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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 8 — Apr. 18, 2005
  • pp: 2961–2968
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The cross waveguide grating: proposal, theory and applications

Pascual Muñoz, Daniel Pastor, and José Capmany  »View Author Affiliations


Optics Express, Vol. 13, Issue 8, pp. 2961-2968 (2005)
http://dx.doi.org/10.1364/OPEX.13.002961


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Abstract

In this paper a novel grating-like integrated optics device is proposed, the CrossWaveguide Grating (XWG). The device is based upon a modified configuration of a traditional ArrayedWaveguide Grating (AWG). The Arrayed Waveguides part is changed, as detailed along this document, giving the device both the ability of multi/demultiplexing and power splitting/coupling. Design examples and transfer function simulations show good agreement with the presented theory. Finally, some of the envisaged applications are outlined.

© 2005 Optical Society of America

1. Introduction

In the last decade, the research field of integration of optical devices in planar chips has received great attention and efforts from research institutions, universities and companies. A considerable number of integrated optics devices are already commercially available, while researchers focus on miniaturisation and combination of different optical devices, both passive and active, in optical chips. One of the key devices enabling high bandwidth core networks has been the Arrayed Waveguide Grating (AWG), first proposed by [1

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

], and that has been subject of extensive research and commercial interest. The AWG is a passive integrated optics device that performs multi/demultiplexing of wavelengths and that has other interesting properties as the Free Spectral Range, enabling the possibility of designing a cyclic router [2

2. H. Takahashi, S. Suzuki, and I. Nishi, “Wavelength multiplexer based on SiO2-Ta2O5 arrayed waveguide grating,” J. Lightwave Technol. 12, 989–995 (1994). [CrossRef]

]. In this paper we propose a modification of the AWGthat adds extra functionality and some novel and potentially interesting properties.

Fig. 1. Layout of (a) a regular AWG and (b) the proposed XWG.

In Section 2, the device layout is presented and a theoretical model to describe its transfer function is developed. Some design examples are given in Section 3. The envisaged applications are presented in Section 4 and finally the conclusions are drawn in Section 5.

2. Device layout and modeling

2.1. Device layout

The modification mentioned above on the AWG to get this novel device, consists on changing the layout of the arrayed waveguides or grating arms. In a regular AWG, two Free Propagation Regions, (FPRs) are connected by a set of waveguides. The path length difference between adjacent waveguides is changed incrementally by a constant amount, typically named in the literature as ΔL, starting from a short waveguide at the bottom part of the array, and ending in a long waveguide at the opposite side. This is shown in Fig. 1(a). The novel device proposed is named Cross Waveguide Grating (XWG) for shortness, though a better name could be the Crossing Focal Points Waveguide Grating (XFP-WG) (the motivation for this name will be understood by the reader later on). The XWG has also this feature, i.e., the path length between adjacent waveguides is changed incrementally by a fixed amount ΔL, as in the AWG. However, the arms layout is such that there are two identical sub-arrays starting from the middle waveguide, which is the shortest, to the upper and lower waveguides, which are the longest. This is shown in Fig. 1(b).

2.2. The first FPR

The first FPR is modelled as a spatial Fourier transform, in such a way that under a Gaussian assumption for the input waveguide mode field (power normalised):

bi(x0)=2πwi24e(x0wi)2
(1)

where wi is the input waveguide (IW) mode field radius, hence the far field, before the grating arms, coordinate x 1 in Fig. 1(b), will be:

Bi(x1)=1α𝓕{bi(x0)}u=x1α=2πwi2α2e(πwi(x1α)24
(2)

with u is the Fourier domain variable, and α the wavelength, λ, to FPR length, Lf , product from Fourier Optics [5

5. J.W. Goodman, “Introduction to Fourier Optics,” McGraw-Hill, ch. 5, pp. 83–90 (1988).

]:

α=cLfnSν
(3)

where c is the speed of light in vacuum, ns the FPR refractive index and ν the frequency. The path length difference is set to an integer number of times m (known as the grating order) the device design wavelength λ0 within the grating waveguides [3

3. P. Muñoz, D. Pastor, and J. Capmany, “Modeling and design of Arrayed Waveguide Gratings,” J. Lightwave Technol. 20, 661–674 (2002). [CrossRef]

]:

ΔL=mλ0nc=mcncν0
(4)

with nc the refractive index of a waveguide in the array.

2.3. The grating arms

The grating arms collect part of the light reaching the end of the first FPR. This can be modelled as sampling the field distribution from Eq. (2) at each waveguide [3

3. P. Muñoz, D. Pastor, and J. Capmany, “Modeling and design of Arrayed Waveguide Gratings,” J. Lightwave Technol. 20, 661–674 (2002). [CrossRef]

]. The distance between adjacent waveguides is given by dw . Hence, the expression for the overall field over the x 1 coordinate is given by:

f1(x1)=B1(0)+r=1N12B1(rdw)δ(x1rdw)+r=N121B1(rdw)δ(x1rdw)
(5)

with N (odd) the total number of AWs. For convenience the two sets of waveguides are splitted in two summations. Hence, the overall field distribution over coordinate x 2 can be derived from the last equation by introducing the following phase change for each waveguide:

Δϕr=(L0+rΔL)β
(6)

where β=2πnc /λ is the propagation constant for an arrayed waveguide, L 0 the length of the centre waveguide, and r is an integer number in [N12,N12]. The modulus operation over the waveguide number r reflects the fact that there are two symmetric sub-arrays, as mentioned previously. The field distribution for each sub-array can be expressed as follows:

f2A(x2,ν)=r=1N12B1(rdw)δ(x2rdw)ejβrΔL
(7)
f2B(x2,ν)=r=N121B1(rdw)δ(x2rdw)e+jβrΔL
(8)

Notice the different sign in the exponentials due to the modulus in the phase change from Eq. (6). Using M=(N-1)/2, it is possible to rewrite the latter expressions as follows:

f2A(x2,ν)=B1(x1)Π(x2dwM2Mdw)r=δ(x2rdw)ejβrΔL
(9)
f2B(x2,ν)=B1(x1)Π(x2+dwM2Mdw)r=δ(x2rdw)e+jβrΔL
(10)

with Π(x)=1 for |x|≤1/2 and 0 elsewhere.

Fig. 2. fM (u,a,b) -blue-, fM(u,a,b) -green- and fM+ (u,a,b) -red-.

2.4. The second FPR

The field distribution over x 3 due to the contribution of each sub-array is given by the following equations:

f3(x3,ν)=r=fM(x3+νγrαdw)
(11)
f3+(x3,ν)=r=fM+(x3νγrαdw)
(12)

fM(u,a,b)=0aB1(x)ej2πuxx
(13)
fM+(u,a,b)=a0B1(x)ej2πuxx
(14)

that correspond to the spatial Fourier transforms of the right side and left side of a Gaussian function, B1(x)=eb2x2, respectively, and their analytical expressions are:

fM(u,a,b)=12bπe(πub)2[erf(ab+jπub)erf(jπub)]
(15)
fM+(u,a,b)=12bπe(πub)2[erf(ab+jπub)+erf(jπub)]
(16)

Note also that in Eq. (11) γ is as in [3

3. P. Muñoz, D. Pastor, and J. Capmany, “Modeling and design of Arrayed Waveguide Gratings,” J. Lightwave Technol. 20, 661–674 (2002). [CrossRef]

] the frequency spatial dispersion:

γ=dwν0αm
(17)

These functions, Eqs. (15), have the same amplitude, but conjugate phases, as plotted in Fig. 2 along with the ordinary M function. Though from the equations it is not clear, from Fig. 2 it is possible to conclude that:

fM(u,a,b)=(fM+(u,a,b))*
(18)
Fig. 3. Focusing properties of the device. Two beams moving in opposite directions are generated, one by each sub-array. For the design frequency ν 0 the beams cross at OW 0.

2.5. End to end field transfer function

Finally, as in [3

3. P. Muñoz, D. Pastor, and J. Capmany, “Modeling and design of Arrayed Waveguide Gratings,” J. Lightwave Technol. 20, 661–674 (2002). [CrossRef]

] the end to end field transfer function is obtained by performing the overlap integral of the total diffraction pattern over x 3, f 3(x 3,ν), with the output waveguide (OW) mode field, bo (x 3):

t0,q(ν)=+f3(x3,ν)b0(x3qd0)x3
(19)

where do is the OW spacing and q the OW number. The result is valid for an IW centred on the first FPR, and as in [3

3. P. Muñoz, D. Pastor, and J. Capmany, “Modeling and design of Arrayed Waveguide Gratings,” J. Lightwave Technol. 20, 661–674 (2002). [CrossRef]

] it can be completed if a different IW is used (i.e. not centred).

3. Device properties derived from the model

The key equation to understand the device functioning is Eq. (11). The important detail is inside the brackets of the M functions. For the same frequency increment (the ν variable), the beam from each array sub-set will move in opposite directions. This is illustrated in Fig. 3(a) with a blue and red beam. Therefore, the same signal frequency components will be present at different output waveguides, so the device acts as a demultiplexer and 3 dB coupler at the same time. That means that waveguides +1 and -1 in the figure, will have the same frequency response, also +2 and -2, and so on.

Notice also that the beams may move the other direction, as in Fig. 3(b), for a contrary frequency increment. Hence, the frequency response for each input-output waveguide pair, will have two passing bands. The separation of these bands depends on the output waveguide position. For example, the separation of the passing bands for output waveguides ±2 will be bigger that for the output waveguides ±1.

The XWG is has also a periodic transfer function, i.e. a Free Spectral Range, as the AWG. This can be understood and derived from the argument in Eq. (11) following the same procedure than in [3

3. P. Muñoz, D. Pastor, and J. Capmany, “Modeling and design of Arrayed Waveguide Gratings,” J. Lightwave Technol. 20, 661–674 (2002). [CrossRef]

]. The result is the same ΔνFSR =ν 0/m.

4. Design example

A XWG device is designed following the design methodology from [3

3. P. Muñoz, D. Pastor, and J. Capmany, “Modeling and design of Arrayed Waveguide Gratings,” J. Lightwave Technol. 20, 661–674 (2002). [CrossRef]

] and simulated using the tools verified in [4

4. P. Muñoz, D. Pastor, J. Capmany, D. Ortega, A. Pujol, and J. Bonar, “AWGModel Validation through Measurement of Fabricated Devices,” J. Lightwave Technol. 22, 2763–2777 (2004). [CrossRef]

]. As top level parameters, the XWG is designed to be a 1×5-channel device with 400 GHz channel spacing and an FSR of 3.2 THz (non cyclic). With this and the design wavelength λ0=1.55 µm, the grating order is m=60. InP substrate values were chosen for the device, using shallowly etched 3 microns width waveguides. The gap between arrayed waveguides 0.6 µm, with N=100 waveguides, the FPR length Lf =0.544462 mm and the OW spacing do =8.92 µm, following a Dragone mounting (two confocal spheres).

The transfer functions from the IW to the five OWs are shown in Fig. 4. First, the green line shows the transfer function for the OW number ‘0’, i.e. the centre OW. Its location is where the two beams from the sub-arrays collide, and therefore there is a single peak with higher energy than the rest. The second green peak corresponds to the one located one FSR away due to the XWG periodicity, which is similar to the AWG.

Second, for the rest of the output ports, not centred, in Fig. 3 note how, as predicted by Eq. 11 and explained above, two peaks appear for a given output port. Each peak corresponds to one of the two beams created from the sub-arrays, that slide over the output focal plane. Each one of the two peaks has also its corresponding peak at the FSR distance, again due to the periodicity of the XWG.

Moreover, the transfer function has the same response for ports located symmetrically around OW number ‘0’ (the centred one). These responses appear superimposed in the figure (dashed vs solid and different colours, refer to the figure caption), i.e. port +1 has the same transfer function as port -1, port +2 has the same transfer function as port -2, and so on. This provides the same signal at two different output locations.

5. Potential applications

From the properties, it is clear that the main abilities of the device are frequency selectivity plus power splitting (or coupling if operated in the reverse direction). Hence, it has the potential applications illustrated in Fig. 5. First in the field of distribution networks, where data traffic is delivered from a central location, the Head End, to different zones. The XWG, not only provides wavelength selectivity, but also the 3 dB splitting, such a way that two distant zones can be provided with the same data. Moreover two wavelengths can be delivered at the same time without the need of using the pass-band available one FSR away as in the AWG-based distribution networks. This is advantageous since the wavelengths are closer and therefore fall within the bandwidth of the optical amplifiers. However, to separate the individualwavelengths, sharper filters are required.

Fig. 4. XWG normalised transfer function [dB] vs. frequency [THz] from the centre IW to OWs numbers -2 (cyan), -1 (red), 0 (green), 1 (blue dashed), 2 (magenta dashed).

Third, in the field of integrated optic devices, a multi-wavelength laser can be built with an XWG and SOAs as shown in the Figure. The SOAs are placed in the ‘+’ outputs of the XWG ending in mirrors, forming a laser cavity with the input waveguide, where another mirror is used. The ‘-’ outputs are coupled to the input, so they are the means of extracting the lasing wavelengths from the cavity. Compared to a multi-wavelength laser with AWGs, the wavelengths are available in pairs, and not as a whole set. However, challenges will appear in the design of the SOAs to have enough gain to lase at two wavelengths, the more for the outer most ports where the two peaks are more separated. Also as commented above, a pair of wavelengths can be modulated with the same information.

Finally, and though other applications can be envisaged, we propose the use of the XWG for distribution networks. Using the ability of two wavelengths per port, one can deliver downstream traffic, while the other one can be delivered unmodulated. In the remote optical node, the wavelengths are separated by means of a simple Optical Add Drop Multiplexer (OADM), and the unmodulated wavelength is used to transmit data in the upstream direction, using an Electro-Optical Modulator (EOM). The wavelengths are not separated the FSR, but the smaller distance shown in Fig. 4. Therefore if bidirectional amplifiers are used, the downstream and upstream wavelengths are closer, avoiding the use of high bandwidth optical amplifiers. This also allows to share the cost of expensive devices for occasional upstream transmissions, as for instance a tunable laser.

Fig. 5. Applications for the XWG.

6. Conclusions

In this paper, a novel device, the Cross Waveguide grating has been proposed, the theory describing its response has been developed and shows good agreement with the simulation of a design example. Envisaged applications have been briefly described, though this part is left open for further research.

Acknowledgments

The authors wish to acknowledge the ePIXnet (European Network of Excellence on Photonic Integrated Components and Circuits) European FP6 research project. P. Muñoz also wishes to acknowledge the Universidad Politécnica de Valencia for funding his stay at TU/e via the Programa Incentivo a la Investigación 2004. P. Muñoz wishes to acknowledge Prof. M.K. Smit, X.J.M. Leijtens and J.H. den Besten from the Opto-Electronic Devices group at the Technical University of Eindhoven (TU/e) for their helpful discussions.

References and links

1.

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

2.

H. Takahashi, S. Suzuki, and I. Nishi, “Wavelength multiplexer based on SiO2-Ta2O5 arrayed waveguide grating,” J. Lightwave Technol. 12, 989–995 (1994). [CrossRef]

3.

P. Muñoz, D. Pastor, and J. Capmany, “Modeling and design of Arrayed Waveguide Gratings,” J. Lightwave Technol. 20, 661–674 (2002). [CrossRef]

4.

P. Muñoz, D. Pastor, J. Capmany, D. Ortega, A. Pujol, and J. Bonar, “AWGModel Validation through Measurement of Fabricated Devices,” J. Lightwave Technol. 22, 2763–2777 (2004). [CrossRef]

5.

J.W. Goodman, “Introduction to Fourier Optics,” McGraw-Hill, ch. 5, pp. 83–90 (1988).

6.

P. Muñoz, D. Pastor, J. Capmany, and S. Sales, “Analytical and Numerical Analysis of Phase and Amplitude Errors in the Performance of Arrayed Waveguide Gratings,” J. Selected Topics in Quantum Elect. 8, 1130–1141 (2002). [CrossRef]

7.

C. Dragone, “An NN optical multiplexer using a planar arrangement of two star couplers,” IEEE Photonics Tech. Lett. 3, 812–815 (1991). [CrossRef]

OCIS Codes
(110.5100) Imaging systems : Phased-array imaging systems
(230.3120) Optical devices : Integrated optics devices

ToC Category:
Research Papers

History
Original Manuscript: February 22, 2005
Revised Manuscript: March 31, 2005
Published: April 18, 2005

Citation
Pascual Muñoz, Daniel Pastor, and José Capmany, "The cross waveguide grating: proposal, theory and applications," Opt. Express 13, 2961-2968 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-8-2961


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References

  1. M. K. Smit, �??New focusing and dispersive planar component based on an optical phased array,�?? Electron. Lett., 24, 385-386 (1988). [CrossRef]
  2. H. Takahashi, S. Suzuki and I. Nishi, �??Wavelength multiplexer based on SiO2-Ta2O5 arrayed waveguide grating,�?? J. Lightwave Technol. 12, 989-995 (1994). [CrossRef]
  3. P. Muñoz, D. Pastor and J. Capmany, �??Modeling and design of Arrayed Waveguide Gratings,�?? J. Lightwave Technol. 20, 661-674 (2002). [CrossRef]
  4. P. Muñoz, D. Pastor and J. Capmany, D. Ortega, A. Pujol and J. Bonar, �??AWG Model Validation through Measurement of Fabricated Devices,�?? J. Lightwave Technol. 22, 2763-2777 (2004). [CrossRef]
  5. J.W. Goodman, �??Introduction to Fourier Optics,�?? McGraw-Hill, ch. 5, pp. 83-90 (1988).
  6. P. Muñoz, D. Pastor, J. Capmany and S. Sales, �??Analytical and Numerical Analysis of Phase and Amplitude Errors in the Performance of Arrayed Waveguide Gratings,�?? J. Selected Topics in Quantum Elect. 8, 1130-1141 (2002). [CrossRef]
  7. C. Dragone, �??An NN optical multiplexer using a planar arrangement of two star couplers,�?? IEEE Photonics Tech. Lett. 3, 812-815 (1991). [CrossRef]

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