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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 7 — Apr. 7, 2014
  • pp: 8533–8540
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An MMI-based wavelength combiner employing non-uniform refractive index distribution

Siddharth Singh, Keisuke Kojima, Toshiaki Koike-Akino, Bingnan Wang, Kieran Parsons, Satoshi Nishikawa, and Eiji Yagyu  »View Author Affiliations


Optics Express, Vol. 22, Issue 7, pp. 8533-8540 (2014)
http://dx.doi.org/10.1364/OE.22.008533


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Abstract

A novel wavelength combiner using non-uniform refractive index distribution within a multimode interference device is proposed and simulated. The refractive index step creates separate localized modes with different effective refractive indices and two modes are strongly excited which form the basis of an interferometer. We applied the concept to 1.30/1.31 μm and 1.31/1.55 μm wavelength combiners on an InP substrate. The lengths of the devices are 1272 μm and 484 μm with simulated insertion losses of 0.6 dB and 0.67 dB respectively.

© 2014 Optical Society of America

1. Introduction

Wavelength combiners are essential components for wavelength division multiplexing (WDM) optical communications systems. There has been interest in InP-based photonic integrated circuits where multiple lasers, modulators and beam combiners can be monolithically integrated on a single chip for WDM optical communications systems. It is therefore desirable to design wavelength combiners on InP substrates.

Several device concepts have been utilized to realize wavelength combiners such as arrayed waveguide devices (AWG) [1

1. Y. Barbarin, X. J. M. Leijtens, E. A. J. M. Bente, C. M. Louzao, J. R. Kooiman, and M. K. Smit, “Extremely small AWG demultiplexer fabricated on InP by using a douoble-etch process,” IEEE Photon. Technol. Lett. 16(11), 2478–2480 (2004). [CrossRef]

], Y branch devices [2

2. N. Goto and G. L. Yip, “Y-branch wavelength multi-demultplexer for λ=1.30 μm and 1.55 μm,” Electron. Lett. 26, 102–103 (2007). [CrossRef]

], Mach-Zehnder interferometer (MZI) devices [3

3. A. Tervonen, P. Poyhonen, S. Honkanen, and M. Tahkokorpi, “A guided-wave Mach–Zehnder interferometer structure for wavelength multiplexing,” IEEE Photon. Technol. Lett. 3, 516–518 (1991). [CrossRef]

, 4

4. C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, and M. K. Smit, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the 7th Eur. Conf on Int. Opt. (ECIO ’95), 275–278 (1995).

] and multimode interference (MMI) devices [5

5. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

] to name a few important ones.

For general power splitters or combiners, MMI devices are particularly attractive as they offer several advantages such as robust fabrication tolerances, ease of fabrication, compact size and low excess loss. However, MMI-based wavelength combiners which are based on the theory of self-imaging will lead to very long devices especially when combining wavelengths which are 10 nm apart due to the fact that the device length needs to equal several odd and even multiples of the beat lengths for both wavelengths. The conventional theory of MMI devices requires that for an MMI device to split two wavelengths λ1 and λ2, the length of the device L must satisfy the condition [5

5. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

],
L=M×Lπ(λ1)=(M+1)×Lπ(λ2)
(1)
where Lπ(λ) is the wavelength-dependent beat length [5

5. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

] and M is a positive integer. The beat length for an MMI device of width W can be approximated by Lπ = 4neffW2/3λ. For 10 nm wavelength spacing one can see that with W = 6μm, L would be over 10 mm long. Although novel MMI-based wavelength combiners have been proposed for InGaAsP/InP and silicon-on-insulator (SOI), they have typically targeted very large wavelength spacings of 240 nm such as 1.31/1.55 μm where it is much easier to design shorter devices [6

6. C. Yao, H. G. Bach, R. Zhang, G. Zhou, J. H. Choi, C. Jiang, and R. Kunkel, “An ultracompact multimode interference wavelength splitter employing asymmetrical multi-section structures,” Opt. Express 20, 18248–18253 (2012). [CrossRef] [PubMed]

, 7

7. Y. Shi, S. Anand, and S. He, “A polarization-insensitive 1310/1550-nm demultiplexer based on sandwiched multimode interference waveguides,” IEEE Photon. Technol. Lett. 19, 1789–1791 (2007). [CrossRef]

, 8

8. M.-C. Wu and S.-Y. Tseng, “Design and simulation of multimode interference based demultiplexers aided by computer-generated planar holograms,” Opt. Express 18, 11270–11275 (2010). [CrossRef] [PubMed]

].

2. Principle and design

The top view of the proposed device is shown in Fig. 1(a), where the lighter green part shows the lower refractive index region, and the rest constitute the higher refractive index regions.

Fig. 1: Top view of the proposed device.

The functional diagram of the proposed device is depicted in Fig. 1(b) and it can be divided into three sections. The 2 × 2 coupler (leftmost section) splits the input field into two and excites the two main modes in the unbalanced interferometer section whose detail will be explained later. The outputs of the unbalanced interferometer are combined into the output port by a 2 × 1 coupler. The taper sections smoothly guide the modes with different waveguide heights.

The cross-sectional view of the interferometer section is shown in Fig. 2. An In1−xGaxAs1−yPy (y = 0.4) core layer sandwiched between an InP substrate and InP cladding layer. The core layer is etched by a small constant thickness Tg at a pre-determined rectangular plus taper shape creating a groove. In order to precisely control Tg, it is possible to insert a thin etch-stop layer which has different In1−xGaxAs1−yPy composition, such as InP. The groove is then filled with an InP regrown layer. This creates nearly-localized propagation modes with distinct effective refractive indices in the MMI, unlike conventional uniform MMIs. Figures 3(a) and 3(b) show the lowest TE mode and the third lowest TE mode respectively, when the total MMI width is W = 6.0 μm, the patch width is W1 = 3.6 μm, core layer thickness is Tcore = 0.5 μm, and groove thickness is Tg = 0.2 μm. The effective high and low refractive indices are 3.3001 and 3.2671 respectively at 1.30 μm and 3.29554 and 3.26303 at 1.31 μm.

Fig. 2: Cross-sectional view of the center section of the proposed device.
Fig. 3: Mode inside the MMI at the cross-section shown in Fig. 2.

In order for the combiner to have maximum efficiency, the following relationship needs to hold,
Δβ1L0Δβ2L0=π
(2)
where Δβ1 and Δβ2 are the differences in the propagation constant of the two modes at λ1 and λ2 respectively, and L0 is the length of the interferometer section. In our case of 10 nm wavelength difference, L0 becomes 893 μm.

Since the interferometer is not symmetric in terms of mode positions, instead of using symmetric 2 × 2 and 2 × 1 couplers, we use an optimization algorithm to design the asymmetric 2 × 2 and 2 × 1 couplers. Multiple parameters were optimized to maximize the output power when λ1 was injected into input port 1 and the output power when λ2 was injected into input port 2 [9

9. S. Özbayat, K. Kojima, T. Koike-Akino, B. Wang, K. Parsons, S. Singh, S. Nishikawa, and E. Yagyu, “Application of numerical optimization to the design of InP-based wavelength combiners,” Opt. Commun. 322, 131–136 (2014). [CrossRef]

]. For the optimization algorithm, we used a covariance matrix adaptation evolutionary strategy (CMA-ES) [9

9. S. Özbayat, K. Kojima, T. Koike-Akino, B. Wang, K. Parsons, S. Singh, S. Nishikawa, and E. Yagyu, “Application of numerical optimization to the design of InP-based wavelength combiners,” Opt. Commun. 322, 131–136 (2014). [CrossRef]

, 10

10. M. D. Gregory, Z. Bayraktar, and D. H. Werner, “Fast optimization of electromagnetic design problems using the covariance matrix adaptation evolutionary strategy,” IEEE Trans. Antennas Propagat. 59(4), 1275–1285 (2011). [CrossRef]

]. We optimized widths and offsets of input/output waveguides and the lengths of the 2 × 2 coupler, unbalanced interferometer, 2 × 1 coupler and taper sections simultaneously. Considering the fabrication repeatability, the width of the tip of the taper is set to 0.2 μm. In the following two sections, we present simulation results for a 1.30/1.31 μm and 1.31/1.55 μm wavelength combiner.

3. Simulation results − 1.30/1.31 μm wavelength combiner

The proposed device is simulated using the commercial software FIMMWAVE [11

11. D. F. G. Gallagher and T. P. Fellici, “Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons,” Proc. SPIE 4987, 69–82 (2003). [CrossRef]

] which uses the eigenmode expansion method to solve the propagation problem. A 3-dimensional finite difference mode solver has been employed as a mode solver in all sections. The optimized lengths of the four sections were found to be L1 = 197.9 μm, L2 = 849.1 μm, L3 = 44.9 μm, and Lt = 89.9 μm. The optimized waveguide widths are Wport = 2.8 μm. The offsets for the input and output ports are Oin = 0.50 μm, Oout1 = 1.50 μm and Oout2 = 1.63 μm.

Figures 4(a) and 4(b) show propagation patterns for 1.30 μm input to port 1, and 1.31 μm input to port 2, respectively. In the interferometer section, two beams are confined into each section. However, since the two modes as shown in Figs. 3(a) and 3(b) are not totally spatially separated, there are interference patterns as can be seen in the interferometer section. The wavelength-dependent transmission for this device is shown in Fig. 5. Since this device was optimized at 1.30 μm and 1.31 μm, the transmittance (ratio of the output power to the input power) is as high as 0.870 (0.6 dB loss).

Fig. 4: Propagation patterns for a 1.30/1.31 μm wavelength combiner. The total MMI length is 1271.7 μm
Fig. 5: Wavelength-dependent transmittance of a 1.30/1.31 μm wavelength combiner.

We also optimized a device without taper sections. In this case, the transmittance was 0.798, which was 7.2% lower than the case with taper sections. Therefore, taper sections play an important role in guiding beams smoothly between sections with different vertical confinement. Also, the optimized interferometer length was 873.0 μm, which is close to the optimum length L0 = 893 μm calculated from Eq. (2). Note that L2 = 849.1 μm when taper sections are used. So the difference between 873.0 μm and 849.1 μm shows the effective length of taper section as part of an interferometer. To the best of our knowledge, no attempt has been made at using MMI-based devices for targeting such a small wavelength spacing to date. The high transmittance achieved using our proposed device concept is promising.

A common device for wavelength splitters or combiners is an AWG. For an InP-based AWG, Barbarin et al. [1

1. Y. Barbarin, X. J. M. Leijtens, E. A. J. M. Bente, C. M. Louzao, J. R. Kooiman, and M. K. Smit, “Extremely small AWG demultiplexer fabricated on InP by using a douoble-etch process,” IEEE Photon. Technol. Lett. 16(11), 2478–2480 (2004). [CrossRef]

] reported very small size of 230 μm × 330 μm. On the other hand, our 1.30/1.31 μm wavelength combiner has a size of 6 μm × 1272 μm. For photonic integrations circuit applications, there may be situations where latter is more favorable than the other.

4. Simulation results − 1.31/1.55 μm wavelength combiner

Another important application of wavelength combiner is for the 1.31 μm/1.55 μm wavelength spacing. For this application, we re-optimized the device parameters. In this case, MMI width is W = 8.0 μm, patch width is W1 = 4.5 μm, input and output waveguide widths of Wport = 3.0 μm were used. We then optimized section lengths and found L1 = 253.5 μm, L2 = 11.7 μm, L3 = 52.9μm, and Lt = 83.1 μm. The offsets for the input and output ports are Oin = 1.46 μm, Oout1 = 1.16 μm and Oout2 = 2.58 μm. The total MMI length is 484.3μm.

Figures 6(a) and 6(b) show propagation patterns for 1.31 μm input to port 1, and 1.55 μm input to port 2, respectively. These show the effective combining effect clearly. Note that lower refractive index part is on the lower side of the arm.

Fig. 6: Propagation patterns for a 1.31/1.55 μm wavelength combiner. The total MMI length is 484.3μm.

The wavelength-dependent transmission for this device is shown in Fig. 7. This device was optimized at 1.31 μm and 1.55 μm and the peak transmittance is as high as 0.856 (0.67 dB loss) which is comparable to the 0.87 transmittance acheived for the 10 nm wavelength spacing. This illustrates the suitability of our device concept for a wide range of wavelength spacings.

Fig. 7: Transmittance of a 1.31/1.55 μm combiner as a function of wavelength.

In order to evaluate the tolerance to fabrication error, we first changed the groove thickness Tg. Its nominal value is 0.20 μm and is changed by ±0.01μm which is 5% deviation from the nominal value. As discussed in Section 2, this can be achieved if we use etch-top layer and selective etching, for example. Figure 8(a) shows that the peak wavelength and height are slightly affected. We then calculated the transmittance as a function of wavelength when the groove width W1 was changed by ±0.05μm which can be achieved by the current state-of-theart lithography and etching technologies. The result is shown in Fig. 8(b), and the device still performs satisfactorily as a 1.31/1.55 μm wavelength combiner. Device optimization technique by taking the fabrication error into account has been discussed in [9

9. S. Özbayat, K. Kojima, T. Koike-Akino, B. Wang, K. Parsons, S. Singh, S. Nishikawa, and E. Yagyu, “Application of numerical optimization to the design of InP-based wavelength combiners,” Opt. Commun. 322, 131–136 (2014). [CrossRef]

], and if we had used this scheme for this device, the device would have been better optimized taking into account such fabrication errors.

Fig. 8: Sensitivity analysis of a 1.31/1.55 μm wavelength combiner.

The proposed device concept has thus been shown to perform satisfactorily against variations in its groove thickness and width as can be observed by observing the transmittances for varying groove thickness and width in Fig. 8(a) and Fig. 8(b) respectively.

5. Discussions

With λ = 1.30 μm input to port 1, the relative power (with input power as 1.0) of the lowest TE mode (the lower arm in Fig. 4(a)) is 0.6171, while that of the third lowest TE mode (the lower arm in Fig. 4(b)) is 0.3125. The other modes have a few percent or less. Therefore, these two modes form the basis for the interferometer. Note that our device was optimized such that the transmittance for λ = 1.30 μm input to port 1 and λ = 1.31 μm input to port 2 are maximized simultaneously. If we designed the device as a wavelength splitter, where transmittances for λ = 1.30 μm input to port 2 and λ = 1.31 μm input to port 1 are minimized (in reality the device is used in the reverse direction), we would have different device parameters, and more balanced power for the two MMI modes will be obtained. The maximum transmittance in the current design is limited to 0.87. This can be partly explained by observing that the mode shown in 3(b) has a small distribution in the right hand side, and it is not completely spatially separated from lowest TE mode. Hence the interferometer suffers a small loss.

Even though we have focused on the InP material system in this paper, the device concept could readily be extended to other material systems such as SOI by adjusting the effective refractive index within an MMI. The concept of nonuniform refractive index distribution can potentially be extended to N × 1(N > 2) combiner or splitter. For that, one would need to create a structure with modes having multiple (> 2) effective refractive indices by the combination of different core layer thickness and width of the waveguides.

6. Conclusion

A novel device concept for designing compact MMI-based wavelength combiners has been proposed. A refractive index step in the cross-section of the MMI creates two distinct modes, which can be used for an unbalanced interferometer. Wavelength combiners were designed with 1.30/1.31 μm and 1.31/1.55 μm wavelength spacings as examples. Simulations show that the devices have insertion losses in the range of 0.6 − 0.67 dB. These devices are significantly shorter than conventional MMI-based wavelength combiners. Since their width is much smaller than conventional AWGs and MZIs, they may have a potential for high density integration on a chip.

References and links

1.

Y. Barbarin, X. J. M. Leijtens, E. A. J. M. Bente, C. M. Louzao, J. R. Kooiman, and M. K. Smit, “Extremely small AWG demultiplexer fabricated on InP by using a douoble-etch process,” IEEE Photon. Technol. Lett. 16(11), 2478–2480 (2004). [CrossRef]

2.

N. Goto and G. L. Yip, “Y-branch wavelength multi-demultplexer for λ=1.30 μm and 1.55 μm,” Electron. Lett. 26, 102–103 (2007). [CrossRef]

3.

A. Tervonen, P. Poyhonen, S. Honkanen, and M. Tahkokorpi, “A guided-wave Mach–Zehnder interferometer structure for wavelength multiplexing,” IEEE Photon. Technol. Lett. 3, 516–518 (1991). [CrossRef]

4.

C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, and M. K. Smit, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the 7th Eur. Conf on Int. Opt. (ECIO ’95), 275–278 (1995).

5.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

6.

C. Yao, H. G. Bach, R. Zhang, G. Zhou, J. H. Choi, C. Jiang, and R. Kunkel, “An ultracompact multimode interference wavelength splitter employing asymmetrical multi-section structures,” Opt. Express 20, 18248–18253 (2012). [CrossRef] [PubMed]

7.

Y. Shi, S. Anand, and S. He, “A polarization-insensitive 1310/1550-nm demultiplexer based on sandwiched multimode interference waveguides,” IEEE Photon. Technol. Lett. 19, 1789–1791 (2007). [CrossRef]

8.

M.-C. Wu and S.-Y. Tseng, “Design and simulation of multimode interference based demultiplexers aided by computer-generated planar holograms,” Opt. Express 18, 11270–11275 (2010). [CrossRef] [PubMed]

9.

S. Özbayat, K. Kojima, T. Koike-Akino, B. Wang, K. Parsons, S. Singh, S. Nishikawa, and E. Yagyu, “Application of numerical optimization to the design of InP-based wavelength combiners,” Opt. Commun. 322, 131–136 (2014). [CrossRef]

10.

M. D. Gregory, Z. Bayraktar, and D. H. Werner, “Fast optimization of electromagnetic design problems using the covariance matrix adaptation evolutionary strategy,” IEEE Trans. Antennas Propagat. 59(4), 1275–1285 (2011). [CrossRef]

11.

D. F. G. Gallagher and T. P. Fellici, “Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons,” Proc. SPIE 4987, 69–82 (2003). [CrossRef]

12.

Y. P. Li, C. H. Henry, E. J. Laskowski, H. H. Yaffe, and R. L. Sweatt, “Monolithic optical waveguide 1.31/1.55 μm WDM with −50dB crosstalk over 100 nm bandwidth,” Electron. Lett. 312100–2101 (1995). [CrossRef]

OCIS Codes
(230.1360) Optical devices : Beam splitters
(230.3120) Optical devices : Integrated optics devices
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Integrated Optics

History
Original Manuscript: February 13, 2014
Revised Manuscript: March 24, 2014
Manuscript Accepted: March 25, 2014
Published: April 2, 2014

Citation
Siddharth Singh, Keisuke Kojima, Toshiaki Koike-Akino, Bingnan Wang, Kieran Parsons, Satoshi Nishikawa, and Eiji Yagyu, "An MMI-based wavelength combiner employing non-uniform refractive index distribution," Opt. Express 22, 8533-8540 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-8533


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References

  1. Y. Barbarin, X. J. M. Leijtens, E. A. J. M. Bente, C. M. Louzao, J. R. Kooiman, M. K. Smit, “Extremely small AWG demultiplexer fabricated on InP by using a douoble-etch process,” IEEE Photon. Technol. Lett. 16(11), 2478–2480 (2004). [CrossRef]
  2. N. Goto, G. L. Yip, “Y-branch wavelength multi-demultplexer for λ=1.30 μm and 1.55 μm,” Electron. Lett. 26, 102–103 (2007). [CrossRef]
  3. A. Tervonen, P. Poyhonen, S. Honkanen, M. Tahkokorpi, “A guided-wave Mach–Zehnder interferometer structure for wavelength multiplexing,” IEEE Photon. Technol. Lett. 3, 516–518 (1991). [CrossRef]
  4. C. van Dam, M. R. Amersfoort, G. M. ten Kate, F. P. G. M. van Ham, M. K. Smit, “Novel InP-based phased-array wavelength demultiplexer using a generalized MMI-MZI configuration,” in Proceedings of the 7th Eur. Conf on Int. Opt. (ECIO ’95), 275–278 (1995).
  5. L. B. Soldano, E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]
  6. C. Yao, H. G. Bach, R. Zhang, G. Zhou, J. H. Choi, C. Jiang, R. Kunkel, “An ultracompact multimode interference wavelength splitter employing asymmetrical multi-section structures,” Opt. Express 20, 18248–18253 (2012). [CrossRef] [PubMed]
  7. Y. Shi, S. Anand, S. He, “A polarization-insensitive 1310/1550-nm demultiplexer based on sandwiched multimode interference waveguides,” IEEE Photon. Technol. Lett. 19, 1789–1791 (2007). [CrossRef]
  8. M.-C. Wu, S.-Y. Tseng, “Design and simulation of multimode interference based demultiplexers aided by computer-generated planar holograms,” Opt. Express 18, 11270–11275 (2010). [CrossRef] [PubMed]
  9. S. Özbayat, K. Kojima, T. Koike-Akino, B. Wang, K. Parsons, S. Singh, S. Nishikawa, E. Yagyu, “Application of numerical optimization to the design of InP-based wavelength combiners,” Opt. Commun. 322, 131–136 (2014). [CrossRef]
  10. M. D. Gregory, Z. Bayraktar, D. H. Werner, “Fast optimization of electromagnetic design problems using the covariance matrix adaptation evolutionary strategy,” IEEE Trans. Antennas Propagat. 59(4), 1275–1285 (2011). [CrossRef]
  11. D. F. G. Gallagher, T. P. Fellici, “Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons,” Proc. SPIE 4987, 69–82 (2003). [CrossRef]
  12. Y. P. Li, C. H. Henry, E. J. Laskowski, H. H. Yaffe, R. L. Sweatt, “Monolithic optical waveguide 1.31/1.55 μm WDM with −50dB crosstalk over 100 nm bandwidth,” Electron. Lett. 312100–2101 (1995). [CrossRef]

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