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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 5 — Feb. 27, 2012
  • pp: 5725–5741
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High-performance monolithically integrated 120° downconverter with relaxed hardware constraints

P. J. Reyes-Iglesias, I. Molina-Fernández, A. Moscoso-Mártir, and A. Ortega-Moñux  »View Author Affiliations


Optics Express, Vol. 20, Issue 5, pp. 5725-5741 (2012)
http://dx.doi.org/10.1364/OE.20.005725


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Abstract

A coherent receiver based on a 120° downconverter architecture, inherited from previous approaches at the microwave and optical fields, is proposed, analyzed, numerically evaluated and compared to the conventional 90° downconverter alternative. It is shown that, due to its superior calibration procedure, the new downconverter architecture allows full compensation of the imbalances in its optical front-end thus leading to an extended dynamic range and a broader operating bandwidth than its 90° counterpart. Simulation results from monolithically integrated downconverters show that our approach can be an interesting alternative to support efficient modulation schemes such as M-QAM that is being studied as potential candidate for the next generation of optical communication systems.

© 2012 OSA

1. Introduction

Optical coherent systems have significant advantages as they enable high spectral efficiency via complex modulation formats as M-ary phase shift keying (M-PSK) or quadrature amplitude modulation (M-QAM), high capacity from wavelength division multiplexing (WDM) and electronic compensation of transmission impairments. Polarization multiplexed QPSK has been recently proposed as the transmission modulation for 100Gbps Dense-WDM networks by the Optical Internetworking Forum [1

1. Optical Internetworking Forum (OIF), “100G ultra long haul DWDM framework document,” document OIF-FD-100G-DWDM-01.0 (June 2009), http://www.oiforum.com/public/impagreements.html.

], and higher order QAM formats are being foreseen as a viable alternative to increase a step further system transmission capacity and efficiency. For example, in the frame of the MIRTHE project, 16-QAM monolithically integrated transmitter and receivers for 400Gbps are being pursued [2

2. Mirthe Project, “Monolithic InP-based dual polarization QPSK integrated receiver and transmitter for coherent 100–400Gb Ethernet,” http://www.ist-mirthe.eu/.

] and several groups are investigating the possibilities of high density 64-512 QAM for optical communications in different scenarios [3

3. M. Nakazawa, “Ultrafast and high-spectral-density optical communications systems,” "Ultrafast and High-spectral-density optical communications systems,” in CLEO:2011—Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThGG3.

]. These high order modulation formats benefit from symbol rate minimization thus increasing tolerance to chromatic and polarization dispersion, allowing lower speed electronic devices to be used, and reducing power consumption. Besides that, recent advances in broadband optical amplification technologies would allow to take full advantage of the S- C- and Extended L-band to cover a 1490-1620 nm optical bandwidth [4

4. A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432 x 171-Gb/s) C- and extended L-band transmission over 240 km Using PDM-16-QAM modulation and digital coherent detection,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPB7.

, 5

5. F. Boubal, E. Brandon, L. Buet, S. Chernikov, V. Havard, C. Heerdt, A. Hugbart, W. Idler, L. Labrunie, P. Le Roux, S. A. E. Lewis, A. Pham, L. Piriou, R. Uhel, and J. P. Blondel, “4.16 Tbit/s (104x40 Gbit/s) unrepeatered transmission over 135 km in S + C + L bands with 104 nm total bandwidth,” in 27th European Conference on Optical Communication, 2001. ECOC '01 (2001), vol. 1, pp. 58–59

]. Hence, it is clear that there exist a potential interest in developing high performance receivers capable of demodulating complex modulation signals in wide wavelength spans with the highest quality.

The vast majority of the optical coherent receivers in the bibliography make use of the well-known 90° hybrid based downconverter, a phase diversity coherent receiver which was initially proposed in the eighties [6

6. A. W. Davis, M. Pettitt, J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightwave Technol. 5(4), 561–572 (1987). [CrossRef]

] and which has recently received much attention as it is an important piece of hardware in the optical front end [7

7. Y. Painchaud, M. Poulin, M. Morin, and M. Têtu, “Performance of balanced detection in a coherent receiver,” Opt. Express 17(5), 3659–3672 (2009). [CrossRef] [PubMed]

]. These hybrids can be fabricated in bulk optics [8

8. Optoplex Corportation, “2x4 QPSK mixer-polarization diversified optical hybrid,” datasheet, www.optoplex.com.

] or in integrated optics technology. The later allows photoreceivers to be integrated in the same chip [9

9. A. Matiss, S. Bottacchi, J. K. Fischer, R. Ludwig, C. C. Leonhardt, C. Schmidt-Langhorst, and C. Schubert, “Performance of an integrated coherent receiver module for up to 160G DP-QPSK transmission systems,” J. Lightwave Technol. 29(7), 1026–1032 (2011). [CrossRef]

,10

10. R. Kunkel, H.-G. Bach, D. Hoffmann, C. Weinert, I. Molina-Fernandez, and R. Halir, “First monolithic InP-based 90 degrees-hybrid OEIC comprising balanced detectors for 100GE coherent frontends,” in International Conference on Indium Phosphide & Related Materials (IPRM) (2009), paper TuB2.2, pp. 167–170.

], making it a cost-efficient solution appropriate for commercial applications. Obviously 90° hybrid optical downconverters cannot be designed to have ideal performance in a wide wavelength span, so real hardware suffers from different kinds of unbalances (mainly measured in practice through common mode rejection ratio, CMRR) which usually worsens at the ends of the operative band. Digital signal processing algorithms following photodetection are designed to mitigate this non-ideal performance. This is for example the case of Gram-Schmidt orthogonalization procedure (GSOP) which is used for 90° hybrid quadrature imbalance compensation [11

11. I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008). [CrossRef]

]. However, not all the effects due to 90° hybrid unbalances can be compensated by this kind of approach. Effectively, as it has been shown previously [12

12. A. Moscoso-Martir, I. Molina-Fernandez, and A. Ortega-Monux, “Signal constellation distortion and ber degradation due to hardware impairments in six-port receivers with analog I/Q generation,” Prog. Electromagn. Res. 121, 225–247 (2011). [CrossRef]

], hybrid imbalances introduce two types of distortion on the received signal constellation: linear and nonlinear; and as will be shown in the following Section 4.3 GSOP algorithms only compensates for the linear type of distortion.

Fortunately, other types of phase diversity downconverters exist which are not based on the 90° hybrid. This is the case of the 120° phase diversity receiver, a type of the well-known multiport radiofrequency receiver [13

13. J. Li, R. G. Bosisio, and K. Wu, “Computer and measurement simulation of a new digital receiver operating directly at millimeter-wave frequencies,” IEEE Trans. Microw. Theory Tech. 43(12), 2766–2772 (1995). [CrossRef]

], which has been recently used as a wide bandwidth, hardware-impairment tolerant receiver at microwave frequencies [14

14. P. Pérez-Lara, I. Molina-Fernandez, J. G. Wanguemert-Perez, and A. Rueda-Perez, “Broadband five-port direct receiver based on low-pass and high-pass phase shifters,” IEEE Trans. Microw. Theory Tech. 58(4), 849–853 (2010). [CrossRef]

]. This kind of 120° downconverters, although not very frequent, have also been reported for optical communications by making use of 3x3 fiber couplers: 680 Mbps Amplitude-Shift Keying demodulation was already demonstrated in the eighties [6

6. A. W. Davis, M. Pettitt, J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightwave Technol. 5(4), 561–572 (1987). [CrossRef]

], and 1.4 Gbps 4-QAM has been recently reported based on this approach [15

15. T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, and R. Noé, “Coherent optical communication: towards realtime systems at 40 Gbit/s and beyond,” Opt. Express 16(2), 866–872 (2008). [CrossRef] [PubMed]

].

This paper is organized as follows; standard 90° and proposed 120° downconverter architectures are shown in Section 2 and 3 respectively. There, analytical bit error rate (BER) estimation is carried out for an ideal hardware including noise sources. In Section 4, via numerical simulation, the performance degradation due to hardware non-idealities is carried out for each scheme, and the superior benefits of our proposal due to its superior calibration procedure are demonstrated. Finally Section 5 provides the main conclusions of this paper.

2. 90° Hybrid downconverter

2.1 General setup

Figure 1
Fig. 1 90° hybrid coherent receiver.
shows the schematic of the standard 90° downconverter, with a 90° hybrid and photodiodes in balanced configuration, for receiving in-phase and quadrature signal components [10

10. R. Kunkel, H.-G. Bach, D. Hoffmann, C. Weinert, I. Molina-Fernandez, and R. Halir, “First monolithic InP-based 90 degrees-hybrid OEIC comprising balanced detectors for 100GE coherent frontends,” in International Conference on Indium Phosphide & Related Materials (IPRM) (2009), paper TuB2.2, pp. 167–170.

]. After obtaining electrical signal components, they are digitized in two analog-to-digital converter (ADC) and combined to be processed in the digital signal processor (DSP). Assuming polarization control or polarization diversity, the electric fields of the received signal (neglecting transmission impairments) and the LO laser can be written in terms of their complex envelopes as

es(t)=Re{e˜sejωot}
(1)
eLO(t)=Re{e˜LOejωot}
(2)

For homodyne detection the angular frequency ωo of signal and LO is assumed to be the same, so that any frequency or phase mismatch between them would be corrected digitally afterwards in the ideal DSP block.

Considering Ps=|e˜s|2and PLO=|e˜LO|2 as signal and LO power respectively, slowly varying complex signal envelope can be expressed as
e˜s=Ps(I+jQ)+nASE
(3)
where nASE represents the complex amplified stimulated emission (ASE) noise introduced by the optical amplification along transmission, being modeled as an additive white Gaussian noise (AWGN) with single-sided power spectral density NASE. On the other hand, I and Q are the normalized in-phase and quadrature components of the incoming modulated signal.

The signal and LO are combined in the optical 2x4 90° hybrid, with scattering parameters Sik defined between its six ports, and detected at the four output ports through photodiodes with responsivities Ri. Then, neglecting the noise contribution, the output photocurrents can be calculated as

ii=Ri|Si1e˜s+Si2e˜LO|2;i=3,...,6.
(4)

Defining the received symbolΓs=e˜s/e˜LO, in the complex plane, and the 90° hybrid centers as the ratio qi=Si2/Si1, Eq. (4) can be rewritten as

ii=Ri|Si1|2PLO[|qi|2+|Γs|22Re(qi*Γs)];i=3,...,6.
(5)

Output photocurrents iI and iQ, for in-phase an quadrature components, can be now obtained differentially from balanced detection, as shown in Fig. 1, and be described in matrix form as

[iIiQ]=[i3i4i5i6]=[αIαQ]+[γIγQ][I2+Q2]+[uIuQvIvQ][IQ]
(6)

Table 1

Table 1. Parameters Derived in [12] to Characterize 90° Hybrid Integrated Coherent Receiver

table-icon
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shows the parameters introduced in Eq. (6). Three terms can be identified at right-hand side of Eq. (6): DC offset term (α), non-linear rectified wave distortion term (γ) and linear axes transformation terms (u,v). As it was demonstrated in [12

12. A. Moscoso-Martir, I. Molina-Fernandez, and A. Ortega-Monux, “Signal constellation distortion and ber degradation due to hardware impairments in six-port receivers with analog I/Q generation,” Prog. Electromagn. Res. 121, 225–247 (2011). [CrossRef]

], and it is repeated here for the sake of completeness, in the receiver performance the effect of DC offset and linear terms have a simple interpretation consisting of a translation α of the origin of coordinates, followed by a rotation and imbalance of reference axes as shown in Fig. 2(a)
Fig. 2 64-QAM constellation distortion for an unbalanced 90° hybrid coherent receiver under ASE noise: (a) linear impairments (γ = 0) causing non-zero DC offset (α≠0), rotation and imbalance of reference axes (u≠j·v); (b) non-linear impairment (γ≠0, α = 0, u = -j·v).
. On the other hand, the non-linear rectified wave distortion term introduces a non-linear error proportional to the Ps/PLO ratio that can severely distort the receiver constellation, as shown in Fig. 2(b), and whose effect will be considerable for spectrally-efficient high-order M-QAM modulation.

2.2 Analytical BER estimation including noise sources for ideal hardware implementation

For a perfectly balanced receiver (photodiodes of same responsivity R = Ri and ideal 90° hybrid with scattering parameters {S31 = S41 = S51 = S61 = S32 = ½, S42 = -½, S52 = j/2, S62 = -j/2}), and in absence of noise, it can be easily obtained that α = 0, γ = 0 and u=jv=RPLOPs, so Eq. (6) becomes

iI=RPLOPsI=RPLORe(e˜s)iQ=RPLOPsQ=RPLOIm(e˜s)
(7)

Therefore, the recovered complex signal can be defined as is = iI + jiQ, whose power can be calculated as <|is|2> (where < > denotes the ensemble average operator).

|is|2=|RPLOe˜s|2=R2PLOPs
(8)

We now consider all relevant noise sources at reception: ASE noise, shot noise at the photodetectors, relative intensity noise (RIN) from signal and LO, and electronic trans impedance amplifier (TIA) noise. As shown in the Appendix, it is observed that for a perfectly balanced receiver ASE-signal beat noise and RIN from LO and signal are cancelled out. Besides TIA noise can usually be neglected, and in phase inoiseI2 and quadrature inoiseQ2 noise components can be calculated as in Eq. (A9), which is repeated here for convenience.
inoiseI2=inoiseQ2=iASELO2+12ishot2=R2PLONBASEe2+qRBe(Ps+PLO)
(9)
where Be is the effective noise bandwidth and q is the electron’s charge. Then the inverse of the signal-to-noise ratio per symbol (SNR) can be written in the following closed form
1SNR=inoiseI2+inoiseQ2|is|2=1OSNR+2qBeR(1PLO+1Ps)
(10)
where OSNR=Ps/NASEBe is the optical signal-to-ASE-noise ratio at the receiver and the second term at right-hand side of Eq. (10) is the shot-noise contribution of the photodiodes. ASE noise will impose in any case the maximum achievable SNR.

If we assume M-QAM modulation with homodyne reception under AWGN noise sources, the bit error rate (BER) is given as a function of SNR (where erfc means the complementary error function) from [16

16. A. B. Carlson, Communication Systems (McGraw-Hill, 1986).

].

BER=1log2M{1[1(11M)erfc(32(M1)SNR)]2}
(11)

Attending to Eq. (10), in the common situation of high LO power, there will be the expected limited shot-noise transmission under low signal power. This is easily appreciable in Fig. 3
Fig. 3 BER performance versus signal power for different LO power for 56 Gbps (a) 64-QAM and (b) 256-QAM transmission, considering an ideal coherent receiver with noise sources (Be = Rs, R = 0.89 A/W).
, where BER performance versus signal power is depicted for different LO power, under 56 Gbps 64-QAM and 256-QAM transmission, when ASE noise is adjusted for a BER = 10−4 in absence of internal receiver noise (OSNR equals to 24.3 dB and 30.2 dB respectively).

3. 120° Coupler downconverter

3.1 Setup

Figure 4
Fig. 4 120° coherent receiver.
shows the scheme of the 120° downconverter, with a 2x3 120° optical coupler and three photodiodes. Photocurrent outputs are digitized in three ADC and processed in the DSP following a simple linear transformation to obtain in-phase and quadrature components. From a similar analysis to that performed in Section 2.1, the signal and LO waves, described by Eq. (1) and (2), will be combined now in the optical five-port, with scattering parameters Sik defined between their ports, being the photocurrents generated at the output ports

ii=Ri|Si1e˜s+Si2e˜LO|2;i=3,...,5.
(12)

Defining the five-port centers qi=Si2/Si1, Eq. (11) can be rewritten as

ii=Ri|Si1|2PLO|Γsqi|2;i=3,...,5.
(13)

In the complex plane, Eq. (13) corresponds to three circles centered in qi (ideally 120° apart) with radius depending on the received symbol. As it was shown in [17

17. P. Perez-Lara, I. Molina-Fernandez, J. G. Wangüemert-Perez, and R. G. Bosisio, “Effects of hardware imperfection on six-port direct digital receivers calibrated with three and four signal standards,” IEE Proc. Microw. Antennas Propag. 153(2), 171–176 (2006). [CrossRef]

], after the work in [18

18. F. M. Ghannouchi and R. G. Bosisio, “An alternative explicit six-port matrix calibration formalism using five standards,” IEEE Trans. Microw. Theory Tech. 36(3), 494–498 (1988). [CrossRef]

], three power readings are enough to establish a linear set of equations to uniquely obtain I-Q signal components under arbitrary hardware unbalances of phase diversity circuit. Consequently, note that the only two power measurements obtained from the standard 90° downconverter (see Fig. 1 and Eq. (6) in Section 2.1), cannot cancel nonlinear constellation distortion (induced by the hardware unbalances of the phase diversity circuit) by linear means.

Equation (12) can be expressed as Eq. (5), or equivalently in matrix form as

[i3i4i5]=[α1α2α3]+[γ1γ2γ3][I2+Q2]+[u1Iu1Qu2Iu2Qu3Iu3Q][IQ]
(14)

Table 2

Table 2. Parameters to Characterize 120° Coherent Receiver

table-icon
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shows the parameters introduced in Eq. (14). Three parameters describe the photocurrents obtained at each of the three output ports: DC offset real parameter (α), signal power-dependent real parameter (γ) and LO-signal power-dependent complex parameter (u).

Attending to the three linear equations formulated in Eq. (14), in-phase and quadrature demodulated components can be easily described in terms of the three photocurrents measurements ii.
iI=i=3,4,5AIiii+CIiQ=i=3,4,5AQiii+CQ
(15)
where coefficients AIi, AQi, CI and CQ can be determined from a simple calibration procedure, solving the linear equation system obtained from Eq. (15) when transmitting four known symbols [17

17. P. Perez-Lara, I. Molina-Fernandez, J. G. Wangüemert-Perez, and R. G. Bosisio, “Effects of hardware imperfection on six-port direct digital receivers calibrated with three and four signal standards,” IEE Proc. Microw. Antennas Propag. 153(2), 171–176 (2006). [CrossRef]

].

3.2 Analytical BER estimation including noise sources for ideal hardware implementation

For a perfectly balanced 120° downconverter (photodiodes of a same responsivity R = Ri and an ideal 120° coupler with scattering parameter {S31=S41=S51=S42=1/3;S32=S52*=ej120º/3}), and in the absence of noise, from Eq. (14) we obtain

i35=R3{PLO+Ps+2PLORe(e˜sej120º)}=R3{PLO+PsPLOPs[I3Q]}i4=R3{PLO+Ps+2PLOPsI}
(16)

Therefore, for this ideal situation in-phase and quadrature components, iI and iQ, can be easily obtained from the output photocurrents as

iI=0.5i3+i40.5i5=RPLOPsI=RPLORe(e˜s)iQ=32(i3i5)=RPLOPsQ=RPLOIm(e˜s)
(17)

Noise analysis can be carried out in a similar way as for the ideal 90° hybrid. This is detailed in the Appendix, where it is concluded from Eq. (A13) that in-phase and quadrature noise components for the ideal 120° coupler are the same as those obtained for the 90° hybrid from Eq. (9).

Thus it is easily shown that an ideal 120° coherent downconverter responds to the same SNR expression Eq. (10) obtained for an ideal 90° hybrid coherent downconverter. Therefore, this novel proposal does not suffer from additional penalty under ideal hardware realization (same dynamic range restrictions apply) and thus Fig. 3, originally obtained for the ideal 90° downconverter, is also valid for the ideal 120° one.

From this section we conclude that 90° hybrid and 120° coupler downconverter performances are the same in an ideal situation however, as it will be shown in the following sections, in presence of hardware impairments and under high Ps/PLO ratios, the 120° architecture clearly outperforms the classical 90° approach due to its superior correction procedure.

4. Performance comparison of monolithically integrated 90° hybrid and 120° coupler based downconverters

Monolithically integrated downconverters for coherent optical communications are being targeted in several technologies as InP and SoI [19

19. R. Halir, G. Roelkens, A. Ortega-Moñux, and J. G. Wangüemert-Pérez, “High-performance 90° hybrid based on a silicon-on-insulator multimode interference coupler,” Opt. Lett. 36(2), 178–180 (2011). [CrossRef] [PubMed]

] as a mean to reduce complexity and cost of recently demanded 100 Gbps per wavelength optical communication systems. Almost all of the proposals are based on 90° downconverters achieved through a proper combination of 2x2 or 2x4 Multimode Interference Couplers (MMIs). In this section we will study, through simulation, the performance of two monolithically integrated receivers in InP: a classical 90°, and a novel 120° MMI based downconverters. The performance degradation, in terms of expected BER, of 90° and 120° downconverters due to hardware unbalances (2x4 and 2x3 MMIs phase diversity circuits and photodiode responsivity) will be compared to the ideal performance for perfectly balanced hardware described by Eqs. (8)-(11) (see Fig. 3).

4.1. Monolithically integrated downconverters

The monolithically integrated downconverters, including phase diversity passive structures and p-i-n photodiodes, have been designed in InP technology similar to the one employed in [9

9. A. Matiss, S. Bottacchi, J. K. Fischer, R. Ludwig, C. C. Leonhardt, C. Schmidt-Langhorst, and C. Schubert, “Performance of an integrated coherent receiver module for up to 160G DP-QPSK transmission systems,” J. Lightwave Technol. 29(7), 1026–1032 (2011). [CrossRef]

, 10

10. R. Kunkel, H.-G. Bach, D. Hoffmann, C. Weinert, I. Molina-Fernandez, and R. Halir, “First monolithic InP-based 90 degrees-hybrid OEIC comprising balanced detectors for 100GE coherent frontends,” in International Conference on Indium Phosphide & Related Materials (IPRM) (2009), paper TuB2.2, pp. 167–170.

]. The passive circuitries (i.e. interconnection waveguides, tapers, crossings and MMI structures) are based on InP Rib waveguides with core thickness and etch depth around 1 μm and 0.4 μm respectively.

The 90° downconverter is based on a well-known architecture (see Fig. 1) already reported in [9

9. A. Matiss, S. Bottacchi, J. K. Fischer, R. Ludwig, C. C. Leonhardt, C. Schmidt-Langhorst, and C. Schubert, “Performance of an integrated coherent receiver module for up to 160G DP-QPSK transmission systems,” J. Lightwave Technol. 29(7), 1026–1032 (2011). [CrossRef]

]: a 2x4 MMI is monolithically integrated with four waveguide p-i-n photodiodes. Subtraction of these photocurrents in linear differential TIAs yield the two analog baseband signals iI(t) and iQ(t) which are then digitized from two ADC and further corrected by well-known algorithms to get the received symbols. On the other hand, the 120° downconverter is based on a 2x3 MMI coupler monolithically integrated with three waveguide p-i-n photodiodes followed by TIAs (see Fig. 4). These three signals are then digitized from three ADC and finally baseband symbols are obtained from them after a calibration procedure.

MMIs have been carefully designed to minimize amplitude and phase imbalances for the in-plane (TE) polarization wave (notice we are assuming polarization control or a polarization diversity scenario) at its central wavelength. Although the explanation of the design process is out of the scope of this paper, it must be pointed out that it basically consists in the calculation of the geometry of the multimode region (i.e. MMI width and length) and the optimal positions and widths of the access waveguides. A detailed description of MMIs design process can be found in [20

20. R. Halir, A. Ortega-Moñux, I. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, D.-X. Xu, B. Lamontagne, and S. Janz, “Integrated optical six-port reflectometer in silicon-on-insulator,” J. Lightwave Technol. 27(23), 5405–5409 (2009). [CrossRef]

,21

21. R. Halir, I. Molina-Fernandez, A. Ortega-Monux, J. G. Wanguemert-Perez, D.-X. Xu, P. Cheben, and S. Janz, “A design procedure for high-performance, rib-waveguide-based multimode interference couplers in silicon-on-insulator,” J. Lightwave Technol. 26(16), 2928–2936 (2008). [CrossRef]

].

Figure 5
Fig. 5 Amplitude (left) and phase imbalance (right) of 2x4 MMI 90° hybrid (in plane mode) obtained from electromagnetic modeling.
shows the simulated wavelength response (amplitude and phase imbalance) of the designed 2x4 MMI (90° hybrid). We have used FIMMWAVE, a full-vectorial electromagnetic simulator package, to obtain these results. A very low imbalance is observed within a small bandwidth around the central wavelength, thus confirming that the MMI has been properly designed since it completely covers the C-band (1530 to 1565 nm). Nevertheless, the device performance rapidly deteriorates for wavelengths far away from this central region. Imbalance in the lower limit of the S-band (1460 nm) and in the upper limit of the L-band (1625 nm) is too high, so the device cannot be used to cover these bands without an adequate calibration. The same conclusions can be obtained from Fig. 6
Fig. 6 Amplitude (left) and phase imbalance (right) of 2x3 MMI 120° coupler (in plane mode) obtained from electromagnetic modeling.
, where the simulated wavelength behavior of the 2x3 MMI (120° coupler) has been shown. It must be noticed that, although the 2x3 MMI exhibits a better bandwidth performance than the 2x4 MMI, this fact can be predicted using basic MMI theory [22

22. P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12(6), 1004–1009 (1994). [CrossRef]

] and therefore it is not due to a better design.

4.2 Simulation scenario

In this section, main details of the setup adopted in the numerical simulation are shown. For the transmitter, we will assume here a conventional IQ-modulator for M-QAM, consisting on an electrical driver and an optical modulator [23

23. M. Seimetz, “Multi-format transmitters for coherent optical M-PSK and M-QAM transmission,” Proceedings of 2005 7th International Conference Transparent Optical Networks (2005), pp. 225–229, paper Th.B1.5

]. Two orthogonal carriers from a LO are amplitude modulated by two Mach-Zehnder Modulators (MZM), which are biased and driven by electrical data signals, and combined to form optical signal. The pulse-shape modulator corresponds to the impulse response of a 5th order Bessel low-pass filter with electrical bandwidth 0.7·Rs.

The optical channel will be modeled as an AWGN channel degraded by ASE noise. The ASE noise level at the receiver input will be fixed from Eq. (11) to assure the minimum SNR needed for a BER = 10−4 (typical threshold when forward error correction is employed) in a noiseless ideal coherent receiver.

4.3. Performance of the 90° coherent receiver in the C and L bands

It is a well-known fact that hardware unbalances, existing in any realistic 90° downconverter, will cause a non-negligible distortion in received constellation (see Eq. (6) and Fig. 2), so these detrimental effects must be compensated for by a proper DSP correction algorithm. The standard procedure to correct phase and amplitude imbalances in a 90° hybrid coherent receiver is the GSOP method [11

11. I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008). [CrossRef]

] which is based in a Gram-Schmidt orthogonalization. This algorithm has been implemented as an ideal DSP block at the receiver in Fig. 1.

Figure 7
Fig. 7 BER performance versus Ps in 90° downconverter for different PLO when noise sources and hardware impairments are considered for 64-QAM and 256-QAM at central operation wavelength (top) and at the upper limit of the L-band (bottom).
shows 64-QAM and 256-QAM BER performance for the simulated 90° receiver, after GSOP compensation, for different LO and received signal powers and for two different wavelengths, λ = 1.54 μm (top) and λ = 1.62 μm (bottom), corresponding to central and upper L-band limit wavelengths, respectively. Simulations at the central wavelength, where minimum hardware unbalances exist, show a shot noise limited performance at low signal power levels (similar to the one already reported in Fig. 3 for a perfectly balanced hardware) but also show that receiver performance is degraded at high signal power levels. This effect, theoretically explained in [12

12. A. Moscoso-Martir, I. Molina-Fernandez, and A. Ortega-Monux, “Signal constellation distortion and ber degradation due to hardware impairments in six-port receivers with analog I/Q generation,” Prog. Electromagn. Res. 121, 225–247 (2011). [CrossRef]

], is due to the non-linear rectified wave distortion term which introduces a non-linear error proportional to the Ps/PLO ratio which, apparently, is not being removed by the GSOP algorithm. This effect worsens for denser constellations as 256-QAM, where it is observed that, for a typical LO power of 10 dBm, the signal dynamic range (measured at the 1 dB equivalent SNR penalty) is reduced to one decade. As also seen at the bottom of Fig. 7, this behavior worsens for the upper limit of the L-band due to the increase in the downconverter unbalances. In this case, it is observed that no reception is possible for 256-QAM without significant performance degradation.

To gain insight into the causes of receiver degradation at high received signal levels, the 64-QAM constellation, after GSOP compensation, is plotted in Fig. 8
Fig. 8 Corrected 64-QAM following GSOP in 90° downconverter at the upper limit of the L-band for 10 dBm LO power when Ps/PLO ratio is (a) −20 dB (left) and (b) −5 dB (right).
for two different Ps/PLO ratios: −20 dB and −5 dB. This situation corresponds to the wavelength at the limit of the L-band where hardware unbalances are more appreciable. In the Fig. 8(a), corresponding to a Ps/PLO ratio of −20 dB, the rectified wave distortion term (γ) of Eq. (6) can be considered negligible. Thus constellation distortion due to hardware unbalances is almost linear (as was illustrated in Fig. 2a) and GSOP algorithm can remove all impairments. On the other hand, in Fig. 8(b), corresponding to a Ps/PLO ratio of −5 dB, the rectified wave distortion term (γ) of Eq. (6) has an important effect which creates a nonlinear distortion of received constellation, as was shown in Fig. 2(b). Being a linear orthogonalization algorithm, the GSOP is unable to remove this effect, yielding the distorted results of Fig. 8(b) which are responsible of the BER increase for high power levels.

4.4 Performance of the 120° coherent receiver in the C and L bands

Following the calibration procedure summarized in Section 3.1 by Eq. (15) for 120° coherent receiver, in-phase and quadrature signal components can be easily obtained from the three diode photocurrents by a simple linear transformation which compensates all hardware non-idealities due to the 120° coupler and photodiode responsivity unbalances. Attending to the computational complexity, signal components for the 120° downconverter are calculated from a pair of linear equations depending on the three output photocurrents, instead of depending on the two differential output photocurrents for the 90° downconverter according to GSOP procedure. Therefore only two additional multiplications and additions are required per symbol, so a superior performance under hardware impairments is obtained with a slightly higher computational complexity.

Finally, comparison of dynamic performance of both types of receiver is plotted in Fig. 11
Fig. 11 Transmitted/demodulated 16-QAM constellation (down) and amplitude eye diagram (up) for 10 dBm LO power when incoming OSNR is fixed for BER = 10−12 in a noiseless ideal coherent receiver at the upper limit of the L-band.
, where transmitted and demodulated I-Q plane and eye diagrams corresponding to a 16-QAM constellation are plotted for different Ps/PLO ratios at the limit of the L-band for a LO power of 10 dBm. These results show again the better performance of 120° receiver.

4.5 Ultra broad-band operation

As the proposed 120° downconverter exhibits a superior performance at both the central operation wavelength and the upper limit of the L-band, it is reasonable to ask ourselves whether the 120° receiver can be made to operate over an even greater wavelength span where much higher imbalances are observed (see Fig. 6). In doing so, we will not only show the possibilities of providing complete S-C-L band coverage with a simple and affordable receiver in monolithic technology, but we will also provide some indirect evidence it can be achieved with relaxed hardware constraints. This can have a dramatic influence on receiver sensibilities to fabrication tolerances and thus can greatly improve fabrication yield of practical integrated receivers.

Figure 12
Fig. 12 BER performance versus wavelength for the 90° (top) and 120° (bottom) downconverters for different signal to LO power ratios (LO power fixed to 10 dBm except in the insets where signal and LO power are equal to 0 dBm) under 64-QAM and 256-QAM modulation.
shows the estimated BER for the 90° and 120° receivers for the complete wavelength span of 1.4-1.7μm for different Ps/PLO ratios and two different modulation scenarios: 64-QAM and 256-QAM. Again the performance of 90° receiver followed by GSOP algorithm is compared with 120° receiver using the simple calibration linear algorithm described in Eq. (15). It is clearly shown that 90° receiver performance is only reasonable good for the center wavelength (where 90° hybrid has been designed and thus minimum hardware unbalances occur) and under low Ps/PLO ratios which, as already shown, minimize the nonlinear signal constellation distortion which GSOP algorithm is unable to compensate for. Thus great SNR penalty is introduced by the 90° receiver far away from the designed wavelength or if the low Ps/PLO ratios assumption does not hold. On the contrary, due to its superior calibration procedure, the 120° receiver is able to almost completely compensate the detrimental effects due to hardware unbalances occurring outside the designed wavelength range, and this compensation can be done for a wide variety of Ps/PLO ratios (the inset of Figs. 12.c) and d) show that wideband operation can be achieved even for a low signal and LO power of 0 dBm).

5. Conclusion

Appendix A: Noise-induced degradation

Here, noise-induced degradation is evaluated in the 90° y 120° downconverter. The following noise sources will be considered and modeled as AWGN.

  • Optical ASE noise, see Eq. (3), that will manifest after mixing with signal and LO at the output ports through ASE-LO and ASE-signal beat noise terms.
  • LO and signal electrical shot noise. If a single photodiode received the LO and signal, it would generate an electrical shot noise proportional to its mean photocurrent <i>. So, the noise power contribution in an electrical receiver bandwidth Be, considering q the electron’s charge and R the responsitivity of the photodiode, would correspond to
    ishot2=2qBei=2qRBe(Ps+PLO)
    (A1)

    Under an ideal realization, the received LO and signal will be equally split between the k = 4 output ports of the 90° hybrid and k = 3 output ports of the 120° coupler. In the following ishot i will represent the statistically independent shot noise in each photodiode, proportional to its mean photocurrent <ii>.
    ishoti2=2qBeii=ishot2k;i=3,...,k+2
    (A2)

  • Relative intensity noise (RIN) from LO and signal. The statistically dependent electrical noise power contribution at each of the k photodiodes will be proportional to the square of their mean photocurrent <ii> through the RIN parameter (typically described in dB/Hz) as
    iRIN_i2=RINBeii2;i=3,...,k+2
    (A3)
  • Trans impedance amplifier (TIA) noise. The amplification of in-phase and quadrature photocurrents in the 90° hybrid coherent receiver (after balanced detection), or output photocurrents in the 120° coherent receiver, will generate a current noise contribution, iTIAI /iTIAQ and iTIAi respectively, of power
    iTIA2=iTIAI2=iTIAQ2=iTIAi2=αTIA2Be
    (A4)

    where αTIA corresponds to the noise current density, described in A/√Hz.

  • Thermal noise or dark current can be neglected.

A.1. Noise-induced degradation in 90° hybrid coherent receiver

From Eq. (6), considering ideal and perfect balanced hardware realization, we get the resulting photocurrents iI and iQ,
iI=RPLORe(e˜s+nASE)+ishot3ishot4+iTIAI=RPLORe(e˜s)+inoiseIiQ=RPLOIm(e˜s+nASE)+ishot5ishot6+iTIAQ=RPLOIm(e˜s)+inoiseQ
(A5)
where the noise sources contribution are included on the last terms of Eqs. (A5) from

inoiseI=iASEILO+ishot3ishot4+iTIAIinoiseQ=iASEQLO+ishot5ishot6+iTIAQ
(A6)

Note that common mode noise, as ASE-signal beat noise or RIN from LO and signal, will be cancelled under ideal hardware. However ASE-LO beat noise, iASEI-LO and iASEQ-LO, appreciable from the noise contribution in the first term of Eqs. (A6), will remain. The power noise contribution of this latter will be

iASELO2=iASEILO2=iASEQLO2=R2PLOnASE22=R2PLONBASEe2
(A7)

The total power noise contribution to in-phase and quadrature signal components can be now easily expressed from Eqs. (A6), neglecting TIA noise, as

inoiseI2=inoiseQ2=iASELO2+2ishoti2+iTIA2
(A8)

Finally, substituting Eq. (A2) and Eq. (A7) into Eq. (A8) yields (under low TIA noise assumption),

inoiseI2=inoiseQ2=iASELO2+12ishot2=R2PLONBASEe2+qRBe(Ps+PLO)
(A9)

A.2. Noise-induced degradation in 120° coherent receiver

From Eq. (14), the output photocurrents including optical and electrical noise sources can be expressed as

{PLO+Ps+2PLORe((e˜s+nASE)ej120º)+2Re(e˜s*ns)}+ishot53+iRIN53+iTIA53i4=R3{PLO+Ps+2PLORe(e˜s+nASE)+2Re(e˜s*ns)}+ishot4+iRIN4+iTIA4
(A10)

ASE-LO and ASE-signal beat noise contributions are now appreciable on the third and fourth term respectively of Eqs. (A10). In addition to that, on each of the three output photocurrents, there will be an identical RIN noise contribution attending to Eqs. (16) and (A3).

Under ideal hardware realization, iI and iQ can be obtained from the algebraic relation derived in Eq. (17).

iI=0.5i3+i40.5i5=RPLORe(e˜s)+inoiseIiQ=32(i3i5)=RPLOIm(e˜s)+inoiseQ
(A11)

Noise sources contribution are included on the last term of Eqs. (A11) from

inoiseI=iASEILO0.5(ishot3+ishot5+iTIA3+iTIA5)+ishot4+iTIA4inoiseQ=iASEQLO+32(ishot3ishot5+iTIA3iTIA5)
(A12)

As it happened in the ideal 90° hybrid coherent receiver, common mode noise as RIN from LO and signal or ASE-signal beat noise will be once again cancelled under ideal performance. From Eqs. (A2) and (A12) the total power noise contribution to in-phase and quadrature components then becomes (under low TIA noise assumption),
inoiseI2=inoiseQ2=iASELO2+32ishoti2=iASELO2+12ishot2
(A13)
where ASE-LO beat power noise contribution is expressed as in Eq. (A7). Note that in-phase and quadrature noise components derived here for the ideal 120° coherent receiver are the same as those obtained in Eq. (A9) for the ideal 90° hybrid coherent receiver.

Acknowledgments

The authors gratefully acknowledge the design support from Robert Halir and Sebastián Romero-García, and the fruitful discussion with Oriol Bertran-Pardo. This work has been partially funded under Andalusian Regional Ministry of Science Innovation and Business project P09-TIC-5268, Spanish Ministry of Science and Innovation project TEC2009-10152 and EU 7th Framework Programme project MIRTHE ICT-2009-5 no. 257980.

References and links

1.

Optical Internetworking Forum (OIF), “100G ultra long haul DWDM framework document,” document OIF-FD-100G-DWDM-01.0 (June 2009), http://www.oiforum.com/public/impagreements.html.

2.

Mirthe Project, “Monolithic InP-based dual polarization QPSK integrated receiver and transmitter for coherent 100–400Gb Ethernet,” http://www.ist-mirthe.eu/.

3.

M. Nakazawa, “Ultrafast and high-spectral-density optical communications systems,” "Ultrafast and High-spectral-density optical communications systems,” in CLEO:2011—Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThGG3.

4.

A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432 x 171-Gb/s) C- and extended L-band transmission over 240 km Using PDM-16-QAM modulation and digital coherent detection,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPB7.

5.

F. Boubal, E. Brandon, L. Buet, S. Chernikov, V. Havard, C. Heerdt, A. Hugbart, W. Idler, L. Labrunie, P. Le Roux, S. A. E. Lewis, A. Pham, L. Piriou, R. Uhel, and J. P. Blondel, “4.16 Tbit/s (104x40 Gbit/s) unrepeatered transmission over 135 km in S + C + L bands with 104 nm total bandwidth,” in 27th European Conference on Optical Communication, 2001. ECOC '01 (2001), vol. 1, pp. 58–59

6.

A. W. Davis, M. Pettitt, J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightwave Technol. 5(4), 561–572 (1987). [CrossRef]

7.

Y. Painchaud, M. Poulin, M. Morin, and M. Têtu, “Performance of balanced detection in a coherent receiver,” Opt. Express 17(5), 3659–3672 (2009). [CrossRef] [PubMed]

8.

Optoplex Corportation, “2x4 QPSK mixer-polarization diversified optical hybrid,” datasheet, www.optoplex.com.

9.

A. Matiss, S. Bottacchi, J. K. Fischer, R. Ludwig, C. C. Leonhardt, C. Schmidt-Langhorst, and C. Schubert, “Performance of an integrated coherent receiver module for up to 160G DP-QPSK transmission systems,” J. Lightwave Technol. 29(7), 1026–1032 (2011). [CrossRef]

10.

R. Kunkel, H.-G. Bach, D. Hoffmann, C. Weinert, I. Molina-Fernandez, and R. Halir, “First monolithic InP-based 90 degrees-hybrid OEIC comprising balanced detectors for 100GE coherent frontends,” in International Conference on Indium Phosphide & Related Materials (IPRM) (2009), paper TuB2.2, pp. 167–170.

11.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008). [CrossRef]

12.

A. Moscoso-Martir, I. Molina-Fernandez, and A. Ortega-Monux, “Signal constellation distortion and ber degradation due to hardware impairments in six-port receivers with analog I/Q generation,” Prog. Electromagn. Res. 121, 225–247 (2011). [CrossRef]

13.

J. Li, R. G. Bosisio, and K. Wu, “Computer and measurement simulation of a new digital receiver operating directly at millimeter-wave frequencies,” IEEE Trans. Microw. Theory Tech. 43(12), 2766–2772 (1995). [CrossRef]

14.

P. Pérez-Lara, I. Molina-Fernandez, J. G. Wanguemert-Perez, and A. Rueda-Perez, “Broadband five-port direct receiver based on low-pass and high-pass phase shifters,” IEEE Trans. Microw. Theory Tech. 58(4), 849–853 (2010). [CrossRef]

15.

T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, and R. Noé, “Coherent optical communication: towards realtime systems at 40 Gbit/s and beyond,” Opt. Express 16(2), 866–872 (2008). [CrossRef] [PubMed]

16.

A. B. Carlson, Communication Systems (McGraw-Hill, 1986).

17.

P. Perez-Lara, I. Molina-Fernandez, J. G. Wangüemert-Perez, and R. G. Bosisio, “Effects of hardware imperfection on six-port direct digital receivers calibrated with three and four signal standards,” IEE Proc. Microw. Antennas Propag. 153(2), 171–176 (2006). [CrossRef]

18.

F. M. Ghannouchi and R. G. Bosisio, “An alternative explicit six-port matrix calibration formalism using five standards,” IEEE Trans. Microw. Theory Tech. 36(3), 494–498 (1988). [CrossRef]

19.

R. Halir, G. Roelkens, A. Ortega-Moñux, and J. G. Wangüemert-Pérez, “High-performance 90° hybrid based on a silicon-on-insulator multimode interference coupler,” Opt. Lett. 36(2), 178–180 (2011). [CrossRef] [PubMed]

20.

R. Halir, A. Ortega-Moñux, I. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, D.-X. Xu, B. Lamontagne, and S. Janz, “Integrated optical six-port reflectometer in silicon-on-insulator,” J. Lightwave Technol. 27(23), 5405–5409 (2009). [CrossRef]

21.

R. Halir, I. Molina-Fernandez, A. Ortega-Monux, J. G. Wanguemert-Perez, D.-X. Xu, P. Cheben, and S. Janz, “A design procedure for high-performance, rib-waveguide-based multimode interference couplers in silicon-on-insulator,” J. Lightwave Technol. 26(16), 2928–2936 (2008). [CrossRef]

22.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12(6), 1004–1009 (1994). [CrossRef]

23.

M. Seimetz, “Multi-format transmitters for coherent optical M-PSK and M-QAM transmission,” Proceedings of 2005 7th International Conference Transparent Optical Networks (2005), pp. 225–229, paper Th.B1.5

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications
(250.3140) Optoelectronics : Integrated optoelectronic circuits
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: December 2, 2011
Revised Manuscript: January 13, 2012
Manuscript Accepted: January 16, 2012
Published: February 24, 2012

Citation
P. J. Reyes-Iglesias, I. Molina-Fernández, A. Moscoso-Mártir, and A. Ortega-Moñux, "High-performance monolithically integrated 120° downconverter with relaxed hardware constraints," Opt. Express 20, 5725-5741 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5725


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References

  1. Optical Internetworking Forum (OIF), “100G ultra long haul DWDM framework document,” document OIF-FD-100G-DWDM-01.0 (June 2009), http://www.oiforum.com/public/impagreements.html .
  2. Mirthe Project, “Monolithic InP-based dual polarization QPSK integrated receiver and transmitter for coherent 100–400Gb Ethernet,” http://www.ist-mirthe.eu/ .
  3. M. Nakazawa, “Ultrafast and high-spectral-density optical communications systems,” "Ultrafast and High-spectral-density optical communications systems,” in CLEO:2011—Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThGG3.
  4. A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432 x 171-Gb/s) C- and extended L-band transmission over 240 km Using PDM-16-QAM modulation and digital coherent detection,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPB7.
  5. F. Boubal, E. Brandon, L. Buet, S. Chernikov, V. Havard, C. Heerdt, A. Hugbart, W. Idler, L. Labrunie, P. Le Roux, S. A. E. Lewis, A. Pham, L. Piriou, R. Uhel, and J. P. Blondel, “4.16 Tbit/s (104x40 Gbit/s) unrepeatered transmission over 135 km in S + C + L bands with 104 nm total bandwidth,” in 27th European Conference on Optical Communication, 2001. ECOC '01 (2001), vol. 1, pp. 58–59
  6. A. W. Davis, M. Pettitt, J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightwave Technol.5(4), 561–572 (1987). [CrossRef]
  7. Y. Painchaud, M. Poulin, M. Morin, and M. Têtu, “Performance of balanced detection in a coherent receiver,” Opt. Express17(5), 3659–3672 (2009). [CrossRef] [PubMed]
  8. Optoplex Corportation, “2x4 QPSK mixer-polarization diversified optical hybrid,” datasheet, www.optoplex.com .
  9. A. Matiss, S. Bottacchi, J. K. Fischer, R. Ludwig, C. C. Leonhardt, C. Schmidt-Langhorst, and C. Schubert, “Performance of an integrated coherent receiver module for up to 160G DP-QPSK transmission systems,” J. Lightwave Technol.29(7), 1026–1032 (2011). [CrossRef]
  10. R. Kunkel, H.-G. Bach, D. Hoffmann, C. Weinert, I. Molina-Fernandez, and R. Halir, “First monolithic InP-based 90 degrees-hybrid OEIC comprising balanced detectors for 100GE coherent frontends,” in International Conference on Indium Phosphide & Related Materials (IPRM) (2009), paper TuB2.2, pp. 167–170.
  11. I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett.20(20), 1733–1735 (2008). [CrossRef]
  12. A. Moscoso-Martir, I. Molina-Fernandez, and A. Ortega-Monux, “Signal constellation distortion and ber degradation due to hardware impairments in six-port receivers with analog I/Q generation,” Prog. Electromagn. Res.121, 225–247 (2011). [CrossRef]
  13. J. Li, R. G. Bosisio, and K. Wu, “Computer and measurement simulation of a new digital receiver operating directly at millimeter-wave frequencies,” IEEE Trans. Microw. Theory Tech.43(12), 2766–2772 (1995). [CrossRef]
  14. P. Pérez-Lara, I. Molina-Fernandez, J. G. Wanguemert-Perez, and A. Rueda-Perez, “Broadband five-port direct receiver based on low-pass and high-pass phase shifters,” IEEE Trans. Microw. Theory Tech.58(4), 849–853 (2010). [CrossRef]
  15. T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, and R. Noé, “Coherent optical communication: towards realtime systems at 40 Gbit/s and beyond,” Opt. Express16(2), 866–872 (2008). [CrossRef] [PubMed]
  16. A. B. Carlson, Communication Systems (McGraw-Hill, 1986).
  17. P. Perez-Lara, I. Molina-Fernandez, J. G. Wangüemert-Perez, and R. G. Bosisio, “Effects of hardware imperfection on six-port direct digital receivers calibrated with three and four signal standards,” IEE Proc. Microw. Antennas Propag.153(2), 171–176 (2006). [CrossRef]
  18. F. M. Ghannouchi and R. G. Bosisio, “An alternative explicit six-port matrix calibration formalism using five standards,” IEEE Trans. Microw. Theory Tech.36(3), 494–498 (1988). [CrossRef]
  19. R. Halir, G. Roelkens, A. Ortega-Moñux, and J. G. Wangüemert-Pérez, “High-performance 90° hybrid based on a silicon-on-insulator multimode interference coupler,” Opt. Lett.36(2), 178–180 (2011). [CrossRef] [PubMed]
  20. R. Halir, A. Ortega-Moñux, I. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, D.-X. Xu, B. Lamontagne, and S. Janz, “Integrated optical six-port reflectometer in silicon-on-insulator,” J. Lightwave Technol.27(23), 5405–5409 (2009). [CrossRef]
  21. R. Halir, I. Molina-Fernandez, A. Ortega-Monux, J. G. Wanguemert-Perez, D.-X. Xu, P. Cheben, and S. Janz, “A design procedure for high-performance, rib-waveguide-based multimode interference couplers in silicon-on-insulator,” J. Lightwave Technol.26(16), 2928–2936 (2008). [CrossRef]
  22. P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol.12(6), 1004–1009 (1994). [CrossRef]
  23. M. Seimetz, “Multi-format transmitters for coherent optical M-PSK and M-QAM transmission,” Proceedings of 2005 7th International Conference Transparent Optical Networks (2005), pp. 225–229, paper Th.B1.5

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