## Abstract

For the first time, a new-type flat focal field arrayed waveguide grating (AWG) demultiplexer, with the focal signals of all wavelengths of operation focusing along a straight line, is designed based on the aberration theory and fabricated based on a newly developed negative tone epoxy Novolak resin (ENR) polymer using electron-beam direct writing. A polymeric four-channel 400GHz spacing flat focal field AWG demultiplexer is fabricated and tested. Four modal images from the output waveguides are observed and the measured transmission spectra is presented. And we make error analysis.

©2005 Optical Society of America

## 1. Introduction

Arrayed waveguide grating (AWG) is one of the most promising devices for multi/ demultiplexer in future wavelength division multiplexing (WDM) system because of its low insertion loss, high stability and low cost [1]. All the reported AWGs are designed based on the conventional Rowland-type, in which the focal line is a circle with radius *R*
_{0}/2 , where *R*
_{0} is the radius of Rowland circle [2–5]. In this paper, a new-type flat focal field AWG, with the focal signals of all wavelengths of operation focusing along a straight line, is designed based on the aberration theory of AWG [6]. The simulation result will show that the focal line is a straight line perpendicular to the propagation direction. In the design, three stigmatic points are introduced as restraints to optimize the structure parameters [7]. Hence, the aberration of the flat focal field AWG is much lower than that of the conventional Rowland-type with only one stigmatic point. Flat focal field AWG is convenient to connect with fiber-array on the straight focal line directly without output waveguides. And because of its low aberration, a flat focal field AWG can also function as a spectrometer if the end face is well polished.

Polymeric AWG multi/demultiplexers have attracted much attention due to their low cost possibility and easy fabrication comparing to silica-based ones [8–10]. Polymeric optical waveguide devices may be fabricated in many ways, such as direct photolithography, reactive ion etching (RIE), molding, and embossing [11,12]. Among them, electron-beam direct writing has the advantages of allowing rapid prototyping without mask and allowing writing complex structure with nanometer pattern flexibly. In this paper, we described a polymeric four-channel 400GHz spacing flat focal field AWG demultiplexer fabricated based on a newly developed negative tone epoxy Novolak resin (ENR) [13,14] polymer using electron-beam direct writing. Four modal images from the output waveguides are observed and the measured transmission spectra is presented. And we make error analysis.

## 2. Design of a polymeric flat focal field AWG

#### 2.1 Flat focal field AWG

The conventional Rowland-type AWG has three essential features [2,3]. The first, the input and output apertures of phased-array are typical examples of Rowland-type mountings. The second, the ports of phased-array are distributed in uniform positions along the input and output apertures. And the third, the difference in path length of adjacent paths should be a constant. The focal line of a Rowland-type AWG is a circle with radius *R*
_{0}/2 , where *R*
_{0} is the radius of Rowland-circle. All the reported AWGs are designed based on the standard structure with these features [4,5]. However, in the developed general aberration theory of AWG, the standard structure has been generalized [6].

The schematic diagram for AWG aberration analysis is shown in Fig. 1. The coordinate systems of the input and output part, XOY and X’O’Y’, originate at the convex of the grating curves. For the ray emitted from input waveguide at *A*(*x*_{A}*, y*_{A}
) , coupled into phased-array at *P*(*u,w*), propagated through a path, reached *P*′(*u*′,*w*′), and finally coupled into the output waveguide at *B*(*x*_{B}*, y*_{B}
), the optical path function can be written as:

where *N*_{s}
and *N*_{w}
are the effective indices of slab waveguide (of star coupler) and channel waveguide (of phased-array) respectively, *L*(*w*) is the geometrical length of the path between *P* and *P*′, *G*(*w*) is the number of waveguides counted from the origin *O* to the point *P*, *r*_{A}
(*w*) and *r*_{B}
(*w*) are the geometrical lengths in the input and output star couplers respectively, and *m* is the diffraction order.

*F*(*w*), *L*(*w*), *G*(*w*), and the grating curve *u*(*w*) can be expressed as power series:

And *r*_{A}
(*w*) and *r*_{B}
(*w*) have iterative expressions:

$${r}_{\alpha}^{\left(n\right)}\left(0\right)=\frac{1}{2}\sum _{k=1}^{n-1}\frac{{C}_{n}^{k}\left[{u}^{\left(k\right)}\left(0\right){u}^{\left(n-k\right)}\left(0\right)-{r}_{\alpha}^{\left(k\right)}\left(0\right){r}_{\alpha}^{\left(n-k\right)}\left(0\right)\right]}{{r}_{\alpha}}$$

$$\phantom{\rule{1.2em}{0ex}}-\frac{{u}^{\left(n\right)}\left(0\right){x}_{\alpha}}{{r}_{\alpha}}+\frac{\delta \left(n-2\right)}{{r}_{\alpha}}\phantom{\rule{1.2em}{0ex}}\left(n>1\right)$$

$${r}_{\alpha}=\u3008\alpha O\u3009={\left({x}_{\alpha}^{2}+{y}_{\alpha}^{2}\right)}^{\frac{1}{2}}\phantom{\rule{1.2em}{0ex}}\alpha =A,B$$

where ${C}_{n}^{k}$
is the combination number, and *δ*(*q*) is Kronecker function. As a result, the *n*-th aberration coefficient *F*
^{(n)} (0) can be expressed as:

Thus, the aberration of AWG can be analyzed using an iterative method.

From the aberration analysis, the dominant structure parameters of AWG, i.e. the geometry of star coupler *u*(*w*), the ports distribution of phased-array *G*(*w*), and the length increment between adjacent paths *L*(*w*), are all free variables for design. Therefore, the standard structure of Rowland-type AWG has been generalized. Three restraints at most can be imposed on them to obtain new-type AWGs. In the design of flat focal field AWG, three stigmatic points are introduced as restraints to optimize the structure parameters. All the aberration coefficients of the stigmatic points are equal to zero, supposing at wavelengths *λ*
_{1}, *λ*
_{2}, and *λ*
_{3}:

Figure 2 shows the schematic diagram of flat focal field AWG, where *R* is the focal length of slab, and *θ* is the dispersion angle. The output waveguides align along a straight line, and so do the input waveguides. From Fig. 2, for a flat focal field AWG, *r*
_{1}, *r*
_{2}, and *r*
_{3} in the output star coupler (i.e. *r*_{B}
) should be:

$${x}_{k}=R$$

$${y}_{k}=R\bullet \mathrm{tan}\left({\theta}_{k}\right)$$

Using Eq. (3) and Eq. (6), an iterative procedure is carried out to calculate *u*
^{(n)}(0) and ${r}_{k}^{\left(n\right)}$(0) (*n* = 1,…,*N*; *k* = *A*,1,2,3) [7], where *N* is the expansion power. Then, *L*
^{(n)}(0) and *G*
^{(n)}(0) (*n* = 1,…,*N*) can be solved from Eq. (5). And then, *L*(*w*), *G*(*w*), and *u*(*w*) can be obtained from Eq. (2). All the dominant structure parameters of a flat focal field AWG are worked out. The iterative calculation procedure is easy to be implemented on computer.

The flat focal field AWG is convenient to connect with fiber-array on the straight focal line directly without output waveguides, as shown in Fig. 3(a). Compared with the conventional Rowland-type AWG with only one stigmatic point at central wavelength, the flat focal field AWG with three stigmatic points has significantly reduced aberration. Low aberration will result in good spectral response. When the end face of the output star coupler is polished well and the array of photodetectors is placed at the straight focal line as shown in Fig. 3(b), a flat focal field AWG can also function as a spectrometer. However, if the output star coupler directly connecting with fiber-array or photodetectors, the spacing of output focal signals should be determined by the actual size of fiber-array or photodetectors. This will lead to a relatively large chip size of flat focal field AWG, which is not beneficial to large-scale and high-density integration. Therefore, the flat focal field AWG is applicable to medium- or low-channel WDM system, such as coarse-WDM (CWDM).

#### 2.2 Design and simulation results

A four-channel 400GHz spacing flat focal field AWG demultiplexer is designed based on a polymeric single-mode waveguide, which will be described in Sect. 3.1. The design parameters are listed in Tab. 1. For the convenience of testing, the flat focal field AWG demultiplexer contains output waveguides.

The performance of the AWG demultiplexer is simulated by Alcatel planar optical design software, PrometheusDV 4.2 [15]. The 2D beam propagations of four channel wavelengths are shown in Fig. 4. The focal points of all wavelengths of operation are verified to focus on a straight line perpendicular to the propagation direction. Figure 5 shows the transmission spectra.

Figure 6 shows the aberration curve of the polymeric four-channel 400GHz spacing flat focal field AWG with three stigmatic points (1545.752nm, 1550nm, 1554.248nm), comparing with the conventional Rowland-type AWG with only one stigmatic point at central wavelength (1550nm), aberration in unit of wavelength. These two AWGs have the same design parameters. The aberration of the flat focal field AWG is significantly reduced. In the narrow spectral range, the aberration nearly equals to zero.

#### 2.3 Layout design

The layout of the flat focal field AWG is shown in Fig. 7. Each path in the phased-array consists of a (nonconcentric) curved waveguide (of adjustable bending radius) smoothly connected to a straight waveguide on either side. For the *i*-th path, there are two basic equations:

$${S}_{i}\phantom{\rule{.2em}{0ex}}\mathrm{cos}{\phantom{\rule{.2em}{0ex}}\alpha}_{i}+R{c}_{i}{\phantom{\rule{.2em}{0ex}}\mathrm{sin}\phantom{\rule{.2em}{0ex}}\alpha}_{i}=\frac{L}{2}$$

where *l*_{i}
, *Rc*_{i}
, and *α*_{i}
are the length, the bending radius, and the half central angle of the curved waveguide, of the *i*-th path, respectively. *S*_{i}
and *f*_{i}
are depicted in Fig. 7. For given angle and separation of the star couplers, i.e. *α*
_{0} and *L* shown in Fig. 7, *S*_{i}
and *Rc*_{i}
can be worked out using Eq. (7), which determine the geometry layout of the flat focal field AWG.

#### 2.4 Insertion loss

The insertion loss of flat focal field AWG comes from four areas: fiber-to-waveguide coupling, star couplers to phased-array waveguides transition, curved waveguides, and material. The structure and layout parameters of the four-channel 400GHz spacing flat focal field AWG demultiplexer are optimized to reduce the insertion loss.

At the ends of the input and output waveguides, the waveguides are tapered to reduce the fiber-to-waveguide coupling loss. The tapers are optimized as shown in Fig. 8(a), and the coupling loss drops from 2×4.2965dB to 2×2.9168dB. Tapering the phased-array waveguides at the input and output apertures can also lower the star couplers to phased-array waveguides transition loss. The optimized structure is shown in Fig. 8(b). The phased-array with curved waveguides is an important section of AWG. Smaller bending radius will lead to higher pure bending loss. In our design, the minimal bending radius is 2361μm, and the pure bending loss is insignificant. At the junctions of curved and straight waveguides, offsets are adopted between the two segments, and the straight-bent transition loss is minimized to 0.0197dB. As listed in Tab. 2, the total insertion loss is 9.4227dB.

## 3. Fabrication using electron-beam direct writing

The four-channel 400GHz spacing flat focal field AWG demultiplexer designed in Sect. 2.2 is fabricated based on a newly developed negative tone epoxy Novolak resin (ENR) [13,14,16] polymer using electron-beam direct writing. ENR from Microchem Corp. is a cross-linkable polymer, having high refractive index, negative tone property, large hardness, and glass transition temperature (*T*_{g}
) of >200°C for full cross linking. The crucial factor for electron-beam direct writing is that ENR is an electron-beam-sensitive polymer. The saturation dosage is 3.8μC/cm^{2} at 50keV on the silicon substrate. It is 100 times more sensitive than conventional polymethyl-methacrylate (PMMA). Therefore, the writing speed is more than 100 times faster.

#### 3.1 Single-mode polymeric waveguide

A single-mode polymeric waveguide using ENR as the core-layer is designed as shown in Fig. 9. The cladding layer is UV-cured resin Norland Optical Adhesive 61 (NOA61). At 1550nm wavelength, the refractive indices of ENR and NOA61 are 1.575 and 1.54, respectively, giving a super high refractive index contrast between the core and cladding of 2.20%. To meet the requirement of single-mode propagation, a waveguide core with very small cross-section dimension is needed as shown in Fig. 9(a). The core size is 2.7μm×2.7μm. Figure 9(b) shows the field distribution of the fundamental mode. The waveguide structure ensures strong confinement of the light in the waveguide and allows low-loss bend with radius as small as 2mm. The chip size is 7×3mm^{2}.

#### 3.2 Fabrication process

The polymeric four-channel 400GHz spacing flat focal field AWG demultiplexer is fabricated on a 4-inch silicon wafer. The fabrication process is shown schematically in Fig. 10. NOA61, 6μm thickness, is first spin coated on the substrate as the bottom cladding layer and cured for 30min using UV light at a 365nm wavelength and 350W power. To further improve the adhesion, the sample is baked at 50°C for 12h in an oven. ENR, 2.7μm thickness, is then spin coated on as the waveguiding layer. A prebake time of 5min at 90°C is applied before exposure. The pattern exposure is performed using Leica EBL-100L nanowriter system at 50keV, and the electron-beam spot diameter is 70nm. The postexposure bake time is 3min at 90°C. After postexposure baking, the resist is developed for 20s in propylenglygol -monomethylether-acetate (PGMEA), and then rinsed in fresh PGMEA again to form the slab and channel waveguides. No other subsequent process after development is required. Then, the pattern is covered with 3 μm-thick UV-cured NOA61 upper cladding layer.

The layout of the fabricated polymeric flat focal field AWG demultiplexer is shown in Fig. 11(a). Figure 11(b) is the magnified (×200) image of a section of the AWG demultiplexer where tapered phased-array waveguides meet the slab region of output star coupler. The taper has been optimized to reduce the insertion loss as described in Sect. 2.4.

## 4. Testing and error analysis

#### 4.1 Testing result

The polymeric flat focal field AWG demultiplexer is tested. Light from a wide-band erbium-doped optical fiber amplifier (EDFA) (1528-1563nm) is butt-coupled into the input waveguide through standard single-mode fiber (SMF). The input and output waveguides have been tapered to butt-coupling with SMFs more efficiently as described in Sect. 2.4. The signals from the output waveguides are magnified (×20) by lens and received by infrared vidicon camera. Four modal images are observed on the monitor as shown in Fig. 12.

Then, the output signals from the output waveguides are put into optical spectrum analyzer and the transmission spectra is measured as shown in Fig. 13. The channel responses are denoted by circles. From Fig. 13, the channel wavelengths are: 1548.40nm, 1551.25nm, 1554.35nm, 1557.65nm. The average channel spacing is ~3.08nm. The insertion loss and the crosstalk are so high that the channel responses are almost submerged. However, we consider the circle denoted peaks as the channel responses mainly according to: 1) The channel wavelengths locate close to the design wavelengths; 2) The channel spacing equals to the design value approximately; 3) The sequence of the channel wavelengths corresponding to the modal images shown in Fig. 12 is correct; 4) The insertion loss of channels is flat; and 5) The shape of the four channel spectral responses is similar. The wavelength shiftings are: +3.3nm, +2.85nm, +2.75nm, +2.85nm.

#### 4.2 Error analysis

Figure 14(a) is the scanning electron microscope (SEM) image of the cross-section of the fabricated channel waveguide. Because of the small cross-section dimension, the fabrication error is large. The geometry structure of the fabricated channel waveguide is shown in Fig. 14(b), which is trapeziform in shape and much larger in size than design. Mode analysis shows that there is not only the useful fundamental mode in the waveguide, but also higher order modes, such as the first-order mode shown in Fig. 14(c). The first-order mode can be excited at the junctions between straight and curved waveguides of the phased-array and propagate coherently through the array and cause “ghost images”. Because of the difference in propagation constant between the fundamental and the first-order mode, these images will occur at different locations and the “ghost images” may couple to an undesired receiver thus degrading the crosstalk performance. Figure 15 shows the effective refractive index of the fabricated channel waveguide. At the edge regions of both sides, the effective refractive index has a graded distribution and the propagation constant deviates from the design value. As a result, the optical field propagation in these regions will contribute to crosstalk.

The wavelength shifting is mainly caused by environment temperature and fabrication error of channel waveguide. The thermo-optical (TO) coefficient of polymer material is very high. For ENR, the TO coefficient is ~2.5×10^{-4} /*K* . So, the device is very sensitive to the environment temperature. It is designed to work at 20°C, while the measurement temperature is ~30°C. Calculated from the relation between central wavelength of AWG and temperature [17], the wavelength shifting is -2.45nm. Because of the thickness increment of the core as shown in Fig. 14, the effective refractive index of channel waveguide *N*_{w}
is larger than design as shown in Fig. 15, and so is the propagation constant *β*. There is a direct proportion relation between the phase delay difference of adjacent paths of phased-array ∆*φ* and the propagation constant:

where ∆*L* is the length increment between adjacent paths. Here, ∆*L* is an initial value for the iterative design of flat focal field AWG, which is calculated from Rowland-type AWG. As a result, the central wavelength *λ*_{c}
will be red shifted. The amount of the shift *δλ* can be calculated by the following equation:

Taking both of the above-mentioned factors into consideration, we obtain a total wavelength shifting of +3.77nm. It is closed to the measured value.

Because the core thickness increases, the effective refractive index of slab waveguide *N*_{s}
also increases, from the design value 1.5646 to 1.5698. The focal length of slab *R* is directly proportional to *N*_{s}
:

where *Ñ*_{w}
= *N*_{w}
- *λ* ∙ *dN*_{w}
/ *dλ* is the group index of the fundamental mode of channel waveguide, *d*_{a}
is spacing of phased-array (also an initial value for iterative design calculated from Rowland-type AWG), *D* is spacing of output waveguides, and ∆*λ* is channel spacing. In the output star coupler, the output optical field of phased-array takes place multi-beam interference. From Eq. (10), *R* is ~2.4μm larger than design. Therefore, the focal points will locate at ~2.4μm behind the entrance of the output waveguides as shown in Fig. 16, which is a source of insertion loss. Besides, fiber-to-waveguide coupling loss and material absorption also contribute to insertion loss. A two-dimensional tapered waveguide may effectively lower the fiber-to-waveguide coupling loss, but make the fabrication process more complicated. For the purpose of simpleness, we employ one-dimensional taper-end. The propagation loss of ENR measured at 1550nm is 1dB/cm [14]. It’s ultra-low among electron-beam direct writing polymer materials, but still two orders of magnitude higher than silica material with typical propagation loss of 0.017dB/cm measured at 1550nm.

## 5. Conclusions

We have described what we believe to be the first demonstration of a new-type flat focal field AWG demultiplexer fabricated based on a newly developed ENR polymer using electron-beam direct writing. The flat focal field AWG, the focal line of which is a straight line, is designed based on the aberration theory of AWG. Three stigmatic points are introduced as restraints to optimize the structure parameters. A polymeric four-channel 400GHz spacing flat focal field AWG demultiplexer using ENR as the core-layer is designed and fabricated using electron-beam direct writing. The sample is tested. Four modal images from the output waveguides are observed and the measured transmission spectra is presented. Error analysis is made to explain the difference between the measured and simulated transmission spectra.

Up to now, there is no successful precedent of polymeric AWG fabricated using electron-beam direct writing. Especially for the newly developed polymer ENR, both the properties of the material and the fabrication technology should be further investigated. In our work, a polymeric flat focal field AWG fabricated based on ENR using electron-beam direct writing is performed as an initial attempt.

## Acknowledgments

The authors acknowledge the supports of China Postdoctoral Science Foundation (no. 2005037339) and the National Natural Science Foundation of China (no. 69990540).

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