Report Btp (2)

MICRORING RESONATOR ANALYSIS FOR SINGLE CHANNEL DPSK AND WDM DPSK DEMODULATION

THE

LNM INSTITUTE

OF

INFORMATION TECHNOLOGY

BTP REPORT-2009-10

SUPERVISOR : PROF. RANJAN GANGOPADHYAY SUBMITTED BY: RAUNAQ AGARWAL DATE: 5 DEC 2009 TH

CONTENTS 1. Introduction……………………………………………………………………..3 2. Microring resonator basics

2.1 Microring resonator model……………………………………………..4 2.2 Directional Coupler Model……………………………………………..4 2.3 Ring waveguide Model…………………………………………………5 2.4 Combined Model………………………………………………………..6 2.5 The drop response………………………………………………………6 2.6 The through response…………………………………………………...8 3. Objectives of study……………………………………………………………… 9 4. Methodology followed 4.1 Microring resonator based band pass filter design……………………… 9 4.2 Apodization Profiles considered……………………………………….11 5. Results obtained 5.1 OMRA filter performance……………………………………………...12 5.2 OMRA filter for DPSK demodulation………………………………....13 5.2.1 Single channel DPSK demodulation…………………………..14 5.2.2 Demodulation of 3-channel WDM DPSK…………………….15

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6. Conclusion……………………………………………………………………...16 7. Future Work…………………………………………………………………….16 References………………………………………………………………………...17

1. INTRODUCTION There has been recently an increasing interest in the field of microring resonator based devices. Integrated optic microring resonators were first proposed by Marcatili in 1969. Functionally these resonators behave similar to the Fabry-Perot resonator and share its Lorentzian-like frequency response. In an integrated optics FP the cavity the mirrors are commonly created using cleaved facets or reflective gratings, both of which are difficult to integrate when produced on a large scale. However, the use of directional couplers in a microring resonator allows, depending on the index contrast, ring radii as small as a few micrometers. It has been argued that of all photonic devices, micro resonators currently provide the highest dispersion per unit volume. As a consequence of their compact geometry and tailorable dispersive and nonlinear optical properties, micro resonators are expected to play a key role in the large-scale integration of photonic devices. In addition, by careful design of the resonator geometry and choice of the materials system it can be made to perform a wide range of functions like modulation and demodulation, format conversion, dispersion compensation, optical logical gates etc. During the past decade, microring resonators based slow-light structures received substantial attention due to their interesting properties and potential applications [1-4]. Much focus was devoted to two different types of slow-light structures: the CROW (Coupled Ring Optical Waveguide) and the SCISSOR (Side Coupled Integrated Spaced Sequence of Resonators) as shown in Fig.1 The LNM Institute of Information Technology

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Fig. 1. (a) a CROW, (b) a single-channel SCISSOR, (c) a double channel SCISSOR, and (d) a twisted double-channel SCISSOR .

2. MICRORING RESONATOR BASICS 2.1 MICRORING RESONATOR MODEL

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2.2 DIRECTIONAL COUPLER MODEL Transfer Matrix of symmetric couplers can be expressed as

where Χc is the fraction of power lost in the coupler, Leff is the effective coupling length between resonator and waveguides and кc is the coupling constant of the port and resonator waveguides We can also write

where к is the fraction of light that is coupled between ring and port waveguides. The fraction of light that remains in port waveguide is μ and

.

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The values of κc and Leff can be hard to determine when dealing with resonators. Determining the coupling constant of a standard directional coupler that consists of two parallel waveguides is fairly straightforward as it can be found by calculating the modes in a cross-section of the coupler using a 2D modesolver. In the case of the couplers used in the microring resonator, however, determining the coupling constant (and even Leff) can be a very challenging task.

2.3 RING WAVEGUIDE MODEL A ring resonator consists of single circular waveguide. In the model of the resonator, however, this waveguide is split in two halves that are connected to each other via the two couplers. The two halves of the resonator can be described by the field propagation term SR of the light in these waveguides:

In this equation φr is the roundtrip phase and χr is the roundtrip loss factor of the light in the resonator. The roundtrip phase is defined as:

where R is the radius of the ring resonator. The parameter ng is the group index of the mode in the waveguide defined as:

The roundtrip loss factor χr is defined as:

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where αr is the roundtrip loss of the resonator in dB and αdB (αdB >0) is the loss of the mode in the ring waveguide in dB/m.

2.4 COMBINED MODEL

2.5 THE DROP SEQUENCE

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where

H is also the maximum power available in the drop port for a resonator in resonance. Fc is the so-called finesse factor defined as:

The Finesse F of the resonator can be determined from the finesse factor following:

The finesse is a measure of the quality of the micro resonator and can be related to the storage capacity or quality factor Q of the resonator through:

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where FSR is the Free Spectral range of the resonator, defined as the distance between two consecutive fringes or resonance peaks. The free spectral range is determined by:

From the free spectral range and the finesse the bandwidth of the resonator can be calculated. The bandwidth ΔλFWHM is defined as the Full Width at Half Maximum of the drop response and relates to the Finesse and the FSR as:

2.6 THE THROUGH RESPONSE

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where G is given by

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3. OBJECTIVES OF STUDY •

To demonstrate single channel DPSK and simultaneous 3-channel WDM-DPSK demodulation using a periodic microring-resonator based band-pass filter.

•

Investigate several apodization profiles for the resonator filter to decide for the optimal performance.

•

To estimate the actual eye-closure penalty caused by inter-channel interference through filter side lobes as a function of inter-channel spacing in a 3-channel WDM-DPSK.

4. METHODOLOGY FOLLWED The LNM Institute of Information Technology

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As compared to conventional on-off-keying (OOK), differential-phase-shift-keying (DPSK) has higher receiver sensitivity and is more robust to transmission impairments. Typically, a delayline interferometer (DLI) is chosen for demodulating DPSK data [1]. The two DLI outputs are sent to a balanced photodetector and represent the constructive and destructive interference between the phases of adjacent bits. Although the DLI is much simpler than using a stable local oscillator in a true coherent receiver, it suffers from the following significant issues: (i) it is temperature sensitive and requires active stabilization, and (ii) it is not yet inexpensive to produce. Prior to deployment of DPSK systems, alternative, cost-effective and stable solutions for DPSK demodulation may be desirable. One reported alternative to the traditional DLI is a single narrow-bandwidth bandpass filter acting as a frequency discriminator. This filter replicates the main lobe of the DLI frequency response converting DPSK into an optical duobinary (ODB) signal for detection. This technique is cheaper, simpler to implement, and may be easier to stabilize over temperature. We have taken the CROW device as composed of a number of identical sections or unit cells that are cascaded to form the final device. In this case the final filter structure resembles an uniform filter and therefore strong sidelobes are obtained in the bandpass transfer functions.

4.1 MICRORING RESONATOR

BASED BAND PASS FILTER

DESIGN

Fig 2 CROW structure layout

The CROW structure considered is composed of N uncoupled rings of same length La, each ring being coupled to an in (upper) and a drop (lower) waveguide as shown in Fig 2. In analyzing the CROW structure we have used the transfer matrix method [4]. The transfer matrices of arbitrary unit cell MUCi (i = 1, 2,..N-1) and the closing cavity MCN are given respectively by MUCi=1R2iR1iR2i-T1iT2iej∆T2iej∆-T1ie-j∆e-j∆ MCN=1R2NR1NR2N-T1NT2NT2N-T1N1

where The LNM Institute of Information Technology

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R1i=t1i-t2i*t1i2+к1i2τiejδ1-τit1i*t2i*ejδ R2i=t2i-t1i*t2i2+к2i2τiejδ1-τit1i*t2i*ejδ T1i=к1i*к2iτiejδ/21-τit1i*t2i*ejδ

T2i=к2i*к1iτiejδ/21-τit1i*t2i*ejδ

In the above expressions the relevant parameters appearing are the round-trip phase shift  , the loss factor  and the inter-cavity phase-shift  which are given by δ = βLa τ = exp(-αLa) ∆ = βLb where β is the propagation constant, Lc is the length of the ring, α is the attenuation constant and Lb is the ring separation parameter. Assuming K to be the power coupling ratio of the coupler, one has Reflection coefficient к=jK Transmission coefficient t=1-K In an N-segment OMRA, if the coupling coefficients in both buses are apodized such that к1i = к2i = к w(i),where w(i) is the apodization function. The overall transfer matrix is then given by EN+EN-=T11T12T21T22E1+E1-

where

T11T12T21T22=MCNi=N-11MUCi

Finally, the reflection transfer function is given by R=E1-E1+=-T21T22

4.2 APODIZATION PROFILES CONSIDERED Four

families of apodization profiles [3,4] considered in the present investigation . They are:

•

•

Gaussian profile

wi=exp-Gi-N2N2 ⁡

i=0, 1,.….N-1

•

Hamming profile

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wi=1+Hcos2πn1+H

i=0, 1,.….N-1 n=(i-N/2)/N

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•

Kaiser profile

Io is the Bessel function of first kind and zero order.

wi=BKsinBKI0BK1-4n2

i=0, 1,.….N-1 n=(i-N/2)/N

•

Tanh profile

wi=tanh2ai/N 0≤i≤N/2tanh2a(N-i)/N N/2≤i≤ N

where a is a constant

5. RESULTS OBTAINED 5.1 OMRA FILTER PERFORMANCE We first compare the side-lobe suppression obtained in OMRA filter designed with different apodization profiles. Two cases are considered: • 3-ring CROW (N = 3) • 10-ring CROW (N = 10) The choice of apodization parameters G (Gaussian), H (Hamming), βK (Kaiser) and a (Tanh) is made by fixing the 3-dB bandwidth to 7.13 GHz (2/3rd bit-rate) .This has been the design choice for the 10.7 Gb/s DPSK demodulation filter.

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Figure 3 (a) (both upper left and right ones) shows the magnitude and the phase plot of a 10-ring CROW filter and Fig. 3 (b) (both lower left and right ones) shows the same for a 3-ring CROW filter. Values used in the simulation Apodization parameters G

N=3 1.3

N=10 3

H

0.05

0.2

βK

0.01

0.01

a

2.27

3.15

La 6.5*10^-3 Lb 3.25*10^-3 neff 2.5 τ 0.97 K

0.9 Table I Apodization parameter values

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Fig 3 Magnitude and phase plot for the resonator filter (N = 10 and N = 3) for four different apodization profiles.

It is easily appreciated that Tanh apodization shows an improved performance regarding the side-lobe suppression when compared with other apodization profiles.

5.2 OMRA

FILTER FOR

DPSK DEMODULATION

A schematic of a 3-channel WDM-DPSK fibre-optic transmission link with each channel operating at 10.7 Gb/s is illustrated in Fig. 4. After passing through the single-mode fiber, the received DPSK signal is demodulated by the periodic filtering of OMRA. In the figure only the central channel has been shown to be demultiplexed, envelope detected and low-pass filtered (a 5th-order Bessel filter with 3-dB cut-off frequency = 8.56 GHz) before the demodulated eye was observed for each type of apodization used. Also, the eye-closure penalty of the micro-ring resonator filter based DPSK demodulator was computed with reference to the eye opening of a Gaussian filter demodulator (this reference is chosen since the Gaussian filter has no sidelobes and hence it provides almost near-ideal performance as a DPSK demodulator). In the present simulation set-up we have considered the fiber link to be ideal.

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2 link Fiber 5-order 10.7 Microring Eye MUX | |Demux plot GHz low-

λ2 λ2 resonator pass λ1filter λ3 filter

Fig. 4 DPSK transmission link

5.2.1 SINGLE CHANNEL DPSK DEMODULATION The following values are used in the filter simulations for all the cases: L c = 0.65 mm, Lb = 0.5La, neff = 2.5, τ = 0.985, K = 0.16 The choice of the apodization parameters G ( Gaussian), H (Hamming) and a (Tanh) is made by fixing the 3-dB bandwidth equal to 7.13 GHz ( 2/3rd bitrate) .This has been the design choice for the 10.7 Gb/s DPSK demodulation filter. The apodization parameter values of the various profiles are G = 2, H = 0.15 and a = 2.15. Figures 4 (b), (c), (d) show the eye plots of the demodulated DPSK signal for Hamming, Gaussian and Tanh apodizations respectively. Table 2 shows the calculated eye-closure penalty The LNM Institute of Information Technology

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for three apodization profiles when compared with Gaussian band-pass filter as a DPSK demodulator, the eye for which is shown in Fig.5 (a)

Fig. 5 (a) Gaussian filter demodulator (reference) , (b) eye of demodulated DPSK signal using Hamming apodization, (c) Gaussian apodization , (d) Tanh apodization

Table II. EYE CLOSURE PENALTY Apodization

Eye-closure penalty(dB)

Gaussian

1.64

Hamming

1.66

Tanh

1.32

5.2.2 DEMODULATION

OF

3-CHANNEL WDM DPSK

We have also investigated the effect of filter apodization for the case of periodic filtering of the micro-ring resonator filter on simultaneous demodulation of all three channels in WDM-DPSK, The LNM Institute of Information Technology

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as a function of the inter-channel separation (∆f).In each case of apodization profile, the FSR is chosen to be equal to ∆f and the filter 3-dB bandwidth is set to 2/3rd bit rate.The performance of OMRA as the DPSK demodulator with Gaussian (G = 1) and Tanh apodization ( a = 2.1) when ∆f = 2R is depicted in Fig. 6.

Figs 6 (a), (c), (e) periodic micro-ring resonator filter response with no apodization , Gaussian apodization and Tanh apodization. Fig 6. (b), (d) , (f) are the eye plots of demodulated WDM DPSK with no apodization , Gaussian apodization and Tanh apodization respectively.

The values used in the simulation to achieve 3-channel WDM-DPSK for different channel separations are given in Table 3. Table 4 provides the computed values of eye closure penalty for different channel separations with Gaussian and Tanh apodization profiles.It is observed that the largest eye-opening takes place with the Tanh apodization as expected, since it leads to largest sidelobe suppression.

Table-III SIMULATION PARAMETER VALUES FOR 3-CHANNEL WDM-DPSK Channel Separation (∆f) 2 R = 21.4 GHz 2.5 R = 26.75 GHz 3R = 32.1 GHz

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Lc (mm) 5.6 4.5 3.75

K 0.67 0.59 0.53

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Table IV EYE CLOSER PENALTY VALUES FOR 3-CHANNEL WDM-DPSK DEMODULATION Filter apodizations

Channel

Separation

(GHz)

Gaussian apodization

2R 2.36

2.5R 1.16

3R 1.08

Tanh apodization

0.75

0.59

0.44

6. CONCLUSION The present study has clearly established the fact that an un-apodized micro-ring resonator bandpass filter as a DPSK demodulator performs very poorly (due to the presence of sidelobes) in terms of the eye-opening for both single-channel DPSK and WDM-DPSK. Apodization of the resonator filter leads to significant reduction in sidelobes and hence improves the demodulator performance..The actual eye-closure penalty caused by inter-channel interference through filter sidelobes as a function of inter-channel spacing in a 3-channel WDM-DPSK has been quantified for 2 apodization profiles. Tanh apodization always shows the superior performance for both single-channel DPSK and 3-channel WDM-DPSK.

7. FUTURE WORK •

Evaluating the DPSK/ WDM DPSK link performance using the resonator filter demodulator in the presence of dispersion and nonlinearity.

•

Studying the impact of filter apodization on demodulation of DQPSK using a microring resonator based band pass filter.

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REFERENCES [1] S.Gupta , R.Gangopadhyay, G.Prati , “Reach extension of a DPSK optical link using an optical filter demodulator & MLSE receiver”,IEEE Photon. Technol. Lett. ,vol. 20, no. 19 , Oct 2008. [2] L.Zhang , Jeng-Yuan Yang , Muping Song, Yunchu Li, Bo Zhang, Raymond G. Beausoleil and Alan E. Willner, “ Microring based modulation and demodulation of DPSK signal”, Optics Express , vol. 15, no. 18 , Sept 2007, pp 11564- 11569. [3] Karin Ennser , Mikhail N. Zervas , and Richard I. Laming, “ Optimization of apodized linearly chirped fiber gratings for optical communications”, IEEE J. Quantum Elect. , vol . 34 , no. 5, May 1998. [4] J.Capmany, P.Munoz, J.D.Domenech, and M.A. Muriel, “ Apodized coupled resonator waveguides”, Optics Express, vol. 15, no. 16, 6 Aug 2007.

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