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We report a direct DPSK receiver based on polymer planar lightwave circuit technology, which incorporates a 2x25 GHz photodiode (PD) array hybridly integrated via 45° mirrors. In this direct DPSK receiver, a half-wave plate and heating electrodes are implemented to eliminate the polarization-dependent frequency-shift (PDFS) of the delay-line interferometer (DLI). By applying a proper heating current, a residual PDFS of practically zero at 1550 nm and within ±125 MHz was achieved over the full C-band. Integrated with the PD array, the peak responsivity is ~0.14 A/W for orthogonal polarizations over the C-band. To characterize this direct receiver, we introduce an adapted common-mode rejection ratio (CMRR), which takes into account the unequal responsivities of the PDs, the uneven split of the input power by the DLI, the phase error and the extinction ratio of the DLI. The measured CMRR under DC condition is below −20 dB over the C-band.
©2011 Optical Society of America
1. Introduction
For optical TDM and WDM transmission systems, differential phase-shift keying (DPSK) has become an attractive candidate for efficient signal modulation [1]. This class of modulation formats requires a delay-line interferometer (DLI) for demodulation at the receiver, Fig. 1(a) . In such demodulation systems, the polarization dependent frequency shift (PDFS), as illustrated in Fig. 1(b), can degrade the system performance [1] and induce a BER penalty [2]. Thus the requirement for polarization independent response is very critical. For instance, the permitted PDFS for differential quadrature PSK (DQPSK) systems at a bit rate of 25 Gbit/s and 40 Gbit/s / is in the order of only ±125 MHz and ±200 MHz, respectively, to keep the penalty below 1 dB [2]. In the C− and L−band, such PDFS values correspond to a birefringence (n TE−n TM) of ~±1×10−6 /±2×10−6, where n TE and n TM are the refractive indices for the TE (transverse electric) and TM (transverse magnetic) polarization states. Note that the PDFS is defined as frequency shift between TE and TM modes, Fig. 1(b). This definition takes into account that the receiver reported in this work has been designed for use in dual-polarization transmission systems, where the main concern is about how much the transmission functions for the TE and TM states differ.
Fig. 1 (a) Scheme of direct detection receiver for DPSK signals. (b) Illustrative definitions of the polarization dependent frequency shift (PDFS), the free spectral range (FSR) and the polarization dependent loss (PDL) of the delay-line interferometer.
Different birefringence compensation schemes have been proposed and demonstrated. By using a polyimide half-wave plate in a planar lightwave circuit (PLC), PDFS of < 1 GHz corresponding to a birefringence of 10−5 has been achieved [3, 5, 7]. Using stress release grooves, a PDFS value < 2 GHz was obtained [8]. In [9] placing a thin patch of silicon nitride under the silica waveguide core was reported to reduce PDFS to below 10 GHz. Basically, those PDFS values are not yet sufficient to fulfill the requirements of D(Q)PSK systems. In a very recent work applying a free space DLI [10], PDFS has been mitigated by utilizing an adjustable birefringent liquid crystal, and a PDFS < 0.61% of the FSR (corresponding to ~240 MHz at 40 Gbit/s) was accomplished. The interferometer employed in [10], however, appears to be difficult to be integrated on a small chip.
Among these references, the method of using a half-wave plate in a PLC is relative simple and efficient, and potentially very cost-effective. Nonetheless, related results [3, 4. 5] still show a residual PDFS of typically ~1 GHz due to asymmetric demodulator structures and polarization cross-talk of the components inside the PLC based DLI [4, 6, 7]. In ref [11], we briefly showed that by applying thermo-optic phase shifters to the DLI arms, the residual birefringence at 1550nm can be reduced to practically zero. However, in that work, the operation principle, the residual birefringence over the C-band and at different temperatures was not addressed in detail. Also, integration of the photodiodes was not realized.
The fabricated DPSK receiver is based on polymer PLC technology. Polymer PLC technology is regarded attractive because it offers the potential of fairly simple and low-cost fabrication involving low-temperature processes, and of low-cost packaging mainly because passive fiber alignment and attachment is feasible in a fairly simple manner [12, 13]. Meanwhile, great progress has been made in polymers to meet industry reliability requirement [14]. Also, polymers exhibit low thermal conductivity and high temperature coefficient of the refractive index in the 10−4 range [12, 13, 15, 16], which is one magnitude higher than that of silica. These properties lead to lower electric power consumption when controlling any device parameter in a thermo-optical way.
The DPSK receiver comprises a polymer waveguide based DLI with an embedded half-wave plate, heater structures for thermo-optic PDFS control, and a monolithic pair of > 25 GHz bandwidth photodiodes that are vertically coupled to the polymer PLC via integrated 45° mirrors. At heating currents of some 22 mA, we were able to achieve a residual PDFS of practically zero at 1550 nm and within ±125 MHz over the C-band. Indeed, if an active control of the heating current is applied employing techniques similar to optical phase locked loop [17], any remaining PDFS may be virtually eliminated over the full C-band. Application of such phase locked loop techniques is however beyond the scope of this work and will not be considered here. The relative phase between the two outputs of the integrated PD array in the absence of any active control was measured to be within 180°±5°. The measured responsivity of the receiver was ~0.14 A/W for both of the orthogonal polarizations. Using a novel adapted scheme the common-mode rejection ratio (CMRR) under DC condition could be kept below −20 dB over the C-band.
This paper is organized as follows: In Section 2 we first describe the configuration and the operation principle of the method to compensate the PDFS, and respective results are shown and discussed. In Section 3 we address the hybrid integration of the PD-array. Related performance results will be given. Finally, in Section 4, we will introduce an adapted CMRR scheme to characterize the direct detection receiver.
2. Compensation of polarization dependent frequency shift (PDFS)
2.1 Configuration and operation principle
To compensate the PDFS of a delay-line interferometer (DLI), we use a half-wave plate combined with four thermo-optic phase shifter electrodes. This method is proposed in [18]. The schematic layout of the proposed method is shown in Fig. 2(a) . The path-lengths of the longer (upper) and shorter (lower) DLI arms are L+ ΔL and L; the lengths of the strip heaters are δL 1 and δL 2 for the upper and lower path, while δL 2 = δL 1⋅L /(L + ΔL).
Fig. 2 (a) Layout for birefringence compensation in a delay-line interferometer (DLI) by using a half-wave plate combined with four heating electrodes. (b) Cross-section of waveguide structure.
The origin of the PDFS of the DLI is as follows. For different states of polarization, noted by the symbol “ν”, the ideal power transfer functions of a DLI can be written as
where n g,ν is the effective group refractive index for different states of polarization, and ΔL is the length difference between the DLI arms. Due to the birefringence, the power transfer function has a dependence on the state of polarization, i.e. PDFS.In polymer waveguides, the waveguide birefringence B WG is in the order of 10−3 [15]. This birefringence is mainly stress-induced [13]; therefore, it changes linearly with temperature, as shown in Fig. 3 . The slope of this change is S = B WG /ΔT Proc, where ΔT Proc = T f – T 0, with T f denoting the final temperature in the process and T 0 the room temperature. The value of S is always negative and in the order of 10−5/K for polymer waveguides because ΔT Proc is in the order of 100 – 200 K.
Fig. 3 Waveguide birefringence versus the ambient temperature. δB 1 and δB 1 are the birefringence changes when the waveguide temperature changes from a room temperature of 20°C to T 1 or T 2.
A birefringence of 10−5 can be obtained by using a half-wave plate [3, 5]. When such an element is positioned at the center of the DLI arms, the light experiences opposite birefringence before and after passing the half-wave plate. This effect results in reduced PDFS. However, due to any remaining asymmetry of the demodulator structures, there is still a residual PDFS, which is usually above the tight limit given for DQPSK systems [7].
In our proposed method by applying micro-heaters on the DLI arms, as illustrated in Fig. 2(a), the residual birefringence can be further reduced to the order of 10−6 as follows: If the waveguide temperature is increased from room temperature T 0 to T 1 by using the left heaters or to T 2 by using the heaters on the right, the waveguide birefringence decreases by a value δB 1 = S(T 1 −T 0) or δB 2 = S(T 2 −T 0), respectively. For the waveguides under the trimming heaters with a length of δL 1 on the top-left and top-right DLI sections, Fig. 2(a), the corresponding phase changes are Δϕ 1 and Δϕ 2. Their values and their difference Δϕ 2−Δϕ 1 are calculated as:
The residual PDFS, i.e. the residual birefringence B res of 10−5, can be considered as a residual phase difference Δϕ res. For a path-length of the longer DLI arm L + ΔL, we get
For eliminating the residual PDFS, the following condition needs to be fulfilled:
Inserting Eq. (2) and (3) into (4) and with S = B WG /ΔT Proc, the required temperature difference between the right and left heating element is then
Depending on the sign of B res, T 2 − T 1 can be positive or negative, by heating the left and right electrodes separately. As an estimation, B res /B WG is in the order of 10−2 ~10−3, ΔT proc is in the range of 100 – 200 K, and the length factor (L+ ΔL)/δL 1 is in the order of 10, it can be seen that a temperature difference of only a few degrees is sufficient to fully compensate the residual birefringence of the DLI.
For a DLI used in a DQPSK receiver, a heating electrode is needed to compensate the frequency offset between the optical source and the DLI by properly tuning the path-length difference of the delay-line. For polymer waveguides, only a small amount of electric power is needed to produce a large tuning range because of the large thermo-optic coefficient and low thermal conductivity of the polymer materials.
For the case with a half-wave plate, the above heating electrodes for path-length tuning can be placed in the left and right side of the half-wave plate, as seen in Fig. 2(a). The trimming effect for compensating the PDFS can be realized by heating the two heating electrodes at different temperatures. For example, for tuning the path-length difference, the waveguide temperature should be heated to T DLI, the required temperature difference for compensating PDFS is ΔT = T 2 − T 1, then the left and right heating electrodes should be operated at T DLI – ΔT/2 and T DLI + ΔT/2, respectively. This means that no extra structure will be needed, thus leading to a compact, low electric power consumption, and low cost device.
For compensating PDFS of the whole DLI, the lower path in Fig. 2(a) must be trimmed by two heaters simultaneously. If they are set at the same temperature as that of the upper heaters, the length of each heater at the lower arm should be equal to δL 2 = δL 1⋅L /(L + ΔL).
2.2. Results of PDFS compensating method
To experimentally demonstrate and investigate this PDFS-compensating method, polymer based DLI-structures designed for direct detection 25-Gbaud D(Q)PSK receivers were fabricated. The polymer materials utilized for the core and cladding, respectively, are commercial available from ChemOptics [15]. The refractive index contrast was chosen to be ~1.4% leading to a monomodal waveguide cross-section of 3.5 μm × 3.5 μm (refer to Fig. 2(b)). The thickness of each cladding layer amounts to some 16 μm. The chip size is 21.5 mm × 11 mm. The lengths of the longer and shorter arms are 30.6 mm and 22.3 mm, which give a δL 1 of 3.06 mm and a δL 2 of 2.23 mm.
With applying current to the electrodes and heating the respective polymer waveguide sections, we measured the spectra of the DLI for input lights with horizontal and vertical polarization separately. PDFS is calculated between the neighboring minima of the responses, Fig. 1(b). To simplify the measurement setup, we only heated the electrodes on the right side of the half-wave plate, while the temperature of the chip substrate and, hence, the temperature of the waveguides on the left side of the half-wave plate has been held at 20°C or 50°C. For all DLI chips PDL was found to be below 0.3 dB, while the maximum insertion loss over the C-band is 6.3dB for both states of polarization.
The derived PDFS values near 1550 nm wavelength are plotted in Fig. 4(a) in dependence of the heater current. It can be seen that, without any current, the residual PDFS amounts to −2.7 GHz in this case. When the current is increased to 22 mA, PDFS is totally eliminated. With further increasing the current its sign gets reversed. Depending on the electrode width and length the minimum operating electric current/power to eliminate PDFS was as low as 8 mA/16.5 mW [11]. As already pointed out in the introduction, our main attention has been paid to the PDFS between the TE and TM modes. Nevertheless, the transmission for left-handed and right-handed circularly polarized light has also been measured. We found only little residual PDFS of between −100 MHz and 100 MHz near 1550nm for left-handed and right-handed circular states of polarization, as shown in the lower row of Fig. 4. This residual PDFS is believed to be caused by polarization cross-talk inside the DLI [4, 6, 7]. However, the advantage of the proposed PDFS controller is that by adjusting the optimal heating current, the PDFS between left-handed and right-handed circularly polarized lights can also be eliminated.
Fig. 4 (a) PDFS and (b) FSR of the DLI at different heating currents applied to the electrodes on the right DLI arm (see Fig. 2(a)), and at two different substrate temperatures. The lower row shows the transmission spectra at output 2 while the substrate temperature is kept at 20°C. LCP: left-handed circularly polarized; RCP: right-handed circularly polarized.
Figure 4(b) shows the free spectral range (FSR) of the DLI at different substrate temperatures and different heater currents. It can be seen that, firstly, FSR increases by ~45 MHz when the substrate temperature is raised from 20°C to 50°C. This is mainly due to the decrease of the refractive index as a consequence of the negative thermo-optic coefficient of the polymer waveguide [12, 13, 15, 16]. Secondly, the heating current does not alter the FSR of the DLI significantly. The FSR is mainly determined by the length difference between the two DLI arms. The heating current affects only locally δL 1 and δL 2, while the length factors (L + ΔL)/δL 1 and L/δL 2 are above 10. Thus, the FSR stays within acceptable fluctuations. The fluctuations of FSR are assumed to originate mainly from the environment turbulence. On the other hand, the transmission of the DLI shifts at different heating currents, see the lower row in Fig. 4, because the transmission is dependent on the group refractive index, Eq. (1), which changes at different heating currents. Indeed, the PDFS-free transmission curves, the middle subfigure of the lower row in Fig. 4, can be shifted if waveguide sections on the left and right side of the half-wave plate are heated according to T DLI – ΔT/2 and T DLI + ΔT/2 respectively, as explained in the former section.
Of particular interest is the residual PDFS across the C-band. At a heating current of 22 mA and a substrate temperature of 20°C the residual PDFS of both outputs of the DLI were determined in the wavelength range between 1530 nm and 1569 nm. Results are depicted in Fig. 5(a) . From the linear fits of the residual PDFS of either output, indicated by the solid lines in Fig. 5(a), we obtained residual PDFS values within ±125 MHz over the C-band which largely satisfy the requirements of 25 Gbaud DQPSK transmission. If an active control of the heating current would be applied using techniques similar to optical phase locked loop [17], the residual PDFS may be further mitigated to become practically zero within the full C-band. Figure 5(b) also shows the phase relation between the two outputs at the afore-mentioned conditions. This relative phase is calculated from the distance of the transmission minima of the two outputs. The results show that the phase error is well below ± 5°, meeting system requirements given in [19].
Fig. 5 (a) Residual PDFS of the both DLI-outputs at a heating current of 22 mA and a substrate temperature of 20°C. Two solid lines are linear fits of these residual PDFS data. (b) Relative phase between DLI outputs, calculated from optical transmission spectra.
3. Hybrid integration of photodiode array on polymer PLC
To build a complete optical receiver chip the DLI chip needs to be coupled to suitable photodiodes (PD). In our polymer based hybrid integration platform photodiodes are mounted on top of the waveguides using integrated 45° turning mirrors formed in the waveguide, as sketched in Fig. 6(a) . This vertical coupling scheme offers the possibility of semi-automated surface-mount assembly by means of a fine placer machine. The mirror can be created either by applying a dicing saw with an appropriately shaped blade or by locally etching the polymer material using a grey-tone mask. Subsequently a thin metal layer is deposited onto the 45° slope. The typical mirror loss is around 1 dB. Special index matching glue is applied to reduce back reflection and also to fix the PD in place. Alignment of the PDs, deployed as a monolithic array, was accomplished with the help of a guiding red laser light.
Fig. 6 (a) Schematic of hybrid integration of a photodiode on a polymer waveguide chip via a 45° mirror. (b) Small signal frequency response of typical photodiodes used for 25 Gbaud detection.
The used PDs are mesa-type InGaAs/InP p-i-n diodes. They are bottom-illuminated and designed with a full p-metal contact on its top side, which facilitates uniform current flow and concurrently serves as optical reflector. Thus, the incoming light double-passes the absorbing layer. The responsivity of the bare PD at 1550 nm was ~0.62 A/W at a bias of −1V. The thickness and diameter of the absorption layer are ~1 μm and 22 μm respectively, while the center spacing between the PDs within a PD-array is 250 μm. Figure 6 (b) shows the small signal frequency response curves of two PD-arrays mounted on the polymer DLI chip. The measurement was performed directly on the chip using a suitable RF probe head without dedicated electronics for 50 Ω impedance-matching. The 3 dB bandwidth can be seen to reach 25 GHz.
The responsivities of the two mounted photodiodes (PD1 and PD2) were measured for cw input light with TE or TM polarizations. Measured response curves are shown in Fig. 7(a) . From these results the maximum and minimum responsivities are derived and plotted in Fig. 7(b). The extinction ratio is ~20 dB, which is bound by the optical transmission of the DLI. While the maximum responsivities are ~0.14 A/W for TE and TM polarizations, the imbalance is found to be below 0.35 dB over the C-band. Figure 7(c) shows the phase relation between the two current responses, indicating the phase error to be below ±5°.
Fig. 7 (a) Current responses of a PD-array mounted on a DLI chip. (b) Maximum and minimum responsivity of the mounted PDs. (c) Relative phase between two current responses.
4. Adapted common-mode rejection ratio (CMRR) for direct detection receivers
Since the photo currents out of two photodiodes (PDs), I 1 and I 2 as shown in Fig. 1(a), are going to be amplified differentially, we use an adapted common-mode rejection ratio (CMRR) to characterize this direct detection receiver. Normally, CMRR is a measure of the electrical power balance with respect to the PD responsivity and defined as [19]
Typically, a CMRR of < −20 dB satisfies the system requirement [19]. However, this standard CMRR can only be measured when the PDs can be illuminated separately, but with same incident powers.
For DPSK receivers discussed in [20], the standard CMRR was adapted to take into account the unequal responsivities of the PDs and the uneven split of the input power by the optical hybrid. This adapted CMRR is called single-port rejection ratio (SPRR), where the numerator in Eq. (6) is obtained under single-port (of the optical hybrid) illumination of the PDs. However, the errors in the relative phases between the hybrid outputs are not taken into account. Also, the measurement method described in [20] is not applicable to direct detection DLI based receivers, where the condition for single-port illumination does not exist. Yet, to obtain the denominator in Eq. (6), the method described in [20] can be referred to for the direct detection receiver. This possibility lies in the fact that instead of a phase modulator used in [20] a phase variation can be obtained by sweeping the carrier wavelength of the input light to the DLI.
In this work, the standard CMRR has been adapted to the DLI-based direct detection receiver to take into account the unequal responsivities of the PDs, the uneven split of the input power by the DLI, the phase error and the extinction ratio of the DLI. The current responses of the PDs of this receiver are illustrated in Fig. 8 as function of the wavelength/phase of the input light. The parameters I 1,max and I 1,min and I 2,max and I 2,min denote the maximum and minimum photo currents of PD1 or PD2, respectively. The phase relation between two minima, e.g. I 1 as the reference in Fig. 8, is 2π. In an ideal case, the current response I 2 has a relative phase of π to I 1, as shown in Fig. 8(a). The parameters I 1,π/2 and I 1,3π/2 or I 2,π/2 and I 2,3π/2 are the current responses of PD1 or PD2 at the wavelengths, which have a phase relation of π/2 or 3π/2 to the reference wavelength point with 0-phase. First, we define the CMRRπ/2 and CMRR3π/2 at these two wavelength points as
Fig. 8 Illustration of the parameters used in the definition of the adapted CMRR for the cases: (a) no phase error, and (b) with a virtual phase error δφ between currents from the two PDs.
The adapted CMRRDLI is the maximum (i.e. the worst value) of the CMRRπ/2 and CMRR3π/2,
The numerator and denominator of Eq. (7) are now explained with the help of Fig. 8. First, the difference terms |I 1, φ − I 2, φ| for φ = π/2 or 3π/2 are used in the numerator of Eq. (7) rather than |I 1, max − I 2, max| as in [20]. This necessary adaption is due to the fact that two PDs are illuminated with identical incident powers at these wavelength points in the ideal case. This is similar to the situation of single-port illumination in [20]. Without any phase errors, the values of I 1,π/2 and I 1,3π/2 or I 2,π/2 and I 2,3π/2 are the half of the value of I 1,max or I 2,max respectively. Also, the difference terms |I 1,π/2 − I 2,π/2| and |I 1,3π/2 − I 2,3π/2| are the half of the difference term |I 1, max − I 2, max|. Thus, a factor of 2 is added to the terms |I 1, φ − I 2, φ| in Eq. (7). Furthermore, the difference terms |I 1(2), max − I 1(2), min| in the denominator of Eq. (7) are used to take into account not only the unequal responsivities of the PDs and the uneven split of the input power by the DLI, but also the extinction ratio. It can be seen that, in the ideal case without any phase errors and for negligible values of I 1,min and I 2,min, the value of the CMRRDLI is same as the value of the standard CMRR of Eq. (6).
In the presence of a phase error δφ, Fig. 8(b), CMRRDLI is degraded via the change of the difference term |I 1,π/2 − I 2,π/2| or |I 1,3π/2 − I 2,3π/2| accordingly. In reality, the current response I 2 may not be at the ideal (i.e. relative phase of π to I 1) position. If only a phase error is added in Fig. 8(b), the maximum and minimum current values stay the same with respect to those in Fig. 8(a). However, the difference terms |I 1, φ − I 2, φ| change considerably. Comparing Fig. 8(a) and (b), the difference term |I 1,π/2 − I 2,π/2| is smaller while |I 1,3π/2 − I 2,3π/2| is bigger. This leads to smaller (better) CMRRπ/2 and bigger (worse) CMRR3π/2. In this case, CMRRDLI takes the maximum value, i.e. CMRR3π/2, and is degraded by the phase error.
For the current responses of two PDs obtained with launched cw input light of TE or TM polarization, Fig. 7(a), the adapted CMRRDLI is calculated from Eq. (7) and (8), and plotted as black lines in Fig. 9 . Note that the values of I 1, φ and I 2, φ in Eq. (7) are taken at the wavelengths characterized by the relative phase of π/2 or 3π/2 to the reference wavelength point, while the values of I 1,max and I 1,min or I 2,max and I 2,min at the same wavelengths are obtained by interpolating the neighboring peaks. For comparison, CMRRπ/2 and CMRR3π/2 from Eq. (7) and the standard CMRR from Eq. (6) are also plotted as green, red and blue lines in Fig. 9. As expected, the adapted CMRRDLI is the worst case of the CMRRπ/2 and CMRR3π/2, and degraded by the phase error with respect to the standard CMRR.
Fig. 9 Calculated CMRRDLI (black lines) from Eq. (7) and (8) for photo currents induced by cw input lights with (a) TE or (b) TM polarizations. Green and red lines are the alternative CMRRs at the wavelengths with a relative phase of π/2 or 3π/2 to the reference wavelength point. For comparison, the standard CMRR calculated from Eq. (6) are also plotted as blue lines.
Note that the CMRRDLI shown in Fig. 9 is obtained under DC condition, i.e. with cw input lights. CMRRDLI versus the modulation frequency can also be measured, if an intensity modulator is available in the optical source as demonstrated in [20]. Such a measurement was not performed in this work. However, the dependency of CMRRDLI versus the modulation frequency can be estimated as follows.
- • Firstly, the worst standard CMRR in Fig. 9 is −34 dB. Assuming negligible values of I 1,min and I 2,min, and assuming I 1,max ≈I 2,max, we have (I 1,max − I 2,max) ≈10−1.7 ⋅(I 1,max + I 2,max) ≈10−1.7⋅2⋅I 1,max ≈0.04⋅I 1,max.
- • Secondly, assuming that the worst CMRRDLI is −20 dB we have (I 1, φ − I 2, φ) ≈10−1 ⋅(I 1,max + I 2,max) /2 ≈0.1⋅I 1,max, for φ = π/2 or 3π/2. As discussed in Fig. 8, the half of the (I 1,max − I 2,max) is included in (I 1, φ − I 2, φ); thus, the phase error induces an extra difference of 0.08⋅I 1,max in (I 1, φ − I 2, φ).
- • Now, for CMMRDLI(Ω) at different modulation frequency Ω, the current responses are Î1(Ω) and Î2(Ω) . The values of maxima Î1,max(Ω) and Î 2,max(Ω) can be referred to in Fig. 6(b). The largest value of 20⋅log10[Î1,max(Ω) / Î2,max(Ω)] of the PD array from Fig. 6(b) is ~1dB for Ω up to 25 GHz. This gives [Î1,max(Ω) − Î2,max(Ω)] ≈(1−10−0.05) ⋅Î1,max(Ω) ≈0.11⋅Î1,max(Ω). Again, the half of the [Î1,max(Ω) − Î2,max(Ω)] is included in [Î1,φ(Ω) − Î2,φ(Ω)]. Since Î1,max(Ω) does not change considerable with Ω up to 25 GHz, we assume that Î1,max(Ω) ≈I 1,max and the phase error induces a similar extra difference of 0.08⋅Î1,max(Ω) in [Î1,φ(Ω) − Î2,φ(Ω)]. Then, in the worst case, [Î1,φ(Ω) − Î2,φ(Ω)] is 0.135⋅Î1,max(Ω). This estimation leads to the worst CMRRDLI(Ω) of −17.4 dB, which is above the system requirement under AC condition [19].
5. Conclusion
In conclusion, we have demonstrated a hybrid-integrated 25-Gbaud D(Q)PSK direct detection receiver based on polymer planar lightwave circuit. We discussed a thermo-optic control method to efficiently reduce the polarization dependent frequency shift to meet the tight requirements for receivers deployed in DQPSK systems. Applying the proposed method, we achieved a residual PDFS value of practically zero at 1550 nm and within ± 125 MHz over the full C-band. We also discussed the technology how to hybridly integrate the photodiodes (PD) vertically via an integrated 45° mirror on a polymer PLC. The measured peak responsivities are ~0.14 A/W for orthogonal polarizations. Furthermore, we introduced an adapted common-mode rejection ratio (CMRR), which takes into account the unequal responsivities of the PDs, the uneven split of the input power by the DLI, the phase error and the extinction ratio of the DLI. The adapted CMRR under DC condition (with cw input lights) is below −20 dB over the C-band.
Acknowledgments
This work has been conducted in the framework of the 100x100 Optics project partly funded by the Future Fund of the Land Berlin co-sponsored by the European Fund for Regional Development (EFRE). The authors would like to thank Ruiyong Zhang for RF characterization of photodiodes.
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