16

Chapter 2 Arrayed Waveguide Gratings, Application and Design

2.1 Introduction

2.1.1 Optical Communications

Optical fibre is a popular carrier of long distance communications due to its

potential speed, flexibility and reliability. Attenuation and dispersion problems in

fibre, which limit the practical speed and distance of communication, were partially

resolved with the advent of the Erbium Doped Fibre Amplifier (EDFA)[2.1],

eliminating problems caused by attenuation. However, the dispersion qualities of an

optical fibre still force a compromise between transmission distance and bandwidth,

making it necessary to refresh high-speed signals at intervals using opto-electronic

repeaters. Solving the dispersion problem in this manner is expensive, due to the

additional cost of high-speed electronics, and maintaining and upgrading the link is

made more difficult and costly (especially with a buried or under-water link). A more

elegant solution is found using Dense Wavelength Division Multiplexing (DWDM),

which effectively increases the useable bandwidth in a system without electronic

repeaters, and allows realisation of a true photonic network.

2.1.2 Arrayed Waveguide Gratings

Dense Wavelength Division Multiplexing (DWDM) is an efficient method

where several channels, each carried by a different wavelength, are transmitted

through a single optical fibre, utilising more of the available bandwidth without

increasing the effects of dispersion. Each channel, since it is effectively separated

from the others, can be independent in protocol, speed, and direction of

17

communication. DWDM also helps realise an all-optical network architecture where

signals are routed according to wavelength without the need for electro-optical

conversion. As a result, this type of network is potentially faster and more flexible,

and can be less costly to maintain when compared to other methods.

Figure 2.1 : (from [2.2]), An Add/Drop Multiplexer (ADM). Made reconfigurable by using space

division switches (top in “crossed” state)

Figure 2.2 : (from [2.2]) An Optical Cross Connect (OXC) employing a space division switch for

each wavelength. Switch settings determine where each wavelength is routed.

Arrayed Waveguide Gratings (AWGs) are optical wavelength

(de)multiplexers used in DWDM. As well as performing basic (de)multiplexing

functions, they can be combined with other components to create add/drop

multiplexers, Figure 2.1 [2.2], used to pipe single wavelengths on and off the

A D

Demux Mux

MUX

MUX

S W I

T C

H

18

network, and Cross Connects, Figure 2.2, used for routing. These devices can be

passive, where the signal routing is fixed according to wavelength, or active, as in

Figures 2.1 and 2.2, where optical switches are utilised to dynamically route the

signals. Both circuits shown are transparent to the data format, can allow bi-

directional transfer of information, and function entirely in the optical domain. These

functions allow the construction of different transparent optical network topologies,

examples of the three major types of these are described in the following subsection.

2.1.3 Forms of Photonic Network

The simplest form of optical network is the point-to-point network. Optical

multiplexers and de-multiplexers are required at each end of the link. In this

configuration, DWDM simply increases the number of channels available through

one fibre. Passive Optical Networks (PONs) (Figure 2.3) [2.2] use a wavelength

(de)multiplexer as a passive optical router, each wavelength servicing an Optical

Network Unit (ONU). This allows the ONUs to share a single long optical fibre link

back to the central office (CO).

Figure 2.3: A Passive Optical Network

Long haul networks tend to have more than one point where channels are added to

and removed from the system, for example to provide a bi-directional channel to an

optical network unit. To add and remove channels optical add drop multiplexers

(OADMs) and Optical Cross Connects (OXCs) are utilised (Figures 2.1 and 2.2),

λ1

λ2

λ4

λ3

λ1 + λ2 + λ3 + λ4

Passive Router Central Office

ONUs

19

[2.2], to allow single channels to be individually piped off the network, and to route

channels between sections of the network respectively. Figure 2.4 shows an example

configuration of a Long Haul network.

Figure 2.4 : A Long Haul Network, utilising Add-Drop Multiplexers (ADMs) and Optical Cross

Connects (OXCs)

2.1.4 Summary

The Arrayed Waveguide Grating (AWG) plays a crucial role in the realisation of

modern optical networks. The next section introduces the principles of operation of

the AWG, and then examines the design process.

OXC

ADM

ADM

ADM

ADM

ADM

ADM

20

2.2 Arrayed Waveguide Grating (AWG) Operation Principles

2.2.1 Basic Operation of The AWG

In the previous section we established that AWGs are essential components

for the realisation of DWDM and optical networks. In this section, the basic

operation of an AWG as a de-multiplexer is described.

Figure 2.5 shows the structure of an AWG. The input (a) consists of several

channels, typically between 8 and 40 in commercial devices, carried on separate

frequencies. Channel spacings of 100GHz or 50 GHz are common in commercial

devices, although 25GHz [2.3] and 10GHz [2.4] spacings have been achieved under

laboratory conditions. The operational wavelength is commonly around 1.55µm

where attenuation is lowest in optical fibres. All waveguides in the AWG tend to be

single-moded to ensure predictable propagation through the device.

Light couples from the input waveguide (a) into the Free Propagation Region

(FPR) (b) and disperses to illuminate the arrayed waveguides (AWs) starting on a

curved plane as shown in Figure 2.6, along which the light exhibits a constant phase

profile. Each AW increases in length by ∆L compared to the previous one in the

array, where ∆L = m λw / neff, m is an integer number, λw is the central operational

(c) Arrayed Waveguides

(a) Input Waveguide

(b) Input FPR

(d) Output FPR

(e)

Figure 2.5 :[2.2] The structure of an Arrayed Waveguide Grating de-multiplexer.

21

wavelength, and neff the effective refractive index, (β/k0), of the single mode

supported by each waveguide forming the AWG. Consequently, at the central

wavelength, a constant phase profile is exhibited at the end of the AWs, an integer

number of cycles out of phase, along the same plane, as shown in Figure 2.6.

Therefore, at the central frequency, the light focuses at the centre of the plane (e),

where an output waveguide is positioned to capture the focussed light. Different

wavelengths of light will exhibit different amounts of phase change and, due to the

increments in length of each waveguide, the phases will change along the AW output

plane, causing the focal point to move along the focal plane (e) at the end of the FPR.

An output waveguide is positioned on the output plane to pick up each input

frequency (channel).

Figure 2.6 : The Input / Output Free Propagation Region.

2.2.2 AWG tolerances

An AWG is a very large and inherently complex structure, typically several

square centimetres in area and comprised of multiple waveguides. The AWG is

clearly also very sensitive to any phase error, particularly at the end of the Arrayed

Waveguides. Consequently, careful and rigorous design is critical for its correct

θ RFPR ∆s

Arrayed Waveguides

Input / Output

Waveguides

Focal Plane

Ape

ture

Wid

th

22

operation. A design process based on prototyping is prohibitively expensive, both in

terms of cost and time, so it is highly desirable to develop modelling tools that can

provide a detailed analysis of the device operation. However, due to the component

size, even relatively detailed analyses have previously resorted to approximate semi-

analytical methods, e.g. [2.5][2.6], which do not fully characterise the structure

(Chapter 1). Some of the current design methods are reviewed in the following

section.

2.3 Current Design Process of an AWG (Basic De-multiplexer)

2.3.1 Introduction

This section looks at the analytical methods used to design an AWG. The

design of an AWG is covered in detail in [2.2], [2.5], [2.7], and [2.8]. An AWG is

specified by the following characteristics:

• Number of Channels

• Central Frequency fc, and Channel spacing ∆fch

• Free Spectral Range ∆fFSR

• Channel bandwidth

• Maximum insertion loss

• Maximum non-uniformity

• Maximum crosstalk level

• Polarisation dependence

We concentrate first on the basic design rules that govern AWG dimensions.

2.3.2 Receiver Waveguide Spacing

The spacing of the receiver waveguides affects the adjacent-channel crosstalk

of the system and is covered in detail in [2.5] and [2.6]. A calculated crosstalk of

23

around -30dB is normally considered sufficient, where other sources of crosstalk,

resulting from flaws in design and manufacture, normally become dominant.

2.3.3 Free Propagation Region (FPR) length

The length of the Free Propagation Region is determined by the maximum

acceptable channel non-uniformity (expressed in dB). Channel non-uniformity is

defined in [2.5] as the difference in intensity of the central and edge channels of the

AWG, and is the result of the variation of the waveguide mode far field with angle.

Channel non-uniformity can be estimated analytically, as described in [2.5], or

determined through numerical simulation (as will be described in Chapter 8). By

specifying the maximum channel non-uniformity, a value for the maximum

dispersion angle (θMAX) can be obtained. If the distance to the outermost output

waveguide, smax, is known, then the minimum length of the Free Propagation Region,

RFPR, is calculated by using RFPR = smax / θMAX.

2.3.4 Arrayed Waveguide Length Increment, ∆L

The increment in length of the Arrayed Waveguides (AWs) is determined

from the required dispersion D = ds / df, where ds is the displacement of the focal

spot on the image plane, and df is the change in frequency to cause this displacement.

Minimum dispersion is related to the receiver waveguide spacing and the free

propagation length. Dispersion is calculated from [2.7]:

dfdR

dfdsD FPR

θ== (2.1a)

where,

( )aFPRa

FPR

dm

dma

βπφβπφθ 2/2sin −∆

≈⎟⎟⎠

⎞⎜⎜⎝

⎛ −∆= (2.1b)

24

where ∆Ф = β∆L, β is the propagation constant in the waveguides (in rads m-1), and

βFPR that in the Free Propagation Region. The waveguide spacing, da, is chosen to be

as small as possible to maximise coupling efficiency from the FPR to the AWs. m is

the order of the phased array.

2.3.5 Arrayed Waveguide Aperture Width

The aperture width, shown on Figure 2.6, is the effective capture width of the

AWs. The number of AWs, is determined by the aperture width and the crosstalk

characteristics of the waveguides used in the AWG, which affects the separation

between the AWs. It is covered in depth in [2.5] and [2.7]. The aperture size also

affects the amount of light captured by the grating and is normally chosen to capture

the majority of the expanded field at the end of the input FPR.

2.3.6 Free Spectral Range (FSR)

The required frequency range for the arrayed waveguide grating is a

fundamental design factor. FSR is defined as the frequency shift, for which the

phase-shift, ∆Φ, equals 2π, i.e.:

ππ 2~2=∆

∆ LgNcfFSR (2.2a)

where gN~ is the group index of the waveguide mode and c the velocity of light in

free space. The FSR has to be sufficiently large to accommodate the required

operating frequency range. Two frequencies separated by the Free Spectral Range

FSR and input into an AWG de-multiplexer will focus and leave though the same

output waveguide, since their phase at the outputs is the same. It follows from 2.2a

that

dfdN

fNgN gg +=~ (2.2b)

25

so

LNcfg

FSR ∆=∆ ~ (2.2c)

Since the FSR is not constant with frequency the analysis above is only approximate,

but in most cases it is sufficient.

2.3.7 Summary

The parameters described in this section determine the basic dimensions for

the AWG. Although the procedures outlined provide a basic guidance for a working

design, a good design requires the consideration of many other issues, as detailed in

the next section.

2.4 Issues Affecting the Performance of Arrayed Waveguide Gratings

2.4.1 Crosstalk

The causes of inter-channel crosstalk are many, and may be a result of the

design or imperfect fabrication of the AWG. The primary source taken into account

in initial design is the inter-channel crosstalk, caused by the overlap of the focussed

spot in the output FPR with adjacent output waveguides, as covered in [2.5].

Approaches that are more rigorous take into account potential AW phase

inaccuracies, caused by design or fabrication anomalies, which cause the spot to

spread, increasing crosstalk. This form of crosstalk, however, is easily controlled by

increasing the separation of the output waveguides. Often, as evaluated in [2.9], there

are design tradeoffs between crosstalk and other desirable characteristics, such as

insertion loss or channel spacing.

Crosstalk is also likely to occur as a consequence of more complex effects in

the AWs, such as through light propagating in the AWs in modes other than the

26

single-waveguide fundamental modes. This would adversely affect the phase and

amplitude distributions at the output of the Arrayed Waveguides. Due to the

assumptions inherent within AW design using current design tools, these effects are

difficult to evaluate completely. This is an area where an improved understanding is

presented in this Thesis, particularly in Chapters 6 and 7, gained through the

application of advanced numerical design tools.

2.4.2 Insertion Loss

The primary cause for insertion loss in the AWG is due to inefficient

coupling at the interface between the first FPR and the AWs. Due to reciprocity

[2.2], identical loss occurs at the second AW - FPR interface into higher diffraction

orders. Coupling efficiency, and therefore insertion loss is largely determined by the

separation of the AWs at these interfaces, where smaller separations increase the

coupling efficiency [2.2]. However, at small separations, coupling between the AWs

becomes significant. This effect has to be carefully quantified through the Finite

Difference- Beam Propagation Method (FD-BPM) or another simulation method to

avoid phasing errors in the AWs. Other areas that cause loss may include

• Material losses

• Scattering due to fabrication errors and waveguide roughness

• De-focussing of the spot on the output plane due to phase errors, decreasing

coupling efficiency into the output waveguide.

2.4.3 Polarisation Dependent Dispersion

Unless specifically engineered, waveguide boundary conditions cause quasi-

TE and quasi-TM polarised modes to propagate at different speeds (birefringence),

particularly in the case of strongly confining waveguides. As well as birefringence

27

due to waveguide geometry, stresses within the structure may occur due to

fabrication processes that can cause anisotropy and stress birefringence [2.2].

Birefringence causes a second “shadow” spot on the output plane of the FPR, where

the TE- and TM- like polarisations have experienced different phase shifts,

potentially coupling with the wrong output waveguide and causing inter-channel

crosstalk. Several methods have been presented to reduce this polarisation

dependence, such as making the Free Spectral Range equal the difference between

the phase change between TE and TM polarised modes, hence overlapping the

TE/TM spots [2.10], or using a polarisation converting lambda half-plate half way

along the AWs [2.11], causing both polarisations to undergo the same phase change.

Stress birefringence in the waveguides is treated to some extent by coating the

waveguides with a stress inducing film or, as covered in [2.12], in the case of silicon

on Silica waveguides, stress-relieving grooves can be cut either side of the

waveguide.

2.4.4 Polarisation Rotation

Curved waveguides by their nature will exhibit a certain amount of

Polarisation Rotation, where the light energy is transferred from one polarisation to

the other. This effect is exploited in polarisation conversion devices in [2.13][2.14].

Polarisation rotation in the curved waveguides of the AWG is an effect that has not

presently been covered by any paper on the subject of AWGs even though it may be

in some cases a contributor to dispersion in the device.

2.4.5 Passband Shape

A sharp passband, such as the one illustrated schematically in Figure 2.7a,

allows very little error in laser frequency and AWG wavelength tolerance. It is

28

desirable in most circumstances to flatten the passband, as illustrated in Figure 2.7b

so that the device produces a similar output for small changes in laser wavelength.

As stated in [2.2], the ideal shape for the passband of an AWG is to have a flat top,

with a deviation of less than 1dB, for over 70% of the channel separation, and as

wide a -3dB bandwidth (Full Width Half Maximum (FWHM)) as possible without

increasing crosstalk.

Various methods are used to flatten the pass band [2.15], such as broadening

the capture width of the receiver waveguide by using wide, multimode waveguides.

Another approach is to create a spot that has a broad flat centre with steep cut-off at

either side. The latter is achieved by using Multi-Mode Interference Devices (MMIs)

[2.16], y-junctions or a parabolic tapered horn [2.17]. Using these methods, a pass

band of over 50% of the channel separation of 200GHz is achieved in [2.18].

Alternative methods of flattening the spectral response of the AWG are

covered in [2.19], where the spectral response is manipulated by altering the

respective lengths of each arm of the AWG and their positions at the edge of the Free

Propagation Regions (FPRs). The authors of [2.20] take a similar approach through

de-focussing the phase profile in the AWG, to make it near parabolic, again widening

Frequency Gain

Figure 2.7 : (a) a typical AWG channel passband & 2.7b, with

flattened, widened, passband

Frequency Gain

3dB Passband

-3dB -3dB

(a) (b)

29

the pass band. In all cases, flattening the pass band response also increases the

insertion loss of the AWG and often increases crosstalk.

2.4.6 Passband Position

Design or fabrication errors cause a phase error at the end of the AWs which

may shift the focal point away from the expected position, hence affecting the pass-

band position. To compensate for this, the position of the focal point may be shifted

by adjusting the temperature of the AWG [2.4]. If the phase error for each waveguide

is random, causing the spot to defocus, then separate heaters for each individual

Arrayed Waveguide may be implemented. However this approach increases the

energy consumed by the device and requires additional control circuitry, increasing

the cost of manufacture.

2.4.7 Summary

In this section issues that affect the performance of the AWG have been

discussed. All issues that occur in Arrayed Waveguide Gratings brought up in this

section can be attributed to issues with the Arrayed Waveguide part of the structure.

However, due to the complexity of the structure, the Arrayed Waveguides (AWs)

have not previously been fully modelled. Consequently, issues such as crosstalk are

not accurately predicted, since complex propagation mechanisms in the AWs are not

taken into account. It was suggested in Chapter 1 that FD methods, and in particular

the FD-BPM, may be adapted to allow a more thorough investigation into AW

structures, in order to predict or even reduce the impact of unwanted properties of the

AWs, ultimately improving performance and simplifying AWG design. The next

section summarises areas which the FD algorithms can improve analysis of the

AWG, to allow more thorough simulation of the AWs.

30

2.5 Conclusion

This chapter described the basic operation of the AWG and summarised the

methods used for AWG design. However it is highlighted that current methods of

analysis do not accurately predict effects observed in fabricated structures, such as

increased inter-channel crosstalk. It is concluded that although the semi-analytical

analysis methods presented in Section 2.3 are sufficient to design an Arrayed

Waveguide Grating (AWG), these techniques, due to the number of assumptions

made, limit the analysis so that levels of inter-channel crosstalk, and other effects

summarised in Section 2.4, cannot be predicted. Assumptions that are made include:

• Propagation of power in the waveguides of the AW structure is to be wholly

in the fundamental mode of the waveguide

• The field at the end of the first FPR is assumed not to excite modes other than

the fundamental mode of each waveguide in the AW set, such as higher order

and grating modes.

• Coupling, and other propagation effects in the AW structure is normally

ignored

• The propagation is assumed to be constant in waveguides of varying radius.

To improve the analysis, and allow fewer assumptions to be made, a numerical

method may be used, such as the FD-BPM, introduced in Chapter 3, which is popular

due to its relative speed and accuracy. However even FD-BPM has hitherto not

widely been considered to be a viable simulation tool for the full simulation of large

components such as the AWG, due to its memory and processing requirements

although successful simulations of the output Free Propagation Regions and coupling

areas of AWGs have been conducted 2D, and in [2.6] a 3D model of the coupling

regions of the AWs is used to assist in the analysis of coupling and defocusing

31

effects in the AWG. (In this case, for speed of simulation, a Fourier optics modelling

approach is used in conjunction with FD-BPM). However, even in [2.6], the

modelling of the AW structure relies on semi-analytical methods, with all light

energy in the AW structure assumed to propagate in the fundamental mode.

Consequently, in this Thesis, the goal is to improve the understanding of the AW

region of the AWG through the use of improved FD techniques. To achieve this the

basic FD-BPM is extended and improved together with an accompanying FD mode

solver, to allow efficient and accurate modelling of the complex mechanisms present

in the AWs of the AWG.

The next Chapter introduces the theory behind the FD-BPM and FD Mode

Solver in Cartesian co-ordinates, and develops the basic algorithms.

2.6 References

[2.1] P. C. Becker, N.A. Olsson, J.R. Simpson, “Erbium-Doped Fibre Amplifiers”,

Academic Press, 1st edition, May 1999

[2.2] K. A. McGreer, “Arrayed Waveguide Gratings for Wavelength Routing”,

University of Manitoba and TRLabs, IEEE commications Magazine, December

1998.

[2.3] Research by Nippon Telegraph and Telephone Corporation, “400-channel

arrayed waveguide grating with 25GHz spacing”, 2002.

[2.4] Hiroaki Yamada, Kazumasa Takada and Seiko Mitachi, “Crosstalk Reduction

in a 10 GHz Spacing Arrayed-Waveguide Grating by Phase-Error

Compensation”, Journal of Lightwave Technol., vol. 16, no. 3, March 1998

[2.5] M. K. Smit, C van Dam, “Phasar based WDM-devices: principles, design and

applications”, IEEE J Selected Topics in Quantum Electron., Vol. 2, No. 2,

June 1996, pp. 236-250

32

[2.6] A Klekamp and R Munzer, “Imaging Errors in Arrayed Waveguide Gratings”,

IEEE Optical and Quantum Electron., Vol. 35, 2003, pp. 333-345

[2.7] P Munoz, D Pator, and J Capmany “Modelling and Design of Arrayed

Waveguide Gratings”, J. Lightwave Technol., vol. 20, no. 4, April 2002

[2.8] D. Fonseca, R. Luís and A. Cartaxo, “Design and performance of AWG

multiplexer / demultiplexer in WDM systems”, 3ªConferência Nacional de

Telecomunicações, Figueira da Foz, Portugal, 2001, pp. 164-168.

[2.9] J Lam and L Zhao “Design Trade-offs For Arrayed Grating DWDM

MUX/DEMUX”, SPIE Proc. Volume 3949, WDM and Photonic Switching

Devices for Network Applications, April 2000, pp. 90-98

[2.10] L H Spiekman and M R Amersfoort, “Design and Realisation of polarization

independent phased array wavelength demultiplexers using different array

orders for TE and TM”, J Lightwave Technol., Vol. 14, 1996, pp. 991-995.

[2.11] H Takahashi, Y Hibino, and I Nishi, “Polarization-insensitive arrayed-

waveguide grating wavelength multiplexer on silicon” Opt. Lett., Vol. 17, No.

7, 1992, pp. 499-501

[2.12] Christoph K Nadler et al, “Polarisation Insensitive, Low-Loss, Low-Crosstalk

Wavelength Multiplexer Modules”, J. Selected Topics in Quantum Electron.,

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[2.13] C. van Dam et al, "Novel compact polarization converters based on ultra

short bents", IEEE Photon. Technol. Lett., vol.8, 1996, pp.1346-1348

[2.14] W.W. Lui, , T Hirono, , K Yokoyama and Wei-Ping Huang, “Polarization

Rotation in Semiconductor Bending Waveguides : a coupled-mode theory

formulation”, J. Lightwave Technol., Vol. 16, No. 5 , 1998, pp. 929 -936

33

[2.15] C. Dragone, “Efficient Techniques for widening the passband of a

wavelength router”, J of Lightwave Technol., Vol. 16, No. 10, 1998, pp. 1895

– 1906.

[2.16] P. Munoz, D. Pastor and J. Capmany, “Analysis and design of arrayed

waveguide gratings with MMI couplers”, Optics Express, 2001, Vol. 9, No. 7

[2.17] K.Okamoto and A. Sugita, “Flat Spectral response Arrayed Waveguide

Grating multiplexer with parabolic waveguide horns” Electron. Lett., Vol. 32,

1996, pp. 1661-1662

[2.18] S. Suzuki, “Arrayed Waveguide Gratings for dense-WDM systems”,

IEEE/LEOS Summer Topical Meeting WDM components Technology,

Montreal, Canada, Aug 11-15, 1997, pp. 80 – 81

[2.19] T Kamalakis and T Sphicopoulos, “An Efficient Technique for the Design of

an Arrayed-Waveguide Grating with Flat Spectral Response”, J Lightwave

Technol., Vol. 19, No. 11, 2001, pp. 1716-1725

[2.20] M C Parker and S D Walker, “A Fourier-Fresnel Integral-Based Transfer

Function Model for a Near-Parabolic Phase Profile Arrayed Waveguide

Grating”, IEEE Photon. Technol. Lett., Vol. 11, No. 8, 1999, pp. 1018-1020