## Abstract

We developed an InP-based 4x1 transversal filter (TF) with multi-mode interference couplers (MMIs) as a compact wavelength multiplexer (MUX) 1700 μm x 400 μm in size. Furthermore, we converted the MMI-based TF to a reflection type to obtain an ultra-compact MUX of only 900 μm x 50 μm. These MUXs are made with a simple fabrication process and show a satisfactory wavelength filtering operation as MUXs of monolithically integrated light source arrays, for example, for 100G bit Ethernet.

© 2014 Optical Society of America

## 1. Introduction

A low loss and compact wavelength multiplexer (MUX) is a key component of InP-based photonic integrated circuits (PICs) for use in compact optical communication transmitters with a large output power. There are various InP-based laser diode (LD)-array-type PICs in which light sources and MUXs are monolithically integrated, such as wavelength division multiplexing (WDM) light sources [1–4], and tunable lasers [5]. Low-loss MUXs contribute to the large output power of the LD-array-type PICs. Furthermore, since a MUX tends to require a large space on a PIC chip, compact MUXs are also important for obtaining a high PIC yield and a small transmitter size.

An Nx1-channel multi-mode interference coupler (MMI) is commonly used as a MUX for LD-array-type PICs because of its compact size, ease of fabrication, and low wavelength dependence. However, when we use an Nx1-MMI as a MUX, there is an inevitable excess loss, namely, the input light power decays to 1/N. The fundamental MUX loss of conventional MMI MUXs means they have poor scalability as regards number of channels.

Arrayed waveguide gratings (AWGs) [6,7] are widely used instead of MMI-MUXs. The wavelength filtering characteristics of AWGs mean that unlike MMIs they have no fundamental loss. Furthermore, slab couplers in an AWG provide high scalability with respect to channel number. Although AWGs perform well as MUXs, there is a trade-off between the number of delay lines and insertion loss, which means that we need more than N lines for an N-channel MUX. And even when we choose a suitable number of lines, AWGs also tend to suffer from coupling loss between the slab coupler and the delay lines. Although a low-loss junction structure between those waveguides can be obtained by engineering the fabrication process [7], a simpler fabrication process contributes to the high yield of a monolithically integrated light source chip.

To fabricate a low-loss and compact MUX simply, we use an MMI-based transversal filter (MMI-TF) as a MUX. An MMI-TF has already been demonstrated as a demultiplexer (DEMUX) for an optical orthogonal frequency division multiplexing receiver on a silica planar lightwave circuit [8]. We have tried to use the MMI-TF as a MUX for an LD-array-type PIC. Since the MMI-TF is an interferometric MUX like a Mach-Zehnder interferometer [4] rather than a diffractive MUX like an AWG, it can provide a low loss MUX with just N delay lines for an N-channel configuration. And relatively low-loss coupling between an MMI and a single waveguide can be obtained with simple structures, resulting in a simple fabrication process.

In this paper, we describe a compact, low loss InP-based MMI-TF for the MUX of an LD-array-type PIC. We designed and fabricated an MMI-TF for the first time on an InP wafer. Our fabricated MMI-TF shows practical filtering characteristics as the MUX of a monolithically integrated 100G bit Ethernet (100GbE) WDM light source chip, and it is compact at ~1700 μm x ~400 μm. Moreover, we also report our newly developed reflection-type MMI-TF (RTF), which is extremely compact at only ~900 μm x ~50 μm. A fabricated RTF also exhibits a satisfactory MUX operation.

## 2. Design of MMI-TF

In this section, we describe the design of a 4-channel MMI-TF, which can operate as the MUX of a 4-channel LD array. Although we intend to use the 4x1 MMI-TF as a MUX, here we consider a “1x4” MMI-TF as a DEMUX for ease of understanding. The relationship between the input signal, *x(t)*, and the discrete Fourier transform (DFT) output, *X(f)*, of a standard TF is as follows:

Equation (1) means that *x(t)* is sampled at every interval time, *Δt*, from the start time, *t _{0}*, and as a result, four

*X(f)*values are output as the DFT coefficients of

*x(t)*.

*Δf ( = 1/4Δt)*and

*f*are the frequency resolution and center frequency of the TF, respectively. In the MMI-TF we express Eq. (1) with the transfer matrices of a 1x4 MMI (

_{0}*T*), a 4-array delay line (

_{1x4MMI}*T*), and a 4x4 MMI (

_{4delay}*T*). Namely, we can obtain the four sampled

_{4x4MMI}*x(t)*values by splitting the input light with a 1x4 MMI and adding adequate time delays to each beam with a delay-line array. And we input the four beams into a 4x4 MMI designed as a 4x4 DFT circuit.

The 1x4 MMI operates as a 1x4 splitter. When we consider the phase relationship between the four outputs of the 1x4 MMI, the transfer matrix of a 1x4 splitter, *T _{1x4splitter}*, is expressed as

*T*, as follows:

_{1x4MMI}In Eq. (2), we assume that a light phase decreases with distance traveled. We can obtain *T _{1x4splitter}* by multiplying

*T*by a diagonal matrix whose elements compensate for the phase difference between the output ports of a 1x4 MMI. In an actual device, multiplying

_{1x4MMI}*T*by the diagonal matrix means that we add a phase-shifter array at the output of the 1x4 MMI, as shown on the right in Fig. 1(a).

_{1x4MMI}The length of the 4-array delay line determines the free spectral range (FSR) of the filter. As with AWGs, the length of each line changes in *ΔL = c/n _{g}ν_{FSR}* steps. Here,

*c*,

*n*and

_{g}*ν*are the speed of light in a vacuum, the group refractive index in the delay lines and the FSR of the filter, respectively. If we consider a single frequency, or propagation constant,

_{FSR}*β*,

*T*is expressed with

_{4delay}*ΔL*and

*β*, in the form

We obtain the transfer matrix of a 4x4 DFT circuit, *T _{4x4DFT}*, by a two-step conversion of

*T*. The first step consists of interchanging the row and column elements of

_{4x4MMI}*T*as follows:

_{4x4MMI}The second step involves multiplying the element-interchanged MMI matrix by appropriate diagonal matrices from both the left and right sides so that the MMI matrix conforms to *T _{4x4DFT}*.

To implement the conversion, we have more than one possible row and column combination of the MMI matrix to be interchanged, and there are additional phase shifts associated with the interchange. As described in [8], if we define * _{4x4MMI}* and

*T*as

_{4x4DFT}*and*

_{4x4MMI}≡ [b_{ij}]*T*, the conversion of

_{4x4DFT}≡ [d_{ij}]*T*to

_{4x4MMI}*must be implemented so that*

_{4x4MMI}*satisfies*

_{4x4MMI}Equation (6) is derived from the fact that the two matrices by which we multiply * _{4x4MMI}* to obtain

*T*in Eq. (5) should be diagonal matrices. In the actual device, the conversion means that we interchange the order of the input/output (I/O) ports of the MMI and add phase shifters at each port as shown on the left in Fig. 1(a).

_{4x4DFT}We can obtain the transfer matrix of an MMI-TF, *T _{MMI-TF}*, from the product of Eqs. (2), (3), and (5), namely

*T*. Figure 1(b) shows the schematic structure of an MMI-TF. Since we interchange the rows and columns of

_{MMI-TF}= T_{4x4DFT}T_{4delay}T_{1x4splitter}*T*, we need to cancel the interchange to avoid intersecting delay lines. And, when we use the MMI-TF as the MUX of an LD array, we can remove the phase-shifters at the DFT output ports (MUX input ports).

_{4x4MMI}Figure 2 shows the wavelength-domain transmittance of _{MMI-TF}, which is obtained by modifying *T _{MMI-TF}* through canceling the interchange and removing the phase-shifters at the DFT output ports. Labels #1 to #4 correspond to the numbers in Fig. 1(b). Wavelength dependence is not considered in the calculation. So, in a practical design, we need to adopt adequate MMIs so that transmittance peaks of MMIs correspond to the wavelength band of the input light.

We found that _{MMI-TF} expresses the wavelength filtering operation, and transmittance peaks appear periodically in the order channel #1-#2-#4-#3-#1…, according to the increase in the input light wavelength. Since we interchange the 4x4-MMI ports in the design stage, as shown on the left in Fig. 1(a), DFT outputs, *X(f)*, *X(f + Δf)*, *X(f + 2Δf)*, *X(f + 3Δf)*, appear in ports #4, #2, #1, #3 respectively. The order is reversed for the wavelength domain expression in Fig. 2.

## 3. Experimental characteristics of MMI-TF

We fabricated an MMI-TF with a semiconductor wafer by conventional photolithography and dry etching in the form of inductively coupled plasma reactive ion etching. The wafer consists of an InP clad (1500 nm), an InGaAsP core (1.15Q, 300 nm), and an InP substrate. The waveguide has a high-mesa structure which is advantageous in terms of realizing a compact device and can be integrated with other optical devices such as ridge lasers [1–4]. A photograph of the fabricated MMI-TF is shown in Fig. 3(a). The effective device size is about 1700 μm x 400 μm. The widths of the two MMIs for a 4x4 DFT circuit and a 1x4 splitter are the same of 16 μm, and the lengths are 630 μm and 160 μm, respectively. The unit length of delay lines (*ΔL*) is about 25 μm and each width is 2 μm. Since we adjust the length of each line to obtain suitable phase shifters as shown in Fig. 1(b), the length differences among the lines are not strictly equal to the integral multiple of *ΔL*. And it is found that the lengths of the lines are determined almost by the distance of the two MMIs because even the length of 3*ΔL* is about 75 μm.

Figure 3(b) shows the experimental transmission characteristics of the fabricated MMI-TF with amplified spontaneous emission (ASE) light from a praseodymium-doped fiber amplifier. The fabricated MMI-TF is designed for use in the MUX of a 100GbE light source PIC. Labels #1 to #4 correspond to the numbers in Fig. 3(a). In the experimental device, we set each transmittance peak at a 100GbE grid wavelength. The transmittance was obtained by subtracting the coupling loss between a lensed fiber and the chip facet from the fiber-to-fiber transmittance of the MMI-TF. We observed the basic filtering characteristics of the MMI-TF, and the transmittance peak of each channel was about 3-4 dB. We estimated that the loss mainly derives from the coupling loss between the MMI and single waveguides, and it is about 0.5 dB per coupling. One of advantages of the MMI-TF is that we can obtain such relatively low-loss couplers with a simple fabrication process. The dashed line at −7 dB in Fig. 3(b) indicates the experimental transmittance of our 4x1 MMI [1]. So, when we integrate LDs with the MMI-TF and set all the lasing wavelengths so that they correspond to the transmittance peaks of the MMI-TF, we can improve the MUX loss by about 3 dB compared with that when using an MMI-MUX.

## 4. Conversion to reflection-type MMI-TF

As described in the previous section, we observed the basic filtering operation of the MMI-TF. The next challenge is to reduce its size, which is a critical factor as regards realizing LD-array-type PICs with a high yield. We have two possible approaches for the reduction.

The first is to shorten the MMI length by reducing its width. The advantages of a shorter MMI are the smaller wavelength dependence of its transmittance and a high device yield. On the other hand, if we adopt a narrower MMI, we have to choose a narrower I/O port width and gap between those I/O ports, which is unsuitable from the viewpoint of fabrication tolerance. A narrow I/O port leads to an MMI-TF with a narrow delay line, which results in phase error [9] in a propagating beam unless we employ tapered waveguides of an appropriate length. We should avoid phase error in an interferometric filter such as our MMI-TF.

The second approach involves shortening the delay-line length. The lengths of delay lines in an MMI-TF are the total of the integral multiples of *ΔL* and less than half the wavelength of the phase shifters as shown in Fig. 1(b). Although an essentially required line length is less than 100 μm even for the longest delay line of our 4x1 MMI-TF, in the actual device there is a “reference” delay line whose length is the shortest and is determined by the distance between the 4x4 and 4x1 MMIs. Therefore, the actual length of each delay line is the sum of the above “essential” delay length and the reference length. Although we can reduce the reference line length by placing the two MMIs closer together, such an MMI-TF requires bent waveguides with a smaller radius of curvature for the delay lines in which propagating beams tend to exhibit phase error and excite higher order modes.

As a way to reduce the size of the MMI-TF without employing a narrow MMI and/or a small radius of curvature for the delay lines, we converted our conventional MMI-TF to a reflection-type MMI-TF (RTF). To convert a 4x1 MMI-TF to a 4x1 RTF, we designed a “symmetric 5x1” TF using the same approach that we employed for the 4x1 MMI-TF. That is, a 5x5 MMI is used for the output-side coupler instead of a 5x1 MMI as shown in Fig. 4(a). As with design of 4x1 MMI-TF, we make a 1x5 splitter of a 5x5 MMI by adding suitable phase shifters at each output port. And we also convert another MMI to a 5x5 DFT circuit by interchanging the order of the I/O ports and adding phase shifters. Since both the input- and output-side couplers are 5x5 MMIs, the device structure is symmetric. Hence, by folding the 5x1 TF at its center position we can obtain a 5x1 RTF (Fig. 4(b)). When we input light whose wavelength matches the transmittance peak of the 5x1 RTF into only four of the five input ports we can use the 5x1 MUX RTF as a 4x1 MUX RTF. The greatest merit of the RTF is that we can remove the reference delay line from the conventional MMI-TF as shown in Fig. 4, which helps make the RTF compact.

## 5. Experimental characteristics of RTF

We fabricated an RTF with the same InP wafer as we used for our conventional MMI-TF. After forming the waveguides, we made Au mirrors with high reflectance [10] at the etched facet of the delay lines. Figure 5 is a photograph of the fabricated 4x1 RTF. The RTF effective device region is ~900 μm x ~50 μm. The device consists of one 5x5 MMI (~800 μm x 20 μm) and five delay lines. We adopt *ΔL* of *~20/2 = ~10* μm for delay lines, and the factor of 1/2 is derived from the fact that the lines of the RTF are reflection type. The width of each line is 2.6 μm which is wider than that of our conventional MMI-TF, since we do not need any bent structure for the delay lines of the RTF. Thanks to the removal of the reference delay line as described in the previous section, we obtain very compact RTF whose length is about half that of the conventional MMI-TF. As regards the width, it is less than 50 μm and is determined solely by the 5x5-MMI width. The conventional MMI-TF needs a width of ~400 μm because of its bent delay lines.

The designed and experimental transmissions of a 4x1 RTF are shown in Fig. 6(a) and (b), respectively. Labels #1 to #4 correspond to the numbers in Fig. 5. The peak intervals between the four channels are also set at 4.5 nm as with the conventional MMI-TF. In Fig. 6(a), the dashed curve indicates transmittance which we can obtain when we input light from the MUX output port. In other words, it is a “reflectance” curve of the MUX output port, which can be understood by comparing Fig. 4(a) and (b). Since we did not measure the “reflectance” in the experiment, it is not shown in the Fig. 6(b). The designed transmittance is calculated by the eigenmode expansion method rather than with a transfer matrix model as shown in Fig. 2. So, the calculation includes actual waveguide characteristics such as the wavelength dependence of a 5x5 MMI which is also shown in Fig. 6(a) as a round-trip transmittance since input light twice propagates in the MMI. We calculated the round-trip transmittance by halving a total of transmittances of five split beams when we input light from the center input port of a 5x5 MMI.

We observed comparable filtering performance to the conventional MMI-TF, and the MUX loss was about 4 dB at each peak wavelength. We assume that the loss difference between the RTF and the MMI-TF is caused by an optical decay of about 0.5 dB in the Au mirrors at the etched facets [10]. And, the difference can arise from the fact that the input light propagates twice in a 5x5 MMI for the RTF. We assume that the 5x5 MMI has a somewhat larger insertion loss than that of the 1x4 MMI of a conventional MMI-TF.

When we integrate the RTF with an LD array as a MUX, the compactness can become a large advantage by devising the device layout. In monolithically integrated WDM light sources, the array distance is generally a few hundred μm to prevent radio frequency crosstalk from each light source. As described above, since the RTF width is a few tens of μm, we can place the RTF between the light sources as shown in Fig. 7, which means that we do not need additional chip space for a MUX.

## 6. Conclusion

We described the design of an MMI-TF for the MUX of a 100GbE light source PIC and observed its experimental filtering operation. Furthermore, to reduce the device size, we converted the MMI-TF to the RTF and also obtained its filtering operation experimentally. Both of them show comparable wavelength filtering and they are beneficial to the reduction of the MUX loss of LD-array-type PICs. The RTF is particularly compact at about 900 μm x 50 μm, and it does not need additional chip space for a MUX by placing the RTF between the light sources. We believe that our RTF can help to enhance the output power and reduce the chip size of LD-array-type PICs for optical communication.

## References and links

**1. **T. Fujisawa, S. Kanazawa, H. Ishii, N. Nunoya, Y. Kawaguchi, A. Ohki, N. Fujiwara, K. Takahata, R. Iga, F. Kano, and H. Oohashi, “1.3-μm 4 x 25-Gb/s Monolithically Integrated Light Source for Metro Area 100-Gb/s Ethernet,” IEEE Photon. Technol. Lett. **23**(6), 356–358 (2011). [CrossRef]

**2. **S. Kanazawa, T. Fujisawa, A. Ohki, H. Ishii, N. Nunoya, Y. Kawaguchi, N. Fujiwara, K. Takahata, R. Iga, F. Kano, and H. Oohashi, “A Compact EADFB Laser Array Module for a Future 100-Gb/s Ethernet Transceiver,” IEEE J. Sel. Top. Quantum Electron. **17**(5), 1191–1197 (2011). [CrossRef]

**3. **T. Fujisawa, S. Kanazawa, K. Takahata, W. Kobayashi, T. Tadokoro, H. Ishii, and F. Kano, “1.3-μm, 4 × 25-Gbit/s, EADFB Laser Array Module with Large-output-power and Low-driving-voltage for Energy-efficient 100GbE Transmitter,” Opt. Express **20**(1), 614–620 (2012). [CrossRef] [PubMed]

**4. **T. Fujisawa, S. Kanazawa, Y. Ueda, W. Kobayashi, K. Takahata, A. Ohki, T. Ito, M. Kohtoku, and H. Ishii, “Low-Loss Cascaded Mach–Zehnder Multiplexer Integrated 25-Gbit/s x 4-Lane EADFB Laser Array for Future CFP4 100 GbE Transmitter,” IEEE J. Quantum Electron. **49**, 1001–1007 (2013). [CrossRef]

**5. **H. Ishii, K. Kasaya, and H. Oohashi, “Spectral Linewidth Reduction in Widely Wavelength Tunable DFB Laser Array,” IEEE J. Sel. Top. Quantum Electron. **15**(3), 514–520 (2009). [CrossRef]

**6. **Y. Hibino, “Recent Advances in High-Density and Large-Scale AWG Multi/Demultiplexers with Higher Index-Contrast Silica-Based PLCs,” IEEE J. Sel. Top. Quantum Electron. **8**(6), 1090–1101 (2002). [CrossRef]

**7. **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 Double-Etch Process,” IEEE Photon. Technol. Lett. **16**(11), 2478–2480 (2004). [CrossRef]

**8. **K. Takiguchi, T. Kitoh, M. Oguma, Y. Hashizume, and H. Takahashi, “Integrated-optic OFDM Demultiplexer using Multi-mode Interference Coupler-based Optical DFT Circuit,” in Proc. OFC 2012 OM3J.6 (2012). [CrossRef]

**9. **T. Goh, S. Suzuki, and A. Sugita, “Estimation of Waveguide Phase Error in Silica-Based Waveguides,” J. Lightwave Technol. **15**(11), 2107–2113 (1997). [CrossRef]

**10. **T. Segawa, S. Matsuo, T. Kakitsuka, Y. Shibata, T. Sato, Y. Kawaguchi, Y. Kondo, and R. Takahashi, “Monolithically Integrated Wavelength-Routing Switch using Tunable Wavelength Converters with Double-Ring-Resonator Tunable Lasers,” IEICE Trans. Electron. **E94-C**(9), 1439–1446 (2011). [CrossRef]