The quality of balanced detection in a coherent receiver is analyzed theoretically and experimentally. The impact of the characteristics of the optics on the balanced detection is presented. A parameter that characterizes the performance of the balanced detection suitable for the whole optical front-end is proposed.
©2009 Optical Society of America
In response to the ever increasing demand in transmission capacity, future telecommunication systems that will operate at 100 Gb/s are already under development. Field trials have been realized over existing deployed systems using a conventional direct detection approach [1–2]. A most important challenge at such high speed transmission is the spectral efficiency required to increase the transmission capacity over existing transmission links. New approaches based on coherent detection appear as the most promising [3–4]. They enable polarization multiplexing  and the mitigation of transmission impairments through digital signal processing in the electrical domain [6–7].
In coherent detection, the optical signal is demodulated by mixing with a reference, the ensuing beats being detected by photodiodes . The resulting electrical signals are further digitized and processed in the electrical domain. The mixing and detection are achieved using an assembly of optical and optoelectronics components such as shown in Fig. 1. This assembly is referred to as the optical front-end (OFE) of the coherent receiver.
The purpose of the optical front end illustrated in Fig. 1 is to provide four electrical signals allowing the determination of the amplitude, phase and polarization of the optical signal Es. It separates the incoming signal Es and a reference field produced by a local oscillator ELO into x and y polarization components that are properly aligned for maximum interference and fed into two 90° optical hybrid mixers. These mixers provide in-phase and quadrature signals allowing unambiguous determination of the amplitude and phase of each polarization component Esx and Esy. The beats between the signal polarization components and the reference field are detected by photodiodes. Resulting photocurrents are amplified and converted to output voltages (Ix, Qx, Iy, Qy) using linear trans-impedance amplifiers (TIA). These voltages can then be digitized and processed to mitigate transmission impairments and decode the incoming signal.
The polarization management function is illustrated schematically by two polarization beam splitters in the figure. Actual implementation may differ. For example, the local oscillator is in general linearly polarized and can be separated into linearly polarized components of equal amplitude by a 3dB splitter. Further components may be required to ensure proper alignment of the signal and reference fields. Moreover, the polarization management and mixing functions can be intertwined to some extent. For example, the reference field can be transformed into a circularly polarized field in order to ensure the quadrature condition . The characterization method presented below is impervious to such details.
In principle, two beat signals in quadrature are sufficient to unambiguously determine the amplitude and phase of an optical field. Two optical outputs from each hybrid with beats in quadrature (e.g Esx + ELO and Esx + jELO) could be detected with single photodiodes to determine the amplitude and phase of the signal. However, important noise terms are not eliminated as in the case of balanced detection, and careful adjustment of the signal and local oscillator powers is necessary to avoid severe system impairment [10–11]. The intensity resulting from the mixing of two optical fields is given by the sum of the individual field intensities and a beat signal carrying the useful phase information. Preferably, the detection process should reject the individual intensity contributions and retain only the useful beat intensities. This is realized with balanced detection as illustrated in Fig. 1 . Mixed optical intensities carrying the same individual intensities but beats that are out of phase by π are detected differentially by balanced photo-detectors. Individual intensities are thus subtracted, whereas the beat intensities are added, doubling the amplitude of the meaningful photocurrent. Balanced detection thus allows using all of the received signal power for detection, while rejecting photons that do not bear useful information. Compared to single-ended detection, the use of balanced detection provides higher optical power dynamic range and longer reaches.
This paper discusses the quality of this rejection in a coherent optical receiver although requirement for proper system performance is out of its scope. Section 2 first discusses the notion of common mode rejection ratio, a parameter that is used to characterize the quality of balanced photo-detectors. Balanced detection rejection is discussed in Section 3 in the context of coherent detection. A new parameter, termed single-port rejection ratio, is introduced to characterize rejection in this case. Section 4 identifies the characteristics of an optical hybrid that can degrade the single-port rejection ratio. Section 5 presents a measurement method of the single-port rejection ratio that requires only access to the input and output ports of the OFE. Experimental results are presented in Section 6. It is to be noted that possible inaccuracies in the quadrature provided by the 90° optical hybrid mixers do not impact on the performance of the balanced detection which is rather associated to individual channels I and Q.
2. Balanced detection and common mode rejection ratio
In balanced detection, two optical signals are detected using similar photodiodes. The resulting photocurrents are amplified differentially in order to produce an electrical signal proportional to their difference. The aim of this differential detection is to highlight the difference between similar optical signals by rejecting their common part. The ability of a pair of balanced photo-detectors to perform this rejection is quantified by the common mode rejection ratio (CMRR) . It corresponds to the ratio of the weak signal measured under equal illumination of both detectors and the strong signal measured when a single detector is illuminated. Figure 2 depicts the three illumination conditions required to measure the CMRR. Under dual-photodiode illumination with the same optical power, a weak photocurrent ∆I is measured while strong photocurrents I1 and -I2 are detected under single-photodiode illumination. The CMRR is defined here as the ratio of these values:
It qualifies the similarity of the photodiodes (responsivity, polarization dependence, frequency response) by quantifying the relative weakness of the output electric signal under equal illumination. The CMRR definition is simple and its measurement appears straightforward but does require some care. Nonlinearity can render the CMRR power dependent. Measurements should thus be carried out with the same power incident on each photodiode surface as illustrated in Fig. 2. Moreover, the frequency response of the photodiodes may differ, rendering the CMRR dependent on the modulation frequency of the incident power. Typically, the CMRR of balanced photodetectors is specified as a function of frequency.
3. Single port rejection ratio
Balanced detection is of particular interest in coherent detection where highlighting the beating between the received optical signal and a reference from a local oscillator is desired. Figure 3 illustrates one of the simplest mixing element, a 3 dB coupler in which the optical signal Es(t) is mixed with the local oscillator field ELO(t) yielding two output fields that are detected by a pair of balanced photodiodes.
The input optical fields can be written in terms of their powers, frequencies and phases:
Assuming a coupler with a perfect 50/50 power splitting and detectors with an identical responsivity R, the output photocurrents are given by:
Each photocurrent comprises three contributions. Two are proportional to the individual power of each interfering field, while the third one is proportional to an interference term dependent on the relative phase between the fields. When the fields oscillate at different optical frequencies, this interference term oscillates as well at the beat frequency ωs-ωLO. The photodiodes are connected together to provide the differential current:
Ideal balanced detection thus doubles the photocurrent associated to the interference beats while rejecting those associated to the individual optical field powers.
This rejection of the interfering field individual powers is a main benefit of balanced detection in coherent receivers and needs to be characterized. As aforementioned, the CMRR compares the weak signal under dual-photodiode illumination of equal power to the strong signals under single-photodiode illumination, as expressed in Eq. (1). In the context of coherent detection, it appears more appropriate to define a parameter that quantifies the weakness of the output electrical signal under illumination through a single optical input port as illustrated in Fig. 4. The question here is weak relative to what? In the configuration of Fig. 4, photocurrents I1 and I2 of individual photodiodes cannot be measured without blocking the light in one output arm of the coupler. This will not be possible, in general, when characterizing a coherent receiver OFE in which the photo-detectors and the optical mixer are integrated. It is more convenient to compare the weak signal measured under the configuration shown in Fig. 4 to the strong signal measured under the configuration shown in Fig. 5. In this new configuration, two optical fields having the same amplitude and state of polarization are launched into the coupler. Depending on their relative phase, a strong output signal can be generated. Assuming a perfect 3 dB coupler, the relative phase φ can be adjusted such that all the light reaches a single photodiode, thus replicating the conditions of the single-photodiode illumination of Fig. 2. Furthermore, the optical field amplitude in Fig. 5 is half that in Fig. 4 in order to illuminate the photodiodes with the same optical power. For an arbitrary coupler, depending on the phase φ of Fig. 5, the output signal ∆Idual is somewhere between two extreme values of strong amplitude:
where ∆I1 (∆I2) is the signal measured when φ is such that the power incident on photodiode 1 (2) is maximized.
Thus, referring to Fig. 4, Fig. 5 and Eq. (7), the single-port rejection ratio (SPRR) is defined as the ratio of the weak photocurrent ∆I 0 under single-port illumination to the strong measurable photocurrents ∆I1 and ∆I2 under dual-port illumination:
This definition looks quite similar to the CMRR but there are important distinctions. The SPRR is degraded not only by unequal responsivities of the photodiodes, but also by an uneven split of the input power by the coupler. Furthermore, the SPRR measured with one input port is not necessarily equal to that measured with the other input port. For example, it may happen that unequal photodiode responsivities compensate for an uneven split by the coupler such that the differential current ∆I 0 measured from one input port vanishes. Both defects will however add-up when measuring ∆I 0 from the other input port. Finally, the SPRR is better adapted to coherent detection in that, referring to Eqs. (4) to (6), it compares the weak photocurrent associated to an individual input optical power, that needs to be rejected, to the strong photocurrent proportional to the interference term that needs to be highlighted by the balanced detection. Notwithstanding these differences, the SPRR becomes equivalent to the CMRR as the characteristics of the optics approach ideal ones such that dual photocurrents ∆I1 and ∆I2 approach photocurrents I1 and I2 in individual photodiodes.
Although the SPRR is defined in reference to Fig. 4 and 5, it also applies to the complete OFE shown in Fig. 1. In this case, eight SPRR values quantify the weakness of the output signals (Ix, Qx, Iy, Qy) under illumination from a single input port (S or LO) with respect to their amplitude under illumination from both input ports. With respect to the single-port condition, the input powers used in the dual-port condition should be chosen properly, aiming at operating the photodiodes under the same illumination condition, as discussed in section 5.
4. Impact of the optics on the performance of the balanced detection
Optimal balanced detection is achieved when the optical signal launched into each input is equally split among the different outputs. Synchronization of the optical signals at the photo-detectors is also required. This section discusses the influence of the characteristics of the 90° optical hybrid mixer on the performance of balanced detection assuming otherwise ideal component. This impact is quantified using the SPRR parameter defined in the previous section.
Within the OFE shown in Fig. 1, splitting of the input power is performed by the 90° optical hybrid mixers. This part of the OFE is replicated in Fig. 6 where E1(t) to E4(t) represent the optical fields at the photodiodes for the input conditions shown. These output fields can be written as:
where asi(aLi) are coupling coefficients between input port S(LO) and the four output ports, whereas τsi(τLi) are the time delays from input port S(LO) to the four outputs.
The time delay τ shown in Fig. 6 may serve at compensating for a possible differential delay between the two inputs. It is assumed that it can be adjusted such that:
for all paths simultaneously.
Assuming photodiodes of equal responsitivity R, the differential photocurrent is given by:
The phase φ can be chosen to maximize or minimize the photocurrent. Using the nomenclature of section 3, ∆I1(t) and ∆I2(t) are defined as the value of ∆I(t) when phase φ is adjusted such that cosθ= +1 or -1 respectively:
Assuming that coefficients asi and aLi are of similar amplitudes, the following approximations can be made:
Equations (18) and (19) provide expressions for the two strong photocurrents discussed in section 3 and depicted in Fig. 5, thus allowing calculation of the denominator of the SPRR as defined in Eq. (8). To find the numerator of the SPRR, there must be no input signal at port LO and twice the field amplitude at port S to meet the conditions of Figs. 4 and 5. Mathematically, this can be represented by Eq. (14) in which field Es is doubled and coefficients aLi are put to 0. One then obtains ∆I 0(t) defined as the value of ∆I(t) under this single-port condition:
Using the last three expressions, the SPRR can be calculated according to definition (8). As aforementioned, the CMRR of balanced photodiodes is usually specified as a function of frequency, since their frequency responses may differ. In the present case, even though equal photodiode responsivities are assumed, the SPRR calculated from expressions (18)–(20) can still present a frequency dependence. This is so because of a possible skew between the propagation times from an input port to each photodiode of a pair of balanced detectors. Rejection of a modulated input power can be degraded, especially if this skew becomes comparable to the characteristic period of the modulation. Thus, the SPRR definition in Eq. (8) is transformed into:
where it now characterizes the rejection of a sinusoidal power modulation at frequency f. Using the amplitude of the Fourier transform of Eqs. (18) to (20) as the frequency-dependent photocurrents, one obtains:
In Eq. (21), only the amplitude of the complex expressions resulting from the Fourier transforms are taken, which corresponds to considering only the amplitude of the photocurrents and not their phases. The notation in Eq. (22) is also a reminder that such SPRR parameter is required to characterize the rejection of each input power by each pair of balanced detectors. Four parameters are thus required in the case of the hybrid shown in Fig. 6, whereas eight parameters are needed in the case of an OFE with polarization diversity.
Parameters δsI and δLI represent the imbalance in the optical power distribution among both detectors of channel I for a signal coming from input ports S and LO respectively. Ideally, an even split is desired corresponding to δsI = 0. An imbalance of 2% corresponds to a situation where photodiodes 1 and 2 receive the optical power in proportion of 51% and 49% respectively. The delay ∆τ represents the skew between the two output paths and should ideally be zero.
In Fig. 7, the SPRR is shown on a log scale as a function of frequency, as calculated with Eq. (22) for different combinations of skew ∆τ and imbalance δsI. The SPRR is found to depend very weakly on δLI and ηh, which have been set to 0 and 1 respectively in the calculations shown in Fig. 7. At low frequency, only the imbalance impacts on the SPRR, whereas the skew is responsible for the frequency dependence of the SPRR. As seen in Fig. 7, the 90° optical hybrid mixer has a strong impact on the level of rejection achieved with the balanced detection.
5. Measurement of the SPRR
The SPRR of the complete OFE is measured using the configurations shown in Fig. 8, in which the principles conveyed by Figs. 4 and 5 are applied. The application of the principle shown in Fig. 5 corresponds to forming an interferometer as shown in Fig. 8(a). The following procedure assumes that the power launched at port LO is equally split among the two polarization stages.
A first measurement using the setup illustrated in Fig. 8(a) serves at determining the denominator of the SPRR. The intensity modulated signal is split between two arms and fed to both input ports of the OFE. The optical phase in arm LO is slowly modulated with a phase modulator such as producing an output electrical signal from the OFE with varying amplitude. A polarization controller in arm S is adjusted to maximize this beat output signal. In this condition, one can assume that most of the power at input port S is directed to the polarization stage under test. One also assumes that the input power at port LO is evenly split among the two polarization stages. For this reason, the variable optical attenuator (VOA) in arm LO is adjusted such that the power launched in port LO is twice that launched at port S. Using these input powers, interference of maximum contrast occurs within the interferometer resulting in maximum unequal illumination of the photodiodes (i.e. virtually all light directed to a single photodiode).
Finally, delay lines (DL) are introduced in one arm or both to ensure signal synchronization at the mixing region of the 90° optical hybrid mixer. This synchronization is optimized when the differential delay between both arms of the interferometer is minimized. It can be adjusted by ensuring that the output electrical signal of maximum amplitude over the phase modulator cycle is the largest possible. Alternatively, the differential delay can be measured by scanning the wavelength of the optical signal and evaluating the free spectral range (FSR) of the interferometer. The differential delay is equal to 1/FSR. It is found that this setup skew adjustment with delay lines must be done within about 5 ps in order to determine the value of the SPRR denominator with an accuracy of 0.2 dB. This requirement can be understood as follows. Suppose one has an ideal 90° optical hybrid mixer (τsi = 0, τLi = 0 and all coefficient asi and aLi equal to a) but a non adjusted delay τ between the inputs.
Then, instead of Eq. (14), one has:
Thus, when the phase modulator is adjusted for maximizing the output signal, one measures:
For an input signal having its intensity modulated at a frequency f, one has:
where P 0 is the averaged optical power and ∆P is the amplitude of the modulation. With the signal given by Eq. (30), it is found that the maximum output signal provided by Eq. (29) can be approximated by:
This means that the measured signal at frequency f is decreased by a factor cos(π f τ) with respect to its value with perfect synchronization (τ = 0), hence an acceptable delay τ = 5 ps for an underestimation of the maximum output signal amplitude by 0.2 dB at f = 20 GHz.
A second measurement using the setup shown in Fig. 8(b) serves at determining the numerator of the SPRR. Arm LO of the interferometer is now disconnected, thus providing the single input port condition as per the condition of Fig. 4. The polarization controller must be kept adjusted in the same manner such that one can still assume that most of the power launched into port S is directed to the polarization stage under test. However, the VOA on the S arm must be adjusted such that the power launched into the OFE is increased by a factor of 4 in order to illuminate the photodiodes with the same optical power as discussed in section 3.
6. Experimental results
The procedure described in the previous section was adapted to a single-polarization OFE such as illustrated in Fig. 6. A Lightwave Control Analyzer (LCA) model 8703A from Agilent fed with a DFB laser provided the intensity modulated optical signal at a frequency scanned from 130 MHz to 20 GHz together with the detection system.
The configuration in Fig. 8(a) was built using a 3 dB fiber coupler, two VOAs, and a lithium niobate phase modulator. Fiber patch cords of adjusted lengths were used as delay lines. The FSR of the interferometer formed by the measurement setup was measured to be 250 GHz, thus corresponding to a differential delay of 4 ps between the two arms. Using the VOAs, the optical powers were adjusted to 17 μW in both the S and LO ports. The phase modulator was fed with a triangular wave at a frequency of 1 Hz and an amplitude slightly larger than required to produce a phase modulation of ±π. A polarization controller on arm S was adjusted to maximize the interference signal. The phase modulation was not synchronized with the frequency scanning of the LCA. Accordingly, maximum output signals occurred at different frequencies during successive scans. Figure 9 shows the RF power of the measured output modulated signal as a function of the frequency during two successive scans, as well as the curve of maximum values over 18 successive scans. Figure 9 shows the frequency response over a limited range of 5 GHz to better show the difference from scan to scan. In Fig. 10, the whole frequency response is shown from 0 to 20 GHz for a single scan as well as for the maximum over 18 scans. Although the phase of the measured modulation could serve at distinguishing between the strong photocurrents ∆I1 and ∆I2, only the maximum between these two was selected and used as the denominator of the SPRR.
Arm LO of the interferometer was disconnected as per Fig. 8(b). The VOA in arm S was adjusted to 68 μW in port S, thus a factor 4 larger than the power used in the dual-port measurement. The resulting output signal RF power as a function of the modulation frequency is shown in Fig. 11 and was used as the numerator of the SPRR.
Shown in Fig. 12 is the SPRR taken as the ratio of the curve in Fig. 11 and twice the maximum curve in Fig. 10, together with a fit to Eq. (22). The fit provided a skew ∆τ= 0.74 ps and an imbalance δsI = 0.48% (ηI and δLI were set to 1 and 0 respectively). For comparison with the CMRR, photocurrents I1 and I2 on individual photodiodes were also measured using a successive disconnection of the fiber-connected photodiodes in the setup in Fig 8(b). The RF powers measured under this single-port illumination (and single-photodiode as well) are also shown in Fig. 10. The sum of these two photocurrents was used as the denominator of the CMRR, which is also shown in Fig. 12. The SPRR, a parameter that can be measured end-to-end on the OFE provides virtually the same information as the well known CMRR which requires disconnection inside the OFE to access the photocurrents of individual photodiodes. It should be noted also that the CMRR and SPRR shown in Fig. 12 contains the same noise, which is mainly determined by their common numerator, i.e. the signal shown in Fig. 11. The good match with the theoretical expression is an indication that in this case, the performance of the balanced detection was mainly determined by the characteristics of the 90° optical hybrid mixer.
A new parameter, the single-port rejection ratio (SPRR) was introduced to quantify the performance of balanced detection in a coherent receiver. This new parameter is similar to the well known common-mode rejection ratio (CMRR) defined for balanced detectors. While measurement of the CMRR requires disconnections inside the OFE to access photocurrents of balanced detectors under single-photodiode illumination, the SPRR can be measured end-to-end using only available input and output ports.
A theoretical analysis of the OFE was also provided and shows that the performance of balanced detection strongly depends on the characteristics of the optics used in front of the balanced photodetectors.
The performance of balanced detection can depend on the input and output ports of the OFE being considered. As a result, for the OFE shown in Fig. 1 having two optical inputs and four electrical outputs, eight different frequency-dependent SPRRs must be measured.
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