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In this paper, we propose a novel 1 to N optical power splitter and a 1 to N optical switch for a multi-core fiber (MCF) with N circularly aligned cores. The splitter and the switch are based on the multimode interference (MMI) effect inside a ring core fiber. The MMI effect will convert one image into N output images in the ring and therefore, the ring shape MMI coupler can act as a 1 to N power splitter. These images will have different phases. If two ring shape MMI couplers are used and a tunable phase shifter array and a fixed phase shifter array are placed between them, by properly setting the phases of the N images in the middle of the MMI couplers, the images will converge to one output port of the 2nd MMI coupler. The output port number can be changed by tuning the phase shifters. In this way, the input signal at one of the cores of the MCF can be switched to the other core, and a 1 to N switch can be realized. In the analysis, it is found that only one control parameter is required for the phase adjustment of the tunable phase shifter array in order to achieve the switching between the cores.
© 2015 Optical Society of America
1. Introduction
Multi-core fibers (MCFs) have recently emerged as a new candidate to further increase the transmission capacity of the optical communication systems [1–8 ]. It is reported that a MCF with 19 cores have been successfully fabricated [5] and experimentally demonstrated during the transmission [6].
There are several ways to arrange the cores in MCFs. The cores can be arranged in a hexagon lattice [5,6 ], in a linear array [7] or in a circular ring [8]. In comparison with the popular hexagon lattice arrangement, the ring structure has some advantages, such as no strict limitation on the core pitch (distance between adjacent cores) because of the elimination of the center core, no excessive degradations for the crosstalk performance of the inner cores, and limited number of the adjacent cores that could reduce crosstalk [8]. Furthermore, as will be shown in this paper, MCFs with a ring shape core alignment can be more adaptive to the novel optical network structure.
Recently, optical network structures with reconfigurable optical add/drop multiplexers (ROADMs) have been proposed [9]. These structures are reliant on the devices called multi-cast switches, which are composed by 1 to N power splitters and 1 to N optical switches [9]. Since these devices are usually designed with single mode fibers (SMFs) at the input and the output, it becomes difficult for MCFs to be adapted into these network structures. In order to split the signals propagating inside one of the cores into multiple other cores or to switch the signals between the cores inside the MCF, a great number of MCF to SMF couplers are required.
If power splitting and optical switching can be accomplished with a compact structure which is compactable with the MCF technology, great efforts can be saved to integrate MCFs into the novel network structures. In this paper, we propose to realize power splitters and optical switches for MCFs based on the multimode interference (MMI) effect in a ring core fiber.
It is well known that MMI effect exists in planar waveguides, which can convert one input image into multiple duplicated images with different phases. Many functional devices such as optical power splitters [10], optical switches [11], mode converters [12] have been proposed based on this phenomenon.
Recently, it is discovered that MMI effect also exists inside circular ring core fibers [13]. Similar to planar waveguide case, it converts a single input image into multiple duplicated images with different phases. The MMI effect inside the ring core fiber can be understood by considering the ring core fiber as a planar MMI coupler “folded” in the angular domain. Hence, a ring shape MMI coupler can act as a 1 to N power splitter. After passing these images through a fix phase shifter array [13], the phases can be changed to −2πmn/N, where N is the number of the images at the output, n the nth output image, m the input port number. If the N images with such a phase distribution are injected into the other MMI coupler with the same fixed phase shifter array at the input, the output optical wave will concentrate on the (N-m)th output port (if the number N-m≥N or <0, calculate the reminder of (N-m)/N as the output port number). Therefore, by using two MMI couplers, along with a fixed phase shifter array and a tunable phase shifter array in the middle of them, a 1 to N optical switch for the MCF can be realized. The tunable phase shifter array adjusts the value of m to m' in order to achieve the phase distribution of −2πm'n/N. And this results in the change of the output port number from (N-m) to (N-m'). Such a 1 to N optical splitter and a 1 to N optical switch can be very useful in the popular optical networks with ROADMs.
2. Theory for the MMI effect inside a ring core fiber
The detailed description of the theory for MMI process inside ring core fibers can be found in [13]. For readers' convenience, it is briefly illustrated as follows. If the ring is relatively “thin”, i.e. the radius of the ring a is much larger than its width, and the ring core fiber is single mode in the radial direction and multimode in the angular direction, MMI effect will take place when the length of the ring shape MMI coupler is [13],
where N is the number of duplicated images to be generated, k = nk0, n the refractive index of the ring core, k0 the free space wave number, a the radius of the ring.
Assuming that there are N input ports and N output ports distributed evenly along the ring, which is the typical core alignment for a MCF, and denoting the coefficients for fields at input/output ports as vector a/b, they are linearly related to each other by [13]
where T is a matrix with the element of [13]
3. Working principle of the ring shape MMI coupler based power splitter and switch
According to Eqs. (2)-(3) , if signal is injected into one of the input port of the ring shape MMI coupler, it will be converted into N duplicated images at the output. Therefore, it can act as a power splitter for a MCF with circularly aligned cores.
To realize an optical switch, one needs two MMI couplers with phase shifters. If an array of fixed phase shifter are placed at the output of the first MMI coupler, and the phase shift is [13]
The transfer matrix T in Eq. (3) will be modified as T' [13] with the element of T' as [13]
With input signal at the m th input of the first MMI coupler, if the common phase term is neglected, the phase distribution at its output fulfills -2πmn/N. From the following Eq. (6), it can be inferred that if these N output images are injected into the other MMI coupler with the same fixed phase shifter array at the input, the output optical wave will concentrate on the (N-m)th output.
In order to achieve switching, we place a tunable phase shifter array between two MMI couplers with fixed phase shifter arrays, and it can alter the phases as -2πm'n/N, where m' is another integer which is different from m. In this case, if the signal is injected into the m th input port, the generated N images at the output of the first MMI coupler will have the phase distribution of -2πm'n/N after the phase adjustment by the fixed phase shifter array and the tunable phase shifter array. These N images will merge into one image at the (N-m')th output port of the second MMI coupler. In this way, optical switching from the m th core of the MCF to the (N-m')th core is accomplished.
The tunable phase shifters are very easy to control, as their expected phase shift are always in the form of
where l is a integer. By mechanisms like thermal-optical effect, electro-optical effect, one is able to tune phase shifters, i. e. to change the value of the only control parameter l, and the phases of the images will be changed from -2πmn/N to -2π(m-l)n/N.
4. Numerical simulations
Numerical simulations based on the beam propagation method (BPM) have been performed to verify the concept proposed in this work.
A MCF with 8 cores is used as an example. The MCF has the cladding refractive index as 1.45 and the core refractive index difference is 1.2% [14], since the index difference is relatively small, the polarization effect is negligible. The radius of each core is 2.5 μm. The 8 cores are equally spaced in a circle with the radius of 48 μm, which corresponds to the distance between the adjacent cores, i.e. the core pitch, as 36.7 μm. Such a core pitch was proposed in [8] to achieve reasonable crosstalk performance.
A ring core fiber with the same refractive indexes for the core and the cladding is used as the MMI device (It is worth emphasizing that the MMI process takes place inside the ring core fiber, not in the MCF as the cores of the MCF are very far away and the coupling between the cores is negligible). The ring has the radius of 48μm and the width of 5 μm, so as to adapt to the size of the MCF. The operation signal wavelength is 1550 nm, and the length of the ring shape MMI coupler is calculated by Eq. (1) and optimized in the simulation as 10858 μm.
The number of modes in the radial direction can be checked by comparing the normalized frequency V and the mth order radial mode cut-off frequency Vm [15]
where, b is the outer radius of the ring, ρ the ratio between the inner radius and the outer radius of the ring. It should be noted that such a ring core fiber can have two radial directional mode groups. One is symmetrical and the other is asymmetrical in the radial direction. Since the input modes of the MCF cores are symmetrical in the radial direction, only the symmetrical mode group will be excited. Also, the asymmetrical mode group has less angular modes and has less significant MMI effect. Therefore, the device can still be regarded as single mode in the radial direction during the operation. During the design of the MMI device, Eq. (8) can be very useful to check whether it will be well operational. Also the angular modes cut-off frequencies should be examined to ensure the existence of enough angular modes to enable high quality MMI process. According to the author's investigation, the normalized frequency V should fulfill the following inequality to get the best device performance.
The cross section and the port labeling of the MMI device is illustrated in Fig. 1(a) .
Fig. 1 (a) cross section of the MMI device used for the power splitter and the optical switch (b) schematic of the power splitter.
There is only one piece of ring core fiber (MMI device) in our splitter design. The schematic is illustrated in Fig. 1(b). The signal is injected into one of its input port, e.g. the 0th input port. After the injection, the optical field will undergo the multimode interference process in the ring shape MMI coupler as shown in Fig. 2 (b-d) . There will be 8 duplicated images at the output which fit the eight cores of the output MCF as illustrated in Fig. 2 (d). It can be seen from the figure that the optical power distributes evenly among the 8 outputs. The insertion loss for each port is very close to 9 dB, which indicates very low excessive insertion loss. The insertion loss deviation for each port is less than 0.3 dB.
Fig. 2 input and output field of the MMI coupler and the evolution of the field inside the ring core fiber if the input is injected into the 0th input port (Visualization 1 and Visualization 2).
To demonstrate the propagation of the beam inside the ring core fiber, two videos demonstrating the evolution of the amplitude and phase inside the ring core MMI coupler are included as the supplementary files (Visualization 1 and Visualization 2). The readers are encouraged to refer to these files for detailed illustrations.
After the simulation of the power splitter, the proposed optical switch is simulated. The optical switch is composed of four parts. The first ring shape MMI coupler will convert one input image into 8 duplicated images, just like the power splitter. The phase of each image will be modified by a fixed phase shifter array and a tunable phase shifter array. These images will converge at the output of the 2nd ring shape MMI coupler. The device structure is illustrated in Fig. 3 . It should be noted that fixed phase shifters are actually realized by a MCF, they are joined with the multi-core fibers at the output/input of the ring core fibers.
The fixed phase shifter array will have the phase shift of
which is twice the phase shift in Eq. (4). This is because each of the MMI coupler requires a fix phase shifter array with the phase shift indicated by Eq. (4), and they are combined as one fixed phase shifter array and the corresponding phase shift is the value indicated by Eq. (10). The tunable phase shifter can provide the phase shift of
where l is a integer to be tuned. If the signals are injected into the m th input port, the output signal will appear at the (N-m + l)th output port (if the number N-m + l≥N or <0, calculate the remainder of (N-m + l)/N as the output port number). In this way, by changing the control parameter, i.e. l, signal at any of the cores inside the MCF can be switched to any other cores within the MCF. In this way, the 1 to N optical switch can be realized.
There are many ways to realize the phase shifter array, such as the external phase shifter approach [16], the arrayed waveguides with different length [17], or the arrayed waveguides with different refractive indexes [14]. In this work, the fixed phase shifter array is realized by a MCF whose cores are with different refractive indexes followed by an external tunable phase shifter array, which is able to tune the control parameter l. In the BPM simulations, the tunable phase shifters are simulated by an array of perfect phase plates which can alter the phases of the beams in the waveguides. The length of the array is 200 μm. The 0th phase shifter has the lowest core index, which is 1.4674 (index difference of 1.2%), while the 1st phase shifter has the index of 1.4662 (index difference of 1.12%). The rest of the phase shifters have the other indexes accordingly. The index difference between the phase shifter and the ring core fiber could introduce additional reflection, which can be avoided by anti-reflection coating before joining them together. It should be noted that the tunable phase shifter array can also be realized in other ways.
The simulation results for the optical switch are plotted into Fig. 4 . The input signal is injected into the 0th input port of the 1st ring shape MMI coupler. It can be seen from the figures that with the adjustment of the control parameter l from 0 to 3, the optical field concentrates at different output ports of the 2nd ring shape MMI coupler. The optical isolation, which is defined as the optical power at the corresponding output port over the optical power at other output ports, is quite low. In the worst case, the isolation reaches 28dB.
Fig. 4 the output of the switch when the input is injected into the 0th input port and the control number l varies from 0 to 3.
If the input is injected into the m th input port, the output field will concentrate at the (N-m + l) th output port. The output pattern will be very similar to those in Fig. 4.
To demonstrate the functionality of the MCF switch when there are multiple input signals at different cores, two input signals are assumed to be injected into the 0th and the 1st input ports of the switch. The input signal distribution is illustrated in Fig. 5(a) , with the power ratio of 1:2. Assuming the control parameters l = 0, and after switching, the signal are expected to appear at the 0th and the (N-1)th (i. e. the 7th) cores of the MCF, and the results are plotted in Fig. 5(b), which is in agreement with the theoretical prediction.
Fig. 5 the input and output signal amplitudes in the MCF before and after switching, the control number l is 0.
Afterwards, the fabrication tolerance of the proposed device is investigated. As the length of the MMI coupler varies, the power balance for the optical splitter and the isolation performance for the optical switch degrade. If the length of the MMI coupler changes by 1%, which is about 100 μm, the splitter will have the insertion loss deviation as 0.35 dB and the optical switch will have the worst case isolation as 27 dB. The performance degradation is almost negligible in comparison with the optimal case. The deviations in the radius of the ring will also cause performance degradation. However, it can be proportionally related to the length deviation through Eq. (4). Generally speaking, the percentage of the change on the radius is equivalent to the percentage of the change on the length, multiplied by a factor of 2. Therefore, the device is quite robust with respect to geometrical variations. Furthermore, the current fiber technology allows quite accurate fabrication of the ring core fiber and the performance of the device can be guaranteed.
Another source of the degradation comes from the phase inaccuracies of the phase shifters. It is found that if one of the phase shifter changes 20 degree in phase shift, the worst case isolation reduces to 23 dB. (The power splitter will not be affected.) Therefore, although it is still robust with respect to the phase variations, accurate control of the phase in the middle will be the key to keep the performance of the optical switch. For example, the fixed phase shifter array should have the core index variation to be below 0.04%. Fortunately, external phase shifters, which could bring accurate phase shift, can be of great help to achieve the precise phase control.
Operation wavelength range can be inferred from the fabrication tolerance analysis. For the power splitter, the deviation of the wavelength from the center wavelength 1550 nm can be proportionally related to the length deviation [18]. For the optical switch, the wavelength dependence is not only from the wavelength dependence of the MMI coupler, but also the wavelength dependence of the phase shifters. Combining these two effects, the wavelength dependence of the switch can be found. In the simulation, it is discovered, when the operation wavelength range is +/−20 nm around the 1550 nm center wavelength, the splitter insertion loss deviation remains below 0.5 dB, and the isolation of the optical switch remains as high as 21 dB, which is acceptable for the C band WDM operations.
Finally, other impacts on fibers, such as fiber bending, temperature variation, as well as fluctuations of core size, core index, and core position are investigated. First of all, as for fiber bending, if the bending radius is 5 cm, which is already very small from a fiber optic point of view, the splitter loss deviation is below 0.5 dB, and the switch isolation is above 25 dB. This is because the length of the ring core fiber is only 1cm, and therefore, such bending will not significantly impact the mode coupling inside it during such a short propagation distance. Secondly, the temperature variation will result in the change of the index, and this will bring change to the interference length of the MMI coupler as indicated in Eq. (1). Such an impact of length deviation has been discussed in the previous paragraphs. Since the temperature induced index variation is small, it will not be a significant problem. Thirdly, the impact of the MCF core size and core index variation seems not to be a major problem, as the interference takes place inside the ring core fiber. This has been proven by simulations. Although appearing as independent phenomena, the variations of the ring core fiber core size and index will have similar impacts on the performance of the MMI coupler as length deviation does. As discussed before, the current fiber technology can guarantee the operation of the device. Finally, the impact of core position misalignment between the ring core fiber and the input/output MCF is investigated. It is found that the misalignment does not impact the performances of the splitter and the switch. When the misalignment is 0.5 μm, the loss deviation of the splitter and the isolation of the switch remain unchanged. Similarly, if the core position of the MCF varies randomly within 0.5 μm, the performance remains unchanged. The above analysis shows the proposed devices are quite robust.
It is worth noting that the devices proposed here can be extended for MCF with cores arranged in multiple rings. It can be briefly described as follows. The power splitting and switching between cores inside the same ring can be realized by the devices proposed in this work. The power splitting and switching between the cores in different rings can be realized by rectangular core fibers, which can act as rectangular MMI couplers. The discussion of such devices is beyond the scope of this paper and will be presented elsewhere.
5. Conclusion
In summary, we have proposed a novel 1 to N power splitter and optical switch for the circularly aligned MCFs based on the MMI effect inside a ring core fiber. The structures of these devices are simple, e.g. the power splitter is directly realized by a ring shape MMI coupler and the optical switch is realized by two ring shape MMI couplers, one fixed phase shifter array and one tunable phase shifter array. Detailed numerical simulations validate the functionalities of the devices. The concept can be extended for the MCF with cores arranged in multiple rings. The proposed device will help the MCFs to be integrated into the current optical networks.
Acknowledgment
The author would like to thank the two anonymous reviewers as well as the associate editor for their rigorous comments during the review process. This work is partially supported by the National Science Foundation of China (Grant No. 61201068) and the Fundamental Research Funds for the Central Universities of China.
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