nm, which has been explored as one possible VCSEL wavelength [18].

In this paper, we extended the work in [18] to understand its performance in practically deployed conditions. We found that despite the high-bandwidth two-mode behavior of some step-index single-mode fibers around 1060 nm, LP11 mode is highly bending-sensitive and can lose its power even with moderate bending. We have further studied the transmission performance with and without the bending. In order for such a fiber to be useful as a high bandwidth two-mode fiber, it is necessary to have a fiber that is bending-insensitive for both LP01 and LP11 modes, such as using a trench-assisted step-index profile. We explored such fibers and demonstrated that a bending-insensitive fiber can deliver the desired high bandwidth with good bending performance for both LP01 and LP11 modes. In Section 2, we discuss the fiber profile design that can lead to a high modal bandwidth through modeling and show the experimental characterizations of a fiber we identified. In Section 3, we study the bending performance of the fiber and conduct new transmission experiments to show its transmission performance in several configurations. In Section 4, we explore the feasibility of a bending-insensitive standard single-mode fiber with a high bandwidth of around 1060 nm and good bending performance for both LP01 and LP11 modes. We also show experimental results on the bandwidth and bending performance of one fiber meeting the requirements. In Section 5, we present discussions of several aspects of the current research as compared to broader research in the field. We draw conclusions in Section 6.

2. Fiber Profile Design and Modal Bandwidth Performance

2.1. Fiber Index Profile with High Bandwidth at 1060 nm

The refractive index profile of a fiber can be described as an α-profile:

$$n\left(r\right)=n_0\cdot \sqrt{1-2\mathsf{\Delta }{(r/a)}^{\alpha }}$$

(1)

where n₀ is the refractive index in the center of the core, a is the core radius, and $\mathsf{\Delta }=\left(n_0^2-n_1^2\right)/\left(2n_0^2\right)$ is the relative refractive index difference between the core center and the cladding, where n₁ is the refractive index of the cladding. The profile shape is dependent on the parameter α. For step-index fibers, the parameter α takes a relatively large value of 5 or higher. We have conducted detailed numerical simulations based on a finite element solver [19] for scalar wave equation [20]. An index profile that can yield a high modal bandwidth as a two-mode fiber of around 1060 nm has been identified, as shown in Figure 1a, while meeting requirements for a standard single-mode fiber for 1310 nm and 1550 nm operations [18]. The wavelength at which the bandwidth is peaked is called the peak wavelength. For this profile, $\mathsf{\Delta }=0.345\%, a=4.707 \mathsf{\mu }\mathrm{m},$ and $\alpha =11.5$. The delta value of 0.345% corresponds to a refractive index value of 1.4575 at 850 nm. When varying the core radius by ±1%, the modeling shows that the peak wavelength varies by ±10 nm. In searching for the optimal profile, the fiber parameters were tweaked in a narrow range starting from a typical step-index profile until the desired fiber was identified. Figure 1b illustrates the modeled bandwidth versus wavelength for this fiber, assuming equal excitations of LP01 and LP11 modes. Additionally, the optical properties of the fiber have been computed. At 1310 nm and 1550 nm, the mode field diameters (MFD) are 9.3 μm and 10.7 μm, respectively. The zero-dispersion wavelength is 1304 nm, the chromatic dispersion at 1550 nm is 17.3 ps/(nm·km), and the cable cutoff wavelength is below 1260 nm. These optical characteristics comply with the ITU-T G.652.D standard. It should be noted that the fiber studied in the current work is referred to as a standard single-mode fiber due to its single-mode performance in the range of 1260–1650 nm and existing naming. They are two-mode around 1060 nm.

2.2. Experimental Characterization of Modal Bandwidth

A frequency domain measurement technique was used to measure a few step-index standard single-mode fibers across the 1010 nm to 1070 nm wavelength range [18,21]. One of the fibers exhibited a significantly high modal bandwidth near 1060 nm. This fiber, which is wound on a shipping reel with a minimum winding diameter of about 165 mm, was characterized using an RF instrument, a vector network analyzer (VNA). The measurement technique involves intensity modulating a narrow linewidth continuous-wave light source at the wavelength of interest using the VNA and then launching the light into the fiber under test (FUT) to excite both modes. The transfer function of the fiber is obtained by measuring the transmission over a range of modulation frequencies after converting the optical signal back to an electric signal through a photodetector (PD). The transfer function contribution from the fiber can be determined with proper calibration.

An analytical model was formulated in [21] to describe the transfer function as related to the fiber properties and to fit the experimentally measured transfer function. The modal delay time t defined as the group delay difference between the LP01 mode and LP11 mode of the fiber is $\tau ={\tau }_2-{\tau }_1={\tau }_0\cdot L$, with ${\tau }_1$ and ${\tau }_2$ being the group delays of LP01 and LP11 modes, and with ${\tau }_0$ being the normalized modal delay time (modal delay per unit length) and L being the length of the FUT. The transfer function in the logarithmic scale (electrical definition) is

$$TF=20\cdot {\mathit{log}}_{10}[1+c^2+2c\cdot \mathit{cos}(2\pi f\tau )]+d,$$

(2)

where $c$ is the ratio of optical powers in the two modes and d is two times of the insertion loss. The minimum bandwidth is achieved when $c=1$ (both modes are equally excited):

$$BW=\frac{1}{3\tau }$$

(3)

From Equation (3) we can obtain the worst-case modal bandwidth that is simply related to the modal delay and is independent of the launch condition.

Using Equation (2), we can obtain the modal delay at each wavelength and further calculate the fiber bandwidth using Equation (3). The modal delays and the bandwidth at different wavelengths are shown in Figure 2a and Figure 2b, respectively. It can be observed that the difference of the group delay for LP01 and LP11 moves from positive to negative over the wavelength. When it is equal to zero, the fiber reaches the peak wavelength, where the bandwidth is infinity, as marked by the dashed vertical line in Figure 2b. For this fiber, the peak wavelength is 1057.4 nm. For this fiber, the wavelength window with a bandwidth of above 2 GHz·km is about 22 nm, which is much narrower compared to the graded-index standard single-mode fiber studied in [17] with a wavelength window of greater than 100 nm. This fiber is ITU-T G652.D compliant with MFD at 1310 nm (1550 nm) of 9.4 μm (10.6 μm), a zero-dispersion wavelength of 1305 nm, a 1550 nm chromatic dispersion of 17.2 ps/(nm·km), and cable-cutoff below 1260 nm.

The bandwidth capability of the two-mode fiber can also be compared with a conventional multimode fiber (MMF) with a core diameter of 50 microns, categorized as OM3 and OM4 fibers, and another type of MMF, plastic optical fiber (POF), which have been used for short reach communication. OM3 and OM4 fibers have effective modal bandwidths of 2000 MHz·km and 4700 MHz·km, respectively, at 850 nm, while a graded-index POF fiber can have a modal bandwidth of up to a few hundred MHz·km [22]. Due to the two-mode nature of the fiber being studied, it can exhibit an infinite bandwidth at certain wavelengths when the two modes have zero differential group delay. For 50-micron core MMF and POF, which have a large number of modes, the differential group delays of modes can be minimized but cannot reach zero. Therefore, they exhibit different wavelength dependences, with the peak bandwidth taking a finite value [23,24].

3. Transmission Experiment and Effects of Bending

Initial transmission experiments were carried out with 1 km of the high bandwidth fiber studied in Section 2.2 with successful 25 Gb/s transmission using 2³¹ − 1 PRBS non-return-to-zero (NRZ) signals as presented in [18]. Upon further investigations, we found that the LP11 mode of the fiber was sensitive to bending; with one loop of bending at a bending diameter of 20 mm at the beginning portion of the fiber, the LP11 mode was stripped out. To see the impact of the mode stripping on the transmission, we carried out more thorough experiments.

The experimental arrangement is depicted in Figure 3. The transmitter utilizes a narrow-linewidth CW laser operating around 1060 nm, followed by an optical isolator. The CW light is modulated by an intensity modulator with a 20 GHz bandwidth from Photline, operating at 25.78125 Gb/s. To change the amount of power coupled to each mode, we used offset launch to change overlap integrals between the two modes and the launching fiber. We found that using a standard single-mode fiber jumper with 3 μm offset splicing in the middle as the mode conditioner could result in a roughly equal excitation of both modes of the FUT. For BER testing, an Agilent BERT system is employed. The controller (N4960A-CJ1) manages the pattern generator (N4951B) and error detector (N4952A-E32) using 2³¹ − 1 PRBS non-return-to-zero (NRZ) signals. Subsequent to transmission through the FUT and a variable optical attenuator (VOA) to regulate the received optical power, the optical signal is detected by a Discovery Semiconductor’s Lab Buddy optical receiver (R409) for 25G transmission and fed into the error detector to obtain the BER.

The transmission performance of the high-bandwidth fiber around 1060 nm was evaluated using a DFB laser from Nanoplus. The laser was operated at wavelengths of 1058.8 nm and 1059.5 nm by setting the temperatures at 40 °C and 50 °C, respectively, with a driving current of 70 mA. The light was launched into the FUT with offset launch or center launch conditions, achieved by splicing two fibers with a controlled offset of around 3 μm. BERs were measured under four configurations: back-to-back (BtB) with a 1 m fiber, a 1 km FUT at 1058.8 nm with center launch, a 1 km FUT at 1058.8 nm with offset launch, and a 1 km FUT at 1059.5 nm with offset launch. The BER as a function of received optical power was obtained by tuning the attenuation using a variable optical attenuator (VOA), as shown in Figure 4. The system achieved error-free performance with around −9.8 dBm received optical power under the BtB condition. The bandwidths at 1058.8 nm and 1059.5 nm were 15.9 GHz·km and 10.2 GHz·km, respectively. The transmission performance over a 1 km FUT was different, with the system achieving better BER at 1058.8 nm (3.7 × 10⁻¹² at −8.06 dBm received optical power) compared to 1059.5 nm (3.4 × 10⁻⁷ at maximum power without VOA). For a center launch condition, the BER performance was better than that with an offset launch condition, as essentially only the fundamental mode was launched. The optical eye diagrams are shown in Figure 5. The eye diagram is a visual representation of digital signals with ‘0’ level signal and ‘1’ level signals overlaying within a few bit periods illustrating the quality and health of the transmitted signals. A good eye diagram is one with wide open eyes and clean, well-defined transitions between the signal levels. At 1058.8 nm, the eye diagram in Figure 5c meets these criteria and is only moderately worse than the BtB case. With the bandwidth reduced at 1059.5 nm in Figure 5d, the eye diagram quality is degraded, with a narrower opening compared to 1058.8 nm, consistent with the BER results. On the other hand, the eye diagram from the center launch condition is similar to the BtB condition. We also show the eye diagram at 1058.8 nm with one loop of 20 mm diameter bending placed at the beginning portion of the FUT in Figure 5e while keeping the same vertical scale as Figure 5b. It can be found that essentially half of the optical power was lost due to the loss of LP11 mode light. However, without LP11 mode contribution, the eye diagram looks clean and wide open similar to the BtB eye diagram. The transmission experiment with the center launch condition excites only LP01 mode and is very similar to the condition after the bending strips out LP11 mode.

Additional fiber cutoff testing was also conducted on the reel of 1 km fiber, and the results are shown in Figure 6. A broadband white light was flood-launched into the fiber, and the output optical power was measured in the spectrum range from 800 nm to 1300 nm. The fiber cutoff behavior can be observed around 1080 nm when LP11 mode loses power and no longer propagates above this wavelength at the shipping reel condition. In another measurement condition, when one loop of 20 mm bending was incurred at the beginning portion of the fiber, the optical power drops at a lower wavelength, indicating LP11 mode was already lost due to the bending, which is consistent with the observation in Figure 5e. The reason that, for a step-index fiber, LP11 mode is bending-sensitive is that a 1060 nm wavelength is close to the cutoff wavelength of LP11 mode, at which point the guiding capability of LP11 is weak.

4. Bending Insensitive Single Mode Fiber with High Bandwidth at 1060 nm AS Two-Mode Fiber

Since the LP11 mode of the fiber studied above is bend-sensitive, LP11 can be stripped out once a moderate level of bending is incurred. One question raised is whether a bending-insensitive step-index single-mode fiber as a two-mode fiber can still exhibit a high modal bandwidth at 1060 nm. Bending-insensitive single-mode fibers were introduced around 15 years ago to address the needs of deploying single-mode fibers in environments with small bending [25]. The main difference of such fibers from conventional standard single-mode fibers is that a low index trench is added to the fiber index profile. The low index trench reduces the amount of power in the cladding, resulting in less power leaking into the cladding and polymer coating when bending is applied. A schematic of the trench-assisted bending-insensitive fiber index profile in terms of the delta or index contrast to the cladding is illustrated in Figure 7. We searched for a high-bandwidth fiber among an existing fiber product, LBL fiber [26]. This fiber is a type of standard single-mode fiber compliant with ITU-T G652.D requirements. A fiber with the desired properties was identified and prepared with a 2 km length deployed on shipping reel. This fiber has an MFD of 8.7 μm at 1310 nm and an MFD of 9.7 μm at 1550 nm. The cable cutoff wavelength is 1246 nm, and the zero-dispersion wavelength is 1312.5 nm.

Utilizing the measurement method outlined in Section 2, as originally developed in [21], we conducted measurements on a 2 km-length fiber to obtain its transfer function when both the LP01 and LP11 modes were excited. Subsequently, in line with the characteristics of Equation (2), we obtained the modal delay at each wavelength and computed the fiber bandwidth using Equation (3). The modal delays extracted at different wavelengths, along with the corresponding fittings, are presented in Figure 8a, while the calculated bandwidths and their fittings are depicted in Figure 8b. Notably, the modal delay undergoes a transition from positive to negative, intersecting the zero line at the 1058.7 nm wavelength. The peak wavelength of this fiber was determined to be 1058.7 nm. The wavelength window, where the modal bandwidth exceeds 2 GHz·km for this fiber, spans 26 nm, representing a moderately wider range compared to the step-index single-mode fiber discussed in Section 2, which had a window width of 22 nm. It is still much narrower than the bandwidth window for a graded-index single-mode fiber as a two-mode fiber studied in [17] with a width greater than 100 nm.

We also conducted a fiber cutoff measurement with one loop of bending at several diameters, as shown in Figure 9, to see whether the fiber was bending-sensitive or not. It can be found that LP11 cutoff occurs at around a 1100 nm wavelength at the shipping reel condition. With one loop of bending at 20 mm and 30 mm diameters, the fiber cutoff behavior is essentially unchanged with the curves overlapping each other. Only when the fiber diameter is reduced to 10 mm, which is considered tight bending, do we observe a moderate loss of optical power near the fiber cutoff transition region. The cutoff measurement results show that this fiber is bending-insensitive for both LP01 and LP11 modes down to a 20 mm bending diameter. Therefore, it is feasible for a step-index-based bending-insensitive single-mode fiber to have a high modal bandwidth of around 1060 nm. The 20 mm bending diameter is similar to what has been specified for 50-micron core bend-insensitive glass MMFs and is smaller than the bending diameter allowed for the step-index plastic based MMF that has been studied in [27,28].

5. Discussions

In this paper, we present a study of a step-index-based standard single-mode fiber as a two-mode fiber around 1060 nm with a high modal bandwidth. The study provides new insights on the bending performance of LP11 mode in addition to high bandwidth capability. Below, we discuss several aspects of the current study as compared to broader study in the relevant field.

• Two-mode FMF based on standard single-mode fiber: Through a series of systematic studies in [16,17,18,21] and the current work, we have explored the novel properties of standard single-mode fiber used in somehow unexpected regime when the operating wavelength is from 850 nm to 1060 nm or below the cable cutoff of the fiber. It can be confusing that the study addresses the two-mode property of the fiber while the fiber is referred to as a ‘single-mode’ fiber. One benefit of using a standard single-mode fiber as two-mode FMF is that they are already produced at a vast volume as a single-mode fiber for single mode transmission. The barrier is much lower if one can adopt them as FMF for MDM transmission.
• High modal bandwidth-capable: As has been shown, some of the step-index standard single-mode fiber as a two-mode fiber around 1060 nm can have a very high modal bandwidth as compared to traditional multimode fibers due to its two-mode nature. When the group delays of LP01 and LP11 modes are equal to each other at certain wavelength, the modal bandwidth reaches infinity. Conventional OM3 and OM4 multimode fibers can have effective modal bandwidths of 2000 MHz·km and 4700 MHz·km, respectively. POF’s bandwidth is even less compared to glass-based MMF.
• Bending Property of LP11 mode: The current work highlights the effect of the bending property of LP11 mode on the two-mode fiber based on the standard single-mode fiber. The bending insensitivity of a standard single-mode fiber has been intensively studied [25]. However, if one wants to use FMF or two-mode fiber for MDM, the bending performance of higher-order modes should be taken into consideration. We show that the low index trench design for bending insensitive standard single-mode fibers can also be applied to LP11 mode to enhance the bending property of two-mode fibers derived from the standard single-mode fiber.
• Working with SM VCESL: Standard single-mode fibers have small cores compared to MMF. Therefore, they are disadvantaged when compared to conventional MMF with much larger cores. However, such fibers are suitable for coupling with SM VCSEL, which has a Gaussian laser beam and therefore is technically feasible to achieve high coupling efficiency. In addition, SM VCSEL has low power consumption, so that a standard single-mode fiber can be an additional transmission medium used with SM VCSEL in addition to MMF.

6. Conclusions

In this paper, we have presented a detailed study of a step-index standard single-mode fiber as a two-mode fiber that can have a high modal bandwidth at 1060 nm. We found that while a simple step-index single-mode fiber can have a high modal bandwidth as a two-mode fiber around 1060 nm, the LP11 mode is quite bend-sensitive. One loop of bending with a diameter of 20 mm is sufficient to strip out LP11 mode. Detailed transmission experiments have been conducted with one fiber we identified, with its modal bandwidth peaking at 1057.4 nm through a custom-built transmitter using a laser source around 1060 nm. We demonstrated the feasibility of 25 Gb/s NRZ transmission over 1 km of the fiber when both LP01 and LP11 modes were excited. We also showed that when only LP01 was excited, the system could perform very close to the BtB condition as the fiber with only one mode excited has an essentially unlimited modal bandwidth.

We further investigated the feasibility of a bending-insensitive single-mode fiber as a two-mode fiber at 1060 nm to have a high modal bandwidth. Through searching over a number of fiber samples, we identified one such fiber. The modal delay and bandwidth of this fiber over 1000–1070 nm were measured. This fiber’s bandwidth peaked at 1058.7 nm, very close to 1060 nm. The wavelength window where the modal bandwidth is 2 GHz·km or above is around 26 nm. The cutoff measurements also confirm that the fiber is bending-insensitive for both LP01 and LP11 modes down to at least a 20 mm diameter. This fiber is truly a two-mode high-bandwidth fiber that can be used in normal deployment conditions with relatively tight bending. The findings in this paper could be potentially useful for future transmission applications with wavelengths around 1060 nm.