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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 9 — Apr. 25, 2011
  • pp: 8781–8794
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Improved arrayed-waveguide-grating layout avoiding systematic phase errors

Nur Ismail, Fei Sun, Gabriel Sengo, Kerstin Wörhoff, Alfred Driessen, René M. de Ridder, and Markus Pollnau  »View Author Affiliations


Optics Express, Vol. 19, Issue 9, pp. 8781-8794 (2011)
http://dx.doi.org/10.1364/OE.19.008781


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Abstract

We present a detailed description of an improved arrayed-waveguide-grating (AWG) layout for both, low and high diffraction orders. The novel layout presents identical bends across the entire array; in this way systematic phase errors arising from different bends that are inherent to conventional AWG designs are completely eliminated. In addition, for high-order AWGs our design results in more than 50% reduction of the occupied area on the wafer. We present an experimental characterization of a low-order device fabricated according to this geometry. The device has a resolution of 5.5 nm, low intrinsic losses (< 2 dB) in the wavelength region of interest for the application, and is polarization insensitive over a wide spectral range of 215 nm.

© 2011 OSA

1. Introduction

The arrayed-waveguide grating (AWG) was first proposed by Smit in 1988 [1

1. M. K. Smit, “New focusing and dispersive planar component based on an optical phased array,” Electron. Lett. 24(7), 385–386 (1988). [CrossRef]

] and subsequently reported by Takahashi et al. in 1990 [2

2. H. Takahashi, S. Suzuki, K. Kato, and I. Nishi, “Arrayed-waveguide grating for wavelength division multi/demultiplexer with nanometer resolution,” Electron. Lett. 26(2), 87–88 (1990). [CrossRef]

] and Dragone in 1991 [3

3. C. Dragone, “An N x N optical multiplexer using a planar arrangement of two star couplers,” IEEE Photon. Technol. Lett. 3(9), 812–815 (1991). [CrossRef]

]. Since then it has developed into one of the most important devices in integrated optics. Its imaging [4

4. N. Ismail, B. I. Akca, F. Sun, K. Wörhoff, R. M. de Ridder, M. Pollnau, and A. Driessen, “Integrated approach to laser delivery and confocal signal detection,” Opt. Lett. 35(16), 2741–2743 (2010). [CrossRef] [PubMed]

] and dispersive properties make it an ideal device for wavelength separation in wavelength-division-multiplexing and spectroscopic applications. The working principle of the AWG is briefly described referring to Fig. 1(a)
Fig. 1 (Color online) (a) Schematic layout of an AWG and (b) schematic of a Rowland grating mounting where the dots indicate the positions of the arrayed waveguides arranged such that the chords have equal projections on the y axis.
.

Light from an input channel waveguide is guided to a free-propagation region (FPR) where it diffracts in the horizontal direction and is coupled to an array of channel waveguides which are arranged on a circle of radius R (grating line) equal to the length of the FPR. On this circle the arrayed waveguides are spaced by a center-to-center distance d << R. Due to the limited number of arrayed waveguides, part of the light is lost to the sides of the array (spillover losses). This arrangement, comprising the input channel, the FPR, and the array of collecting waveguides forms a 1 × N star coupler which couples the light from one input waveguide into N arrayed waveguides. The arrayed waveguides have a linearly increasing length, and the length difference between adjacent waveguides is ΔL = c/n eff, where m is an integer, λ c is the central wavelength of the AWG, and n eff is the effective refractive index of the arrayed waveguides at the central wavelength. Light exiting from the array enters a second FPR where the output terminations of the arrayed waveguides are again arranged on a circle with radius R (as for the input FPR). The center of this circle coincides with the entrance facet of the central output channel of the AWG. With this arrangement, when light at wavelength λ c is sent through the input channel, a circular wave front is generated at the output of the array, and the light is focused into the central output channel. For light at a different wavelength (λλ c) the circular wave front generated at the output is tilted with respect to the one for λ c, and the focal spot is located at a different spatial position. Output channels can be placed at different positions at the output of the second FPR to collect individual spectral components of the input signal. The design just described makes use of a constant angular spacing between the arrayed waveguides. An alternative approach, which has the advantage of reduced aberrations is the Rowland mounting [5

5. M. C. Hutley, Diffraction Gratings (Academic, 1982).

] where the arrayed waveguides, instead of being positioned at a constant angular spacing, are positioned such that chords (or center to center distances) have a constant projection on the y axis, as shown in Fig. 1(b). In this type of mounting the input and output channels are positioned on a circle (Rowland circle) and point towards the center C of the grating line. The Rowland circle has a radius of R/2 and is tangent to the grating line in C.

A typical cause of degradation in the response of an AWG is the presence of phase errors across the arrayed waveguides; these can be regarded as deviations of the optical path lengths from the designed values and can be divided into two categories. The first category comprises phase errors that arise from the device fabrication process; these phase errors are caused by random variations in the waveguide width, which depend on the resolution of the mask used in the photolithographic process [6

6. C. D. Lee, W. Chen, Q. Wang, Y.-J. Chen, W. T. Beard, D. Stone, R. F. Smith, R. Mincher, and I. R. Stewart, “The role of photomask resolution on the performance of arrayed-waveguide grating devices,” J. Lightwave Technol. 19(11), 1726–1733 (2001). [CrossRef]

], as well as waveguide side-wall roughness and non-uniformities of the guiding layer properties, such as its refractive index and thickness [7

7. 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]

]. The second category includes systematic phase errors due to the design of differently bent sections in the arrayed waveguides. In each bend light experiences an effective refractive index which is a function of the bending radius. Usually, the difference between the effective indices in the straight and bent sections of an arrayed waveguide is very small (between 1 × 10−5 and 1 × 10−4); however, when the arrayed waveguide bends over a large angle (i.e. ~π) and has a small bending radius, the induced phase deviation from the designed value may become significant. In particular, in conventional AWG layouts, such as horseshoe and s-shaped AWGs [8

8. R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11(2), 212–219 (1993). [CrossRef]

,9

9. M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2(2), 236–250 (1996). [CrossRef]

] in which the bends in the arrayed waveguides all differ in radius and length, the changes in the optical path length are different from waveguide to waveguide within the array, leading to a distortion of the wave fronts in the second FPR with a consequent defocusing effect.

Systematic phase errors are predictable and can, therefore, be accounted for when designing the relative delays between adjacent arrayed waveguides. However, this requires numerical simulations and may not lead to perfect cancellation of these phase errors due to both, simulation inaccuracies and fabrication tolerances. The AWG introduced by Takahashi et al. [2

2. H. Takahashi, S. Suzuki, K. Kato, and I. Nishi, “Arrayed-waveguide grating for wavelength division multi/demultiplexer with nanometer resolution,” Electron. Lett. 26(2), 87–88 (1990). [CrossRef]

] consisted of identical bends (four 90° bends in each arrayed waveguide), however the input and output sections of the arrayed waveguides were parallel to each other and not arranged on a star coupler. The use of star couplers in AWGs was first proposed by Dragone in 1991, in which two star couplers were interconnected by arrayed waveguides of unequal lengths and with a fixed angular separation [3

3. C. Dragone, “An N x N optical multiplexer using a planar arrangement of two star couplers,” IEEE Photon. Technol. Lett. 3(9), 812–815 (1991). [CrossRef]

]. In the star-coupler configuration the non-zero angle between adjacent waveguides of the array makes it difficult to use identical bends in the AWG layout. A partial solution to the problem was proposed in Ref. 10

10. F. M. Soares, W. Jiang, N. K. Fontaine, S. W. Seo, J. H. Baek, R. G. Broeke, J. Cao, K. Okamoto, F. Olsson, S. Lourdudoss, and S. J. B. Yoo, “InP-based arrayed-waveguide grating with a channel spacing of 10 GHz,” in Proceedings of the National Fiber Optic Engineers Conference (Optical Society of America, Washington DC, 2008), paper JThA23.

, where only bends with equal bending radius were used in the arrayed waveguides. This, however, did not completely cancel the systematic phase errors, since the lengths of the bends were not equal across the array.

In this work we propose a new layout in which all the arrayed waveguides have identical bends. Our design is based on arranging the arrayed waveguides with a constant angular spacing, in this way deviating from the Rowland mounting although the input and output channels are still positioned on the Rowland circle. This deviation, in terms of position of the arrayed waveguides, is in general very small: as will be shown in section 4. In our fabricated device the positions of the arrayed waveguides deviate with respect to the Rowland mounting by 165 nm maximum, which is less than the resolution of the e-beam mask used in the fabrication. In sections 2 and 3, we show that the identical bend layout can be used for both, low-order and high-order AWG designs; besides eliminating the systematic phase errors, in the case of high-order AWGs this layout presents the additional advantage of reduced area compared to the conventional horse-shoe layout. In section 4 we present experimental results on the characterization of a broadband AWG which makes use of the novel design. This AWG, which is designed for a specific application, has a resolution of 5.5 nm and a polarization-independent response over a very large spectral range of 215 nm (the maximum observed shift between the responses for the two polarizations is a factor of 10 smaller than the resolution).

2. The identical-bend design

As a starting point we considered the broadband anti-symmetric AWG model introduced by Adar et al. [8

8. R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11(2), 212–219 (1993). [CrossRef]

]. The geometry is shown in Fig. 2
Fig. 2 Anti-symmetric layout of a conventional broadband arrayed waveguide grating having N arrayed waveguides. The free-propagation-regions (FPRs) are indicated schematically.
.

We have implemented an AWG layout in which all the waveguides make use of identical bends, while the length difference ΔL between adjacent waveguides is obtained in the straight waveguide sections. Our layout is inspired by Adar’s work [8

8. R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11(2), 212–219 (1993). [CrossRef]

], with the main difference that for low-order designs we do not use a central part to introduce the length differences (a central part will be reintroduced for high-order designs, as discussed later); instead, we only use two parts which are shown in Fig. 3
Fig. 3 (Color online) (a) Left half and (b) right half of the identical-bend AWG layout, where waveguides are indicated using a bold line; (c) schematic of the complete layout in which both halves are interconnected.
. A prime is used to distinguish the quantities of the right half, see Fig. 3(b), from those of the left half, see Fig. 3(a).

In Fig. 3(a) we present a schematic of the left half of the AWG. R is the radius of the FPR and N is the total number of arrayed waveguides. For clarity, only the first waveguide (i = 1), which we will refer to as the ‘reference waveguide’, and the last waveguide (i = N) are shown. The angle between any two adjacent waveguides of the array is Δα, while the angle that the reference waveguide makes with the horizontal axis is indicated by α. The device makes use of only two types of bends: type 1 bends by an angle α, while type 2 bends by Δα. These bends are the building blocks to be used in equal numbers in all the arrayed waveguides. As shown in Fig. 3(a), all waveguides are bent to normal incidence on lineAB¯. This means that the waveguide with i = 1 is bent by an angle α, the waveguide with i = 2 by α + Δα, and so on. The i th waveguide, which is bent by α + (i – 1) Δα, has one bend of type 1 and i – 1 bends of type 2.

Figure 3(b) displays a schematic of the right half of the AWG. The waveguides are numbered in the same order as on the left half; the lowest waveguide is number 1 and will be connected to waveguide number 1 of the left half; the uppermost waveguide is number N and will be connected to waveguide number N of the left half. On the right half, waveguide N includes one bend of type 1, waveguide N – 1 has one bend of type 1 and one bend of type 2, and so on. When we connect all the waveguides of the left half with those of the right half, each arrayed waveguide i has the same number of bends, namely two bends of type 1 and N – 1 bends of type 2. Consequently, any bend type (e.g. constant bend, linear bend, nonlinear bend) and length can be chosen. Nevertheless, it is preferable to find a good compromise between the length of a bend and its bending radius to reduce propagation losses as well as the size of the device. For example, the bend of type 2, which is repeated N – 1 times in each waveguide, has typically a very small length (on the order of 10–20 µm), since the angle Δα is typically very small (Δα = d / R ~10−3 rad, see Fig. 1). For this reason, a small bending radius can be used if the number of waveguides N is small, while a larger minimum bending radius is preferable in case of large N, i.e., when many bends of type 2 are connected to each other in sequence. For the bends of type 2, circular bends can avoid bend-to-bend transition losses and undesirable periodicity in each waveguide (as would be the case when connecting many nonlinear bends to each other), whereas nonlinear bends can eliminate the straight-to-bend transition losses introduced by circular bends. Furthermore, in high-index-contrast waveguide systems, an offset is usually required when interconnecting straight and bent waveguides to reduce the mode mismatch at the junction. In this case the proposed AWG geometry gives more flexibility in the design without leading to a higher design complexity than when using the conventional geometry. For example, while the conventional S-shaped AWG has six straight-to-bend interfaces requiring the offset, the proposed AWG only requires four offsets, since the bends of type 1 can be non-linear bends with a gradual straight-to-bend transition. The details of the geometry are discussed in the Appendix. In Fig. 3(c) we present, for clarity, the complete layout of the AWG.

3. Design and simulation of high-order AWGs with the identical-bend layout

As previously anticipated, the proposed identical-bend layout can also be used to design high-order AWGs. Generally, with increasing order of the AWG the device becomes larger; for very high orders the phase errors, in particular those arising from fabrication non-uniformities, may become so significant (tens of radians) that a procedure of photosensitive phase compensation is necessary after device fabrication [12

12. K. Takada, M. Abe, T. Shibata, and K. Okamoto, “1-GHz-spaced 16-channel arrayed-waveguide grating for a wavelength reference standard in DWDM network systems,” J. Lightwave Technol. 20(5), 850–853 (2002). [CrossRef]

]. To limit these phase errors the device size must be reduced; this is done by choosing a smaller value for the minimum bending radius, which, on the other hand, results in increased losses and increased systematic phase errors in a conventional AWG. In contrast, in the case of an identical-bend AWG it results only in an increase of the losses.

As shown in Fig. 4
Fig. 4 Interconnection between the left and right halves of the AWG for high-order designs. The terminal parts of the waveguides of the left and right halves are shown in gray, and are numbered from 1 to N.
, the design of a high-order AWG using the identical-bend layout is performed by simply interconnecting the two parts that have been described in the preceding section through an intermediate part, in order to introduce the necessary length differences. The i th waveguide of the intermediate part, which is connected to the i th waveguides of both, left and right halves, is composed of two equal straight sections, with a length given by (i – 1)ΔL/2, interconnected by a curve with an angle φ = 2arctan(ΔL/2s) which is repeated in all waveguides. In this way, the lengths of the waveguides of the left and right parts can even be designed by imposing m = 0, so that they do not contribute to the path length differences which, in this case, are introduced only by the central part. This design differs from Adar’s design only by the fact that it makes use of identical bends. If desired, it is also possible to distribute the length differences over both, the lateral and central parts.

If the device size is reduced by use of smaller bending radii at the expense of increased losses, the identical-bend design does not incur the systematic phase errors that degrade the performance in the conventional design. In case the minimum bending radius is reduced to 850 µm, we obtain 4.5 cm2 area for the conventional design and 2.1 cm2 for the identical-bend design, corresponding to a reduction of the occupied area of 54% (see Fig. 5
Fig. 5 (Color online) Comparison of the conventional and identical-bend layouts in terms of the occupied area.
). In this case the bending losses (calculated accounting for fabrication tolerances) are around 0.3 dB/cm, resulting in a total bending loss lower than 0.1 dB for the entire device. We simulated the effect of the systematic phase errors on these AWGs. Figure 6(a)
Fig. 6 (Color online) (a) Simulated effect of systematic phase errors on the response of an AWG designed with the conventional layout (red line). These phase errors are not present in the identical-bend layout (black line). Both graphs are for the transverse-electric (TE) polarization; (b) the response of an outer channel of the identical-bend AWG is overlapped with that of the same channel of the conventional AWG to show the difference in passband.
shows a comparison between the identical-bend design, in which the systematic phase errors are not present, and the conventional design. The phase errors in the conventional design produce a shift in the central wavelength of the channels (approximately 0.002 nm), and a deformation in the passband shape. In Fig. 6(b) we overlapped the response of one output channel of the identical-bend AWG with the response of the same output channel of the conventional AWG to show the effect of the phase errors on the passband shape. To better illustrate the difference in passbands the response of the conventional AWG was shifted by 0.002 nm such that the the centers of the two pass-bands coincide.

The systematic phase errors for the two conventional AWGs with r min = 1700 µm and 850 µm, respectively, are displayed in Fig. 7
Fig. 7 (Color online) Calculated systematic phase errors between adjacent waveguides in a conventional AWG design for the transverse-electric (TE) polarization, and for two different values of the minimum bending radius r min. These phase errors are not present in the identical-bend design, whatever value of the minimum bending radius is used (green line).
. The systematic phase errors are considered as the deviations of the phase difference between each two adjacent arrayed waveguides with respect to the intended value of 2mπ (at the central wavelength).

4. Experimental results on a broadband AWG design

In this section we present results of the experimental characterization of a broadband AWG that makes use of the simpler form of the identical-bend layout described in section 2.

For device characterization we used the setup shown in Fig. 8
Fig. 8 (Color online) Setup used to characterize the AWG. PBS = polarizing beam splitter. In the insets we present two enlarged views of the AWG layout pointing at the locations of the bends of type 1 and 2.
. Light from a Fianium super-continuum source (from 400 nm to 1800 nm) was sent through a polarization beam splitter and a red-glass filter (RG715) to suppress the undesired region of the spectrum (400-715 nm). The light was then focused into the input waveguide of the AWG by a microscope objective with a numerical aperture (NA) of 0.65 and a magnification of × 40. The spectral response of the AWG was measured by coupling each output channel to a spectrometer (iHR550 Horiba) through a single-mode fiber. The input and output slit widths of the spectrometer were adjusted to the same value of 0.1 mm and the measurement resolution was 0.25 nm.

The measured response was normalized with respect to the spectrum from a separate reference channel on the same chip and is shown for TE polarization in Fig. 9
Fig. 9 Measured spectral response of the AWG for TE polarization.
. As can be observed, the intrinsic losses (excluding coupling losses and propagation losses) of the AWG are very low, ranging from 1.1 dB for the central channel up to a maximum of 1.8 dB at the edges of the spectral region of interest (830 to 900 nm). We estimate an error in the measured loss value of ~2 dB since it is not possible to achieve the same coupling conditions in all the output channels as those for the reference waveguide. We also measured the total transmission through the device (from input fiber to output fiber) to be 9.6% at a wavelength of 832 nm. The fiber to chip coupling efficiency was estimated to be 70% per facet using mode overlap calculations; the remaining 40% loss is due to propagation losses.

Figure 10
Fig. 10 (Color online) Normalized spectral response of the AWG measured for both, TE and TM polarizations, and for three different spectral regions: a) 740–770 nm; b) 870–900 nm; c) 930–960 nm.
displays the normalized responses for TE and TM polarizations measured for 5 central and 11 outer channels of the device. The measured FSR is 215 nm, and the device is polarization insensitive over the whole spectral range, the maximum shift between TE and TM polarizations being 0.5 nm, which is more than 10 times smaller than the resolution.

We attribute the shoulders to coupling between the output-channels of the AWG which are initially spaced by 6 µm and then separate from each other at an angle of ~0.086 degrees. The small separation distance was chosen in the design phase as a compromise between increased crosstalk due to coupling and reduced size of the device and therefore lower propagation losses. We preferred low losses and higher crosstalk since for our target application (Raman sensing) low losses are a must while there are no stringent specifications on the crosstalk. We also performed 2D BPM simulations (see Fig. 11(b)) adding random phase errors (distributed in the interval 0 – 80 degrees) in all the arrayed waveguides, to show how the effect of these errors increases the noisy background to around −25 dB, which is similar to what we observe in the measurement.

5. Conclusions

We have presented a detailed description of a novel layout for the design of AWGs of any diffraction order. The proposed layout makes use of identical bends across the entire grating, leading to a complete cancellation of systematic phase errors which are intrinsically present in conventional designs. We have shown that our layout occupies a smaller area than the conventional horse-shoe layout and, through simulations, that our layout allows us to reduce the device size more than it would be possible with a conventional design without incurring a significant distortion of the AWG response due to the increase of the systematic phase errors at smaller bending radii. Furthermore, we have designed, fabricated, and characterized a broadband AWG according to the proposed layout and demonstrated low losses and polarization insensitivity of the device over a wide spectral range of 215 nm in the near-infrared spectral region.

Appendix

In this appendix we describe the design of a generic AWG according to our proposed geometry. The procedure does not lead to a single unique design, as it involves a number of arbitrary choices, some of which are restricted by the available waveguide fabrication technology. Other restrictions arise from topological feasibility requirements: waveguides should be laid out in such a way that they are everywhere sufficiently separated from each other and do not intersect with each other. We introduce the design equations, which will need to be solved iteratively.

Our AWG layout is not anti-symmetric. The two halves of the AWG are different and need to be designed in separate steps. We commence with designing the left half:

  • 1. We arbitrarily choose initial values for the constant a, the waveguide separation s on the line AB¯, the angle α, and the lengths of the straight sections lp 1 and lq 1 of the first waveguide (our reference waveguide).
  • 2. Once α is determined, we choose the bend of type 1 and, therefore, the value of P.
  • 3. From simple geometrical relations we find D and H (see Fig. 3).
  • 4. For each waveguide of the left half (i = 2, 3, …, N), we determine the lengths of the three straight sections lpi, lqi, and lri.

Step 4 is performed analytically by solving a system of three equations, which is found in the following way. The i th waveguide has one bend of type 1 and i – 1 bends of type 2 (dotted line in the figure) of length l Δα. The lengths of the waveguides belonging to the left half can be expressed as:

l1=R+lp1+lα+lq1l2=R+lp2+lα+lq2+lΔα+lr2...li=R+lpi+lα+lqi+(i1)lΔα+lri...
(1)

Recalling that the length difference between two adjacent waveguides on the left half is given by a + ΔL/2, we find a first equation by expressing the length difference between the i th waveguide and the reference waveguide as (i – 1) (a + ΔL/2):

lpi+lqi+lri=(i1)(a+ΔL2)+lp1+lq1(i1)lΔα.
(2)

Two other equations can be derived from the requirements that the connection points of the waveguides are all on the line AB¯ and that these end points should be equidistant with a given spacing s. These equations read:

(R+lpi)cos(α+(i1)Δα)+Pcos(α/2+(i1)Δα)+..         +lqicos((i1)Δα)+j=1i1ΔPcos((i1j/2)Δα)+lri=D,
(3)
(R+lpi)sin(α+(i1)Δα)+Psin(α/2+(i1)Δα)+..         +lqisin((i1)Δα)+j=1i1ΔPsin((i1j/2)Δα)=H+(i1)s=Hi.
(4)

For each variation of α the steps 2, 3, and 4 need to be performed. By plotting the solutions of Eqs. (2)(4) as a function of α, we find the range of angles α for which all three lengths are non-negative. The angle α must be between 0 and π/2 (an initial choice could be π/4; the optimum value of α leads to the smallest footprint of the left half). If no value of α exists for which this condition is satisfied, the initial parameters a, s, lp 1, and lq 1 have to be adjusted. The procedure requires solving N linear systems of three equations for three unknowns. The separation s between the arrayed waveguides on line must guarantee that there is negligible coupling between the arrayed waveguides at the point where adjacent waveguides are closest to each other. Since the arrayed waveguides are tapered as they approach the FPR region, lp 1 should be 2 or 3 times the taper length. A large value (2 or 3 times lp 1) must be chosen for lq 1.

For the design of the right half, see Fig. 3(b), of the AWG a similar procedure has to be applied:

  • 1. To determine the lengths of the straight sections l'pN and l'qN of the topmost waveguide (the reference waveguide with number N), we impose two conditions -arbitrary to a degree- intended to make this second half of the AWG of similar size as the first half. The first condition sets the length of this waveguide,
    l'N=R+l'pN+lα+l'qN=l1+(N1)ΔL/2,
    (5)
    • while the second condition is that H'=H, which yields
      Rsin(α)+l'pNsin(α)+Psin(α/2)=H
      (6)
    • It is straightforward to solve this set of equations, as R, l 1, lα, N, ΔL, α, P, and H have been determined before.
  • 2. Subsequently, we find the value of D' (which is different from D) and then proceed, as before, by determining for each waveguide of the right half (i = N – 1, N – 2, …, 1) the lengths of the three straight sections l'pi, l'qi, and l'ri.
    • Our choice of imposing similar footprints makes it more likely that, with a certain choice of initial parameters, meaningful solutions are found for both halves of the AWG, thereby reducing the iteration steps necessary to design the geometry.

Acknowledgment

The authors acknowledge financial support from the IOP Photonic Devices supported by the Dutch funding agencies NLAgency and STW.

References and links

1.

M. K. Smit, “New focusing and dispersive planar component based on an optical phased array,” Electron. Lett. 24(7), 385–386 (1988). [CrossRef]

2.

H. Takahashi, S. Suzuki, K. Kato, and I. Nishi, “Arrayed-waveguide grating for wavelength division multi/demultiplexer with nanometer resolution,” Electron. Lett. 26(2), 87–88 (1990). [CrossRef]

3.

C. Dragone, “An N x N optical multiplexer using a planar arrangement of two star couplers,” IEEE Photon. Technol. Lett. 3(9), 812–815 (1991). [CrossRef]

4.

N. Ismail, B. I. Akca, F. Sun, K. Wörhoff, R. M. de Ridder, M. Pollnau, and A. Driessen, “Integrated approach to laser delivery and confocal signal detection,” Opt. Lett. 35(16), 2741–2743 (2010). [CrossRef] [PubMed]

5.

M. C. Hutley, Diffraction Gratings (Academic, 1982).

6.

C. D. Lee, W. Chen, Q. Wang, Y.-J. Chen, W. T. Beard, D. Stone, R. F. Smith, R. Mincher, and I. R. Stewart, “The role of photomask resolution on the performance of arrayed-waveguide grating devices,” J. Lightwave Technol. 19(11), 1726–1733 (2001). [CrossRef]

7.

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]

8.

R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11(2), 212–219 (1993). [CrossRef]

9.

M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2(2), 236–250 (1996). [CrossRef]

10.

F. M. Soares, W. Jiang, N. K. Fontaine, S. W. Seo, J. H. Baek, R. G. Broeke, J. Cao, K. Okamoto, F. Olsson, S. Lourdudoss, and S. J. B. Yoo, “InP-based arrayed-waveguide grating with a channel spacing of 10 GHz,” in Proceedings of the National Fiber Optic Engineers Conference (Optical Society of America, Washington DC, 2008), paper JThA23.

11.

R. N. Sheehan, S. Horne, and F. H. Peters, “The design of low-loss curved waveguides,” Opt. Quantum Electron. 40(14-15), 1211–1218 (2008). [CrossRef]

12.

K. Takada, M. Abe, T. Shibata, and K. Okamoto, “1-GHz-spaced 16-channel arrayed-waveguide grating for a wavelength reference standard in DWDM network systems,” J. Lightwave Technol. 20(5), 850–853 (2002). [CrossRef]

13.

P. J. Caspers, G. W. Lucassen, E. A. Carter, H. A. Bruining, and G. J. Puppels, “In vivo confocal Raman microspectroscopy of the skin: noninvasive determination of molecular concentration profiles,” J. Invest. Dermatol. 116(3), 434–442 (2001). [CrossRef] [PubMed]

14.

K. Wörhoff, C. G. H. Roeloffzen, R. M. de Ridder, A. Driessen, and P. V. Lambeck, “Design and application of compact and highly tolerant polarization independent waveguides,” J. Lightwave Technol. 25(5), 1276–1283 (2007). [CrossRef]

OCIS Codes
(300.6190) Spectroscopy : Spectrometers
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Integrated Optics

History
Original Manuscript: February 18, 2011
Revised Manuscript: April 15, 2011
Manuscript Accepted: April 17, 2011
Published: April 20, 2011

Citation
Nur Ismail, Fei Sun, Gabriel Sengo, Kerstin Wörhoff, Alfred Driessen, René M. de Ridder, and Markus Pollnau, "Improved arrayed-waveguide-grating layout avoiding systematic phase errors," Opt. Express 19, 8781-8794 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8781


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References

  1. M. K. Smit, “New focusing and dispersive planar component based on an optical phased array,” Electron. Lett. 24(7), 385–386 (1988). [CrossRef]
  2. H. Takahashi, S. Suzuki, K. Kato, and I. Nishi, “Arrayed-waveguide grating for wavelength division multi/demultiplexer with nanometer resolution,” Electron. Lett. 26(2), 87–88 (1990). [CrossRef]
  3. C. Dragone, “An N x N optical multiplexer using a planar arrangement of two star couplers,” IEEE Photon. Technol. Lett. 3(9), 812–815 (1991). [CrossRef]
  4. N. Ismail, B. I. Akca, F. Sun, K. Wörhoff, R. M. de Ridder, M. Pollnau, and A. Driessen, “Integrated approach to laser delivery and confocal signal detection,” Opt. Lett. 35(16), 2741–2743 (2010). [CrossRef] [PubMed]
  5. M. C. Hutley, Diffraction Gratings (Academic, 1982).
  6. C. D. Lee, W. Chen, Q. Wang, Y.-J. Chen, W. T. Beard, D. Stone, R. F. Smith, R. Mincher, and I. R. Stewart, “The role of photomask resolution on the performance of arrayed-waveguide grating devices,” J. Lightwave Technol. 19(11), 1726–1733 (2001). [CrossRef]
  7. 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]
  8. R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11(2), 212–219 (1993). [CrossRef]
  9. M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2(2), 236–250 (1996). [CrossRef]
  10. F. M. Soares, W. Jiang, N. K. Fontaine, S. W. Seo, J. H. Baek, R. G. Broeke, J. Cao, K. Okamoto, F. Olsson, S. Lourdudoss, and S. J. B. Yoo, “InP-based arrayed-waveguide grating with a channel spacing of 10 GHz,” in Proceedings of the National Fiber Optic Engineers Conference (Optical Society of America, Washington DC, 2008), paper JThA23.
  11. R. N. Sheehan, S. Horne, and F. H. Peters, “The design of low-loss curved waveguides,” Opt. Quantum Electron. 40(14-15), 1211–1218 (2008). [CrossRef]
  12. K. Takada, M. Abe, T. Shibata, and K. Okamoto, “1-GHz-spaced 16-channel arrayed-waveguide grating for a wavelength reference standard in DWDM network systems,” J. Lightwave Technol. 20(5), 850–853 (2002). [CrossRef]
  13. P. J. Caspers, G. W. Lucassen, E. A. Carter, H. A. Bruining, and G. J. Puppels, “In vivo confocal Raman microspectroscopy of the skin: noninvasive determination of molecular concentration profiles,” J. Invest. Dermatol. 116(3), 434–442 (2001). [CrossRef] [PubMed]
  14. K. Wörhoff, C. G. H. Roeloffzen, R. M. de Ridder, A. Driessen, and P. V. Lambeck, “Design and application of compact and highly tolerant polarization independent waveguides,” J. Lightwave Technol. 25(5), 1276–1283 (2007). [CrossRef]

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