Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

TO-56-can packaged colorless WRC-FPLD for QAM OFDM transmission at 42 Gbit/s over 25-km SMF

Open Access Open Access

Abstract

The weak-resonant-cavity Fabry-Perot laser diode (WRC-FPLD) with colorless and channelized mode features is a new-class optical transmitter fulfilling the need of next-generation communications. By packaging the colorless WRC-FPLD transmitter with a 10-GHz transistor-outline-56-can (TO-56-can), the premier demonstration on directly modulated 42-Gbit/s/channel quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) transmission is demonstrated via wavelength injection-locking. Enlarging the injection level effectively up-shifts the relaxation oscillation peak and suppresses the relative intensity noise, which facilitates the TO-56-can packaged WRC-FPLD to improve its modulation throughput bandwidth to 9 GHz and enhance its signal-to-noise ratio to 22 dB. By pre-amplifying the directly modulated QAM-OFDM data with a total raw bit rate of 42 Gbit/s, the receiving bit-error-rate (BER) under back-to-back transmission can be reduced below the forward-error-correction (FEC) limited BER of 3.8 × 10−3. Such a colorless WRC-FPLD enables the QAM-OFDM transmission over a 25-km long single-mode-fiber based metropolitan access network with its BER matching the FEC criterion at a receiving power of −2 dBm.

© 2015 Optical Society of America

1. Introduction

To meet the demand of high-speed data transmission in next-generation passive optical network (PON), the optical orthogonal frequency division multiplexing (OOFDM) format has been employed in a new-era optical communication system due to its advantages of high spectral usage efficiency, flexible bandwidth management and resilience to linear dispersion [1–4]. Recently, the M-quadrature amplitude modulation (M-QAM) format is also employed in OOFDM system to further increase its total bit rate by log2(M) times [5–7]. To reduce the cost and compact the scheme of optical access networks, the direct modulation is a preferable method to deliver the QAM-OFDM data with low transferring loss. Various transmitters which facilitate the delivery of OOFDM data were considered and successively demonstrated. At early stage, the direct modulation of single-mode distributed feedback laser diodes (DFBLDs) with sufficiently high modulation bandwidth was considered to carry the high-speed OOFDM data. Tang et al. demonstrated 28-Gbit/s adaptively modulated OOFDM transmission over 300-m multimode fiber with the directly modulated DFBLD [8]. By discretely multi-tone modulating the DFBLD with 10-GHz bandwidth, the OOFDM data with a raw data rate of up to 50 Gbit/s after 20-km single-mode-fiber (SMF) was reported by Tanaka and associates [9].

To meet the demand of cost-effective optical access networks based on the dense wavelength division multiplexed PONs (DWDM-PONs) [10–13], the universal transmitters with broadband spectral coverage profile were considered lately. Among these candidates, the injection-locked reflective semiconductor optical amplifiers (RSOAs) were firstly demonstrated to transmit 10-Gbit/s OOFDM data within a modulation bandwidth of only 1 GHz [14–16]. Alternatively, the injection-locked Fabry-Perot laser diode (FPLD) has also been proposed because of its relatively high coherence [17–19]. The directly modulated and injection-locked FPLD enables over 10-Gbit/s transmission with general 16-QAM OFDM transmission [20–22]. Afterwards, a new class of injection-locked weak-resonant-cavity FPLD (WRC-FPLD) [23–25] by imperfectly anti-reflection (AR) coating the front-facet of a long-cavity FPLD was proposed as the promising colorless transmitter for DWDM-PON. Such a design effectively reduces its longitudinal mode spacing to enrich DWDM channels, and facilitates the power budget required at injection-locking mode. Recently, the injection-locked WRC-FPLD under direct modulation with 16-QAM OFDM data at 20 Gbit/s was successfully demonstrated to transmit over 25-km SMF [26, 27].

In addition to the improvement on mode coherence, another issue focuses on the high-speed but cost-effective package of transmitters. The transistor-outline-can (TO-can) with compact size, simple design and easy package is indeed a better solution than the butterfly package. To overcome the poor frequency response of the TO-can package for encoding the M-QAM and multi-subcarrier OOFDM data, some special designs with unique transmission line and bonding pad structure were reported [28, 29]. By connecting the typical TO-can packaged WRC-FPLD with a specially designed SMA connector, its modulation bandwidth can be enhanced up to 4 GHz for directly encoded M-QAM OFDM transmission [30]. Moreover, the relaxation oscillation frequency of the WRC-FPLD can be up-shifted from 5 to 8 GHz by increasing the injection-locking power [27]. Therefore, it is straightforward to prospect that the WRC-FPLD chip inherently exhibits a bandwidth beyond 5 GHz. Very recently, the 10-GHz TO-56-can package has been rapidly developed and commercialized. With the new package of 10-GHz TO-56-can and the direct M-QAM OFDM modulation, the WRC-FPLD will be a potential candidate for next generation PON architecture.

In this work, we demonstrate a 36-Gbit/s 16-QAM OFDM transmission over 25-km SMF by injection-locking and directly modulating the 10-GHz TO-56-can packaged WRC-FPLD. Coherently injection-locking the 10-GHz TO-56-can packaged WRC-FPLD greatly enhances its direct modulation throughput to handle the 16-QAM OFDM transmission with a data bandwidth beyond 9 GHz. Employing the intense injection plays an important role to up-shift and suppress the relaxation oscillation induced relative intense noise (RIN) response of the WRC-FPLD, which improves the signal-to-noise ratio (SNR) and the bit-error-rate (BER) performances of the directly modulated QAM OFDM data. The compromised optimization on enlarged modulation bandwidth and declined throughput power of the WRC-FPLD under strong injection-locking is considered, and the trade-off between RIN suppression and frequency response degradation with detuning the injection level is also discussed. To enable the 36-Gbit/s 16-QAM OFDM transmission over 25-km SMF with the 10-GHz To-56-can packaged WRC-FPLD, the pre-amplification on electrical 16-QAM OFDM data is employed. To further increase the spectral usage efficiency, the pre-amplified 64-QAM OFDM data-stream is used for 25-km SMF transmission to increase the data-rate up to 42 Gbit/s with the WRC-FPLD based colorless and universal transmitter.

2. Experimental setup

Figure 1 illustrates the 10-GHz TO-56-can packaged WRC-FPLD with a copper-based cooling mount for temperature stabilization. To meet the demand of increasing the usable channels, the front-facet reflectance and cavity length of the WRC-FPLD were reduced from 30% to 1% and increased from 200 to 600 μm, respectively, as compared to a traditional FPLD. In addition, such a design with weak front-facet reflectance also enhances the injection-locking efficiency by reducing the reflection of the externally injected photons. In previous report, the relaxation oscillation frequency of the injection-locked WRC-FPLD can be up-shifted to over 8 GHz [21].

 figure: Fig. 1

Fig. 1 The pictures and illustrations of the 10-GHz TO-56-can packaged WRC-FPLD.

Download Full Size | PDF

That is, the typical TO-can package with its frequency response of up to 4-5 GHz may somewhat limit the modulation bandwidth of the WRC-FPLD chip that exhibits an inherent modulation bandwidth of larger than 8 GHz. Subsequently, the 10-GHz TO-56-can packaged WRC-FPLD was pig-tailed with a single-mode fiber (Corning SMF-28), as shown in Fig. 1. In contrast to a typical TO-56-can, the 10-GHz TO-56-can consist of a thin-film ceramic sub-mount and an attached transmission line with impedance matching enables to extend its frequency response up to 10 GHz. Figure 2 shows the temperature controlling system of the WRC-FPLD with a set of designed copper mount, a TE cooler and a thermistor. The 10-GHz TO-56-can packaged WRC-FPLD is connected with the specifically designed SMA jack after threading through the reserved hole of the copper mount, as shown in Figs. 2(a) and 2(b). To avoid direct contact between the WRC-FPLD and the copper mount that could affect the frequency response of the WRC-FPLD, the 10-GHz TO-can/jacket-SMA packaged WRC-FPLD is electrically isolated with the mount through the use of plastic screws and nuts accompanying with wrapping a thermal tape around the WRC-FPLD, as shown in Fig. 2(c).

 figure: Fig. 2

Fig. 2 The 10-GHz TO-56-can/jacket-SMA packaged WRC-FPLD with the self-designed temperature control system.

Download Full Size | PDF

The testing bench of the directly modulated and coherently injection-locked WRC-FPLD for transmitting the QAM OFDM data with various bandwidths changing from 5 to 9 GHz is shown in Fig. 3. In our home-made MATLAB program for generating the QAM OFDM data, the OFDM subcarrier numbers of 108, 128, 150, 172, 192 and 214 were variable to occupy the total bandwidths of 5, 6, 7, 8 and 9 GHz, respectively, which effectively delivers the data-stream with raw data rates of 20, 24, 28, 32 and 36 Gbit/s for 16-QAM OFDM and 30, 36, 42, 48 and 54 Gbit/s for 64-QAM OFDM, respectively. A cyclic prefix is added for mitigating chromatic dispersion, and a frequency domain equalizer is also employed to reduce inter-symbol interference (ISI). Each 16-QAM OFDM data was separately delivered by using the scheme consisting of an arbitrary waveform generator (AWG, Tektronix, AWG 70001A) with a sampling rate of 24 GS/s and the scheme with an AWG combining with a linear pre-amplifier.

 figure: Fig. 3

Fig. 3 The testing bench of the injection-locked WRC-FPLD for transmitting the QAM OFDM data delivered by the AWG (a) without and (b) with pre-amplifier. AWG: arbitrary waveform generator, DSO: digital signal oscilloscope, SMF: single mode fiber. PD: photodetector, Amp: amplifier, TL: tunable laser.

Download Full Size | PDF

Both schemes were employed to directly modulate the 10-GHz TO-56-can packaged WRC-FPLD in combination with a DC bias current via a bias tee (Mini-Circuit, ZX86-12G-S + ). The WRC-FPLD exhibits tunable wavelength rage from 1555 to 1580 nm at a bias current of 40 mA (twice the threshold current of 20 mA). A tunable laser (HP, 8168F) was used to simulate the coherent master for externally injection-locking the directly modulated WRC-FPLD after passing through a polarization controller (PC). To optimize the 16-QAM OFDM transmission, the bias current of the WRC-FPLD was tuned from 25 to 60 mA, and the injection-locking power was adjusted from −12 to 3 dBm. The temperature was controlled at 22°C to prevent unexpected wavelength drift. The injection-locked WRC-FPLD carried optical 16-QAM OFDM data was split into 90% and 10% by a 1 × 2 coupler after passing through a 25-km SMF. The 90% path was received by an optical receiver (Nortel, pp-10G) and the converted 16-QAM OFDM data was further amplified by an electrical amplifier (NF1422). The amplified analog data-stream was then sampled by a real-time oscilloscope (Tektronix, DSO 71254) with a sampling rate of 100 GS/s. The 10% path was send into the optical spectrum analyzer (Ando, AQ6317B) to monitor the injection-locked spectrum.

3. Results and discussions

3.1 Frequency response and relative intensity noise of the WRC-FPLD

The relaxation oscillation frequency of the WRC-FPLD can be up-shifted from 5 to >8 GHz by increasing the injection-locking power [28]. That is, the WRC-FPLD has the capacity to overcome its inherently limited bandwidth beyond 5 GHz by coherent injection-locking. Unfortunately, the modulation bandwidth of the WRC-FPLD is limited below 5 GHz by the low-speed TO-can package. To essentially release the limited modulation bandwidth for direct 16-QAM OFDM data modulation, the 10-GHz TO-56-can is used to package the WRC-FPLD, so as to implement the unspoiled frequency response of the injection-locked WRC-FPLD. Figure 4 declares that the conventional TO-can package (see black dashed line) with a low bandwidth of 4-5 GHz apparently damages the throughput response of the injection-locked WRC-FPLD even with the injection power as high as −3 dBm and at a bias current of twice its threshold. With the use of 10-GHz TO-56-can package (see red solid line), the throughput response of the WRC-FPLD under the same operation reveals a significant improvement at frequencies between 6 and 9 GHz. That is, the 10-GHz TO-can packaged and injection-locked WRC-FPLD is enabled to carry the 16-QAM OFDM data with a total bandwidth of up to 9 GHz, as shown in the inset of Fig. 4(a).

 figure: Fig. 4

Fig. 4 (a) The frequency response of the WRC-FPLD with low-speed TO-can package (black dashed line) and 10 GHz TO-can package (red solid line). Inset: The RF spectrum of the 16-QAM OFDM data with various bandwidth carried by the WRC-FPLD, and (b) the simulated frequency responses of the WRC-FPLD obtained at different injection powers.

Download Full Size | PDF

To numerically analyze the frequency response of the injection-locked WRC-FPLD, the simulation starts from the following injection-locked laser rate equations [31, 32].

dN(t)dt=ηiI(t)qN(t)τsvggS(t),dϕ(t)dt=12αΓvggκ(SinjS(t))1/2sin(Δϕ(t))Δwinj,dS(t)dt=ΓvggS(t)S(t)τp+2κ(SinjS(t))1/2cos(Δϕ(t)),
where N(t) denotes the carrier number, ϕ(t) the phase, S(t) the photo number of the WRC-FPLD, ηi the internal quantum efficiency, I(t) the bias current, q the electron charge, τs the carrier lifetime, vg the group velocity, g the gain coefficient, α the linewidth enhancement factor, Γ the optical confinement factor, κ the coupling ratio, Sinj the injected photo number, Δϕ(t) the phase difference between the internal and injected lights, Δwinj the detuning frequency and τp the photon lifetime. By assuming Δwinj = 0 and ignoring spontaneous emission, then setting S(t)≡SB (the steady-state photon number of injection-locked mode) and ϕ(t)≡ϕB (the constant phase change of the injection-locked mode) [33]

ϕB=sin1(Δωinjκ1+α2SBSinj)tan1α=tan1αcos(ϕB)=11α2

With a small signal modulation, the I = IB + i(ω)ejwt, N = NB + n(ω)ejwt, and S = SB + s(ω)ejwt are applied to Eq. (1). The rate equations can be rewritten as

jωn(ω)=ηii(ω)qn(ω)τsvg[gBs(ω)+g'SBn(ω)+g'n(ω)s(ω)],jωs(ω)=Γvg[gBs(ω)+g'SBn(ω)+g'n(ω)s(ω)]s(ω)τp+κ1+α2SinjSB[s(ω)SB]),
where s(ω) denotes the small-signal photon number, n(ω) the small-signal carrier number and g’ the differential gain coefficient (g’ = δg/δn). With this manipulation, the modulation response of s(ω)/i(ω) can be simply described by using the modulation transfer function [34]

H(ω)=s(ω)i(ω)=ηiΓvgg'SBqV{ω2+jω(1τs+vgg'SBκ1+α2SinjSB)+[vgg'SBτpκ1+α2SinjSB(1τs+vgg'SB)]},

As a result, the simulated frequency response of the injection-locked WRC-FPLD at a bias current of twice the threshold is shown in Fig. 4(b). When enlarging the injection power, the relaxation oscillation induced peak response of the WRC-FPLD is gradually diminished, and the bandwidth can also be extended with the sacrifice on the throughput response at low frequencies. Apparently, there exists an optimized injection power for flattening the modulation throughput without sacrificing the low-frequency response too much. Experimentally, the measured frequency response of the injection-locked WRC-FPLD is extended initially but degraded conversely by enlarging the injection power from −12 to 3 dBm, as shown in Fig. 5(a). The shadow zone indicates the unusable bandwidth (for carrying the QAM OFDM data) of the WRC-FPLD packaged by 4-GHz or 10-GHz TO-can. In a typical low-speed TO-56-can packaged WRC-FPLD, the enhancement on its modulation bandwidth is limited and can only be observed at injection power below −12 dBm. Further enlarging the injection power to >-9 dBm conversely decreases its throughput power at frequency beyond 4 GHz, and a significant declination at >6 GHz is also observed at all injection levels. On the contrary, the inherent limitation of the modulation bandwidth is released by using the 10-GHz To-56-can package, which reveals a broadband throughput response of up to 9 GHz. In the 10-GHz TO-can packaged WRC-FPLD, the bandwidth is linearly enhanced by setting the injection power below −6 dBm. When further increasing the injection power from −3 to 3 dBm, the extended bandwidth no longer lasts due to the declined frequency response at below 10 GHz caused.

 figure: Fig. 5

Fig. 5 (a) The measured frequency responses of the injection-locked WRC-FPLD with 4-GHz and 10-GHz TO-can packages, and the RIN spectra of the 10-GHz TO-can packaged and injection-locked WRC-FPLD at different (b) injection powers and (c) bias currents.

Download Full Size | PDF

Concurrently, the relative intensity noise (RIN) response of the 10-TO-can packaged WRC-FPLD can be up-shifted from 5.5 to 10 GHz and suppressed from −96 to −104dBc/Hz at 5.5 GHz when increasing the injection power from −12 to 3 dBm, as shown in Fig. 5(b). For mathematical discussion, the RIN of the injection-locked WRC-FPLD is given by [27]

RIN=16(Δν)ST{ηiΓvgg'q(IBIth')+κ1+α2SinjSB[ηiΓvgg'τpq(IBIth')+1τs]}2τΔN2+2hCλP0[η0(IB+Ith')(IBIth')+(1η0)],
where (Δv)ST denotes the modified Schawlow-Townes linewidth, g' the differential gain coefficient, IB the bias current, Ith the threshold current of the WRC-FPLD at injection-locking condition, τN the differential carrier lifetime, h the Planck constant, C the light speed, λ the wavelength, P0 the output power of the injection-locked WRC-FPLD and η0 the optical efficiency given by αm/(αm + αi), where αi and αm are internal and mirror losses of the WRC-FPLD, respectively. Both the increased injection power and bias current help the WRC-FPLD enlarging its output power and up-shifting its relaxation oscillation frequency, which results in an up-shifted RIN peak with a suppressed RIN level. When keeping the injection power at 0 dBm, the RIN level of the WRC-FPLD can be further suppressed by 2 dB with enlarging bias from 30 to 40 mA, as shown in Fig. 5(c). From these analyses, the suppressed RIN and the declined throughput intensity are correlated with each other.

3.2 Direct 16-QAM OFDM encoding of the injection-locked WRC-FPLD

The received constellation plots of the optical 16-QAM OFDM data carried by WRC-FPLD at free-running and injection-locking cases are shown in Fig. 6(a). Although the constellation plot becomes blurred when transmitting the 16-QAM OFDM data at higher raw data rates by extending the bandwidth, the clearer constellation plot in each case can still be obtained with the use of injection-locking. With an injection-locking power of −3 dBm, the error vector magnitude (EVM) of the decode 16-QAM OFDM data at a raw data rate of 20, 24, 32 and 36 Gbit/s is reduced from 16.43% to 8.49%, from 18.85% to 10.65%, from 24.18% to 15.03% and from 25.79% to 17.31%, respectively. The EVM value is calculated by comparing the generated (ideal case from the program) and experimentally received constellation plots in I-Q domain. Figure 6(b) shows the BER performances of the back-to-back transmitted 16-QAM OFDM data at 20-36 Gbit/s delivered by the WRC-FPLD biased at twice the threshold and injection-locked at different powers. With a broad range of injection-locking power, the 20- and 24-Gbit/s cases easily reduce their receiving BERs to below the forward error correction limit (FEC-limit, at BER = 3.8 × 10−3) at lower injection powers, whereas the 32- and 36-Gbit/s cases strictly require the injection power to be higher than −9 and −3 dBm, respectively.

 figure: Fig. 6

Fig. 6 (b) The constellation plots of the 16-QAM OFDM data received at free-running and injection-locking cases and (a) the BERs of the 16-QAM OFDM data at raw data rate of 20-36 Gbit/s transmitted by the WRC-FPLD at different injection-locking powers.

Download Full Size | PDF

As the injection power enlarges from −12 to −3 dBm, the BER of 32- and 36-Gbit/s cases are only improved by one-order of magnitude, whereas the 20- and 26-Gbit/s cases exhibit more than two-orders of magnitude reduction on BER. Such an improved OFDM transmission performance strongly correlates with the RIN suppression in each case, especially when the RIN peak of the WRC-FPLD is greatly up-shifted and suppressed by enlarging the injection power. On the contrary, the BER is increased when enlarging the injection power beyond −3 dBm because the OFDM data is impaired by the seriously declined frequency response of the WRC-FPLD under intense injection-locking.

It is mandatory to further discuss the 16-QAM OFDM transmission performance affected by the trade-off between the declined throughput and the suppressed RIN within the modulation bandwidth while enlarging the injection power. The measured frequency response, RIN and SNR of the injection-locked WRC-FPLD for transmitting the 20- and 36-Gbit/s 16-QAM OFDM data with required bandwidth of 5 and 9 GHz, respectively, are shown in Fig. 7. Therein, the RIN lines are smoothened to declare the trend clearly. To clarify, the relationship between SNR, RIN and frequency response (FR) can be simply expressed as ΔSNR (dB/Hz) = ΔRIN (dB/Hz) – ΔFR (dB/Hz). In the 20-Gbit/s case, the frequency response of the WRC-FPLD is only declined by 1-2 dB within 4-5 GHz, whereas the RIN is significantly suppressed by 4 dB at offset frequency below 5 GHz, associated with its peak up-shifted to 10 GHz by enlarging the injection level from −12 to −3 dBm, as shown in the upper left of Fig. 7. This causes a 3-dB enhancement on SNR and a decreased BER is also observed. When overly injecting the WRC-FPLD from −3 to 3 dBm, the throughput response of the WRC-FPLD continues to decrease by 1.5 dB as the RIN does not abruptly decrease anymore, as shown in the upper right of Fig. 7, which turns to reduce the SNR and eventually cause the increased BER trend. In the 36-Gbit/s case, the RIN suppression is more significant than that on the decline of throughput caused by enlarging the injection power, as shown in the lower left of Fig. 7. Apparently, the RIN suppression dominates to improve the SNR within the OFDM modulation bandwidth of 9 GHz. In contrast to the 20-Gb/s case with an obviously increased BER when injection beyond −3 dBm, the 16-QAM OFDM transmission covering 9-GHz bandwidth shows a smaller variety on the BER degradation. It is mainly attributed to the continuously suppressed RIN at frequencies beyond 6 GHz when injection-locking beyond −3 dBm. In this case, the effect of the overall suppressed noise and the decreased throughput for the 16-QAM OFDM data carried by the injection-locked WRC-FPLD could compensate each other.

 figure: Fig. 7

Fig. 7 The measured frequency response, RIN and SNR behaviors for 20-Gbit/s (upper) and 36-Gbit/s (lower) transmissions with injection powers ranged from −12 to −3 dBm (left) and from −3 to 3 dBm (right).

Download Full Size | PDF

Figure 8 shows the three-dimensional (3D) BER contour mapping of the back-to-back transmitted 16-QAM-OFDM data carried by the 10-GHz TO-can packaged WRC-FPLD under injection-locking, which is obtained by changing the injection power and the bias current of the WRC-FPLD. The 3D BER contour of the transmitted 32-Gbit/s 16-QAM OFDM data shown in Fig. 8(a) indicates a wide range of parametric tunability to achieve the BER performance below the FEC-limited criterion at all biases by setting the injection power larger than −9 dBm. In contrast, the 36-Gbit/s transmission shown in Fig. 8(b) suffers from a severe operation with narrow bias ranged between 35 and 45 mA and injection-locking power ranged between −3 and 2 dBm. At the optimized point with a bias of 40 mA and an injection power of 0 dBm, the BER for 32-Gbit/s and 36-Gbit/s transmission cases can reduce to 1.3 × 10−3 and 3.4 × 10−3, respectively. When keeping the injection power at 0 dBm, the BER response of the WRC-FPLD is slightly decreased by increasing the bias from 30 to 40 mA as the RIN has already been suppressed by injection-locking. When biasing the WRC-FPLD at larger than 40 mA, the decreased ER of the OFDM data amplitude to noise amplitude turns out to be a dominant effect on decreasing the SNR [35]. With the 10-GHz TO-can package, the directly modulated WRC-FPLD greatly improves its capability of handling high-bit-rate 16-QAM OFDM data after injection-locking.

 figure: Fig. 8

Fig. 8 The 3D contour of the received BER for (a) 32 Gbit/s and (b) 36 Gbit/s 16-QAM OFDM transmissions at different bias currents and injection powers.

Download Full Size | PDF

The BER of the back-to-back transmitted 16-QAM-OFDM data with a total raw bit rate of up to 36 Gbit/s is shown in Fig. 9. To fit the FEC required BER criterion, the receiving power sensitivity of the back-to-back transmitted 16-QAM OFDM data at 20, 24, 28, 32 and 36 Gbit/s carried by the injection-locked WRC-FPLD gradually enlarges to −9, −8, −6, −5, and −4 dBm, respectively. After 25-km SMF transmission, the dispersion strictly affects the 16-QAM OFDM waveform in time domain especially when performing high data-rate transmission. The slightly lagged frequency components reshape the temporal waveform such that the receiving data is distorted before decoding. In addition, the propagation loss of the 25-km SMF limits the maximal receiving power of the current step to −4 dBm, as the maximal output power of the WRC-FPLD biased at 40 mA is only 1.5 dBm. Eventually, the 25-km SMF transmission limits the maximal bit-rate to 26 Gbit/s by checking the BER performance below the criterion of FEC, as shown in Fig. 9(b).

 figure: Fig. 9

Fig. 9 (a) BER vs. receiving power of the injection-locked WRC-FPLD output under back-to-back transmission and (b) the BER vs. raw data rate of the 16-QAM OFDM data after back-to-back and 25-km transmissions.

Download Full Size | PDF

3.3 Pre-amplification for 16-QAM OFDM Transmission

To enable the 36-Gbit/s 16-QAM OFDM transmission over 25-km SMF with the 10-GHz TO-can packaged WRC-FPLD, the pre-amplification of the electrical 16-QAM OFDM data before modulating the WRC-FPLD is demonstrated with a broadband microwave amplifier with 12-dB power gain, which enlarges the peak-to-peak amplitude limited by the current AWG at Vpp,max = 0.5 V. By magnifying the Vpp of the electrical 16-QAM OFDM data from 0.38 to 1.45 V, the SNR of the optical 16-QAM OFDM data transmitted by the injection-locked WRC-FPLD can be greatly improved. The back-to-back and 25-km SMF transmitted BER of the 36-Gbit/s 16-QAM OFDM data carried by the directly modulated and injection-locked WRC-FPLD without (blue) and with pre-amplification (red) are shown in Fig. 10. Meanwhile, the optimized bias current is enlarged from 40 mA (without pre-amplification) to 50 mA (with pre-amplification) under the same injection-locking power of 0 dBm. In comparison with the receiving power sensitivity of −4 dBm only detectable under back-to-back transmission without pre-amplification, the back-to-back receiving power sensitivity is reduced to −8.5 dBm after pre-amplification. In particular, the 36-Gbit/s 16-QAM OFDM transmission over 25-km SMF becomes achievable with its BER less than 3.8 × 10−3 at a receiving power of −3 dBm. To date, this is the premier demonstration on directly modulated 16-QAM OFDM transmission over 25-km with the colorless WRC-FPLD after injection-locking. In experiment, the WRC-FPLD is operated at linear modulation region with an optimized DC bias current of 50 mA and an injection power of 0 dBm. When directly modulating by the pre-amplified 16-QAM OFDM data with 1.45-V peak-to-peak amplitude, the 12-dB sinusoidal-wave gain cannot be applied to the broadband signal amplification as the power gain is broadly distributed over the whole bandwidth of 9 GHz. That is, the 16-QAM OFDM does not receive such large gain after amplification to reduce the received power penalty accordingly.

 figure: Fig. 10

Fig. 10 Upper: the (i) original and (ii) pre-amplified 16-QAM OFDM based direct modulation setup for the colorless WRC-FPLD. Lower: the BER of the 16-QAM OFDM data with and without pre-amplification carried by the injection-locked WRC-FPLD vs. receiving power after back-to-back and 25-km transmissions.

Download Full Size | PDF

The pre-amplified electrical 36-Gbit/s 16-QAM OFDM data also releases a wide operation range on bias current and injection power for the WRC-FPLD to achieve the FEC required BER. The injection power range greatly extends up to 18 dB (from −15 to 3 dBm) when biasing the WRC-FPLD at 60 mA. Alternatively, the biasing range extensively broadens from 35 to 60 mA by injection-locking the WRC-FPLD at 0 dBm. The optimized BER is significantly reduced from 3.4 × 10−3 (without pre-amplifier) to 2.1 × 10−4 (with pre-amplifier), as obtained by slightly enlarging the bias current from 40 to 50 mA at an injection power of 0 dBm. (See Fig. 11.)This change on bias current for the WRC-FPLD is to avoid the 16-QAM OFDM data from distortion during the direct modulation.

 figure: Fig. 11

Fig. 11 The 3D contour of the received BER for 36 Gbit/s 16-QAM OFDM transmission without and with pre-amplification.

Download Full Size | PDF

After implementing the pre-amplified 16-QAM OFDM data and optimizing the injection-locked WRC-FPLD operating condition, the BER performances of the received 16-QAM OFDM data with different data bandwidths transmitted under back-to-back and 25-km SMF cases are shown in Fig. 12. When comparing with the Fig. 8, the receiving power sensitivity of the pre-amplified 16-QAM OFDM data under back-to-back transmission at 20, 24, 28, 32 and 36 Gbit/s is improved to −12, −11.5, −10, −9.5 and −8 dBm, respectively. With pre-amplification, the power penalty between back-to-back and 25-km SMF transmissions increases from 1 to 3.7 dB when transmitting the 16-QAM OFDM data with its bandwidth extending from 5 to 9 GHz. Such a power penalty is still caused by the dispersion of the 25-km SMF. The penalty value has significantly decreased by almost 0.5 dB due to the SNR and ER improvements with the electrical 16-QAM OFDM data pre-amplification. Enlarging the power gain of the electrical pre-amplifier may further improve the receiving sensitivity of the transmitted QAM OFDM data; however, which requires a highly biased WRC-FPLD to avoid the waveform clipping. The trade-off between increasing biased current and reducing injection efficiency occurs as the inherent mode nature strengthens accordingly.

 figure: Fig. 12

Fig. 12 (a) BER performance of the pre-amplified 16-QAM OFDM data at 20-36 Gbit/s transmitted by the injection-locked WRC-FPLD and (b) the corresponding power penalty.

Download Full Size | PDF

3.4 Direct 64-QAM OFDM encoding of the injection-locked WRC-FPLD

To enlarge the spectral usage efficiency, the QAM-level is up-grated from 16 to 64 so that the maximal raw data rate of the OFDM data is increased from 36 to 42 Gbit/s with narrowing the required bandwidth from 9 to 7 GHz concurrently. The transmission performance of the pre-amplified 64-QAM OFDM delivered by the 10-GHz TO-56-can packaged WRC-FPLD optimized at a DC bias of 50 mA and an injection-locking power of 0 dBm is shown in Fig. 13.

 figure: Fig. 13

Fig. 13 BER performance of the pre-amplified 64-QAM OFDM data with bandwidth ranged from 5 to 8 GHz.

Download Full Size | PDF

Note that the clear constellation plot of the decoded 64-QAM OFDM data is obtained by enlarging the injection power from −12 to 0 dBm, which effectively reduces its EVM from 12.5% to 8.5%. By upgrading the QAM level from 16 to 64, the requested SNR criterion for matching the FEC-limited BER at 3.8 × 10−3 also increases from 15.2 to 21.5 dB, which is calculated by [36],

BER=2(11M){erfc[3SNR2(M1)]+erfc[33SNR2(M1)]}log2M,
where M denotes the QAM-level. As a result, all of the receiving power sensitivities for the 64-QAM OFDM data at different bandwidths are slightly worse than that for the 16-QAM OFDM data. The receiving power sensitivity of the back-to-back transmitted 64-QAM OFDM data with its bandwidth extending from 5 to 8 GHz is degraded from −10 to −6.5 dBm. Note that the 64-QAM OFDM data covering 8-GHz bandwidth fails to enter the FEC criterion after 25-km SMF transmission. This sets a limitation on the injection-locked colorless WRC-FPLD with its allowable bandwidth of up to 7 GHz for carrying the 64-QAM OFDM data at a receiving power of −2 dBm, which is corresponding to a maximal raw data rate of 42 Gbit/s. In our work, the WRC-FPLD is called colorless or universal source due to that all channels can use the same device made from same wafer of identical epitaxial and fabricating recipe. Although the wavelength of the WRC-FPLD still needs to be controlled by the master source, the WRC-FPLD with wide injection-locking range, dense longitudinal modes and broad gain spectrum to cover numerous DWDM channels. The WRC-FPLD requires same processes as the typical FPLD, which makes itself cost-effective as compared with other sources proposed for DWDM-PON. Regarding the expense raised from the injection source, the WRC-FPLD can take over the tunable laser to serve as a coherent master for practical application.

4. Conclusion

By replacing the package of the colorless WRC-FPLD from a typical 4-GHz TO-56-can to a 10-GHz TO-56-can, the overall frequency bandwidth at −6 dB decay for the packaged colorless WRC-FPLD can be extended from 5 to 9 GHz. Such a new package not only extends the modulation response of the injection-locked WRC-FPLD but also reduces the throughput intensity declination induced by the intense injection-locking. By injection-locking and directly modulating the 10-GHz TO-56-can packaged colorless WRC-FPLD transmitter, the 16-QAM OFDM transmission at 36 Gbit/s over 25-km SMF is demonstrated. Under back-to-back transmission, the trade-off among the declined frequency response, the suppressed RIN and the enhanced SNR of the injection-locked WRC-FPLD is compromised to optimize the transmitted 16-QAM OFDM data. The BER of the 16-QAM OFDM transmission is minimized with intense injection-locking such that the RIN band up-shifts and attenuates within the data bandwidth. The 3D BER contours of the 16-QAM OFDM data at raw data rates of 32 and 36 Gbit/s are optimized by operating the colorless WRC-FPLD at a DC bias of 40 mA and an injection power of 0 dBm, which results in the lowest BER of 1.3 × 10−3 and 3.4 × 10−3, respectively. After 25-km SMF transmission, the chromatic dispersion and propagation loss limits the maximal bit-rate to 26 Gbit/s with its BER below the FEC criterion. With pre-amplifying the electrical 16-QAM OFDM data, the received SNR of the optical 16-QAM OFDM data essentially enhances, and the injection-locked WRC-FPLD transmitter exhibits a wide operational range on bias current and injection power. The optimized BER of the decoded 16-QAM OFDM data after back-to-back transmission is significantly reduced to 2.1 × 10−4 (with pre-amplification). To increase the spectral usage efficiency and further enlarge the raw data rate of the QAM OFDM data, the 10-GHz To-56-can packaged WRC-FPLD successfully delivers the pre-amplified 64-QAM OFDM transmission over 25-km SMF at a raw bit rate of 42 Gbit/s with allowable bandwidth of 7 GHz under the FEC-limited BER criterion.

Acknowledgments

The authors thank the Ministry of Science and Technology, Taiwan, Republic of China, for financially supporting this research under grants NSC 101-2221-E-002-071-MY3 and MOST 103-2221-E-002-042-MY3.

References and links

1. B. J. Dixon, R. D. Pollard, and S. Iezekiel, “Orthogonal frequency-division multiplexing in wireless communication systems with multimode fiber feeds,” IEEE Trans. Microw. Theory Tech. 49(8), 1404–1409 (2001). [CrossRef]  

2. J. Lowery, L. B. Y. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol. 25(1), 131–138 (2007). [CrossRef]  

3. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]  

4. N. Cvijetic, “OFDM for next-generation optical access networks,” J. Lightwave Technol. 30(4), 384–398 (2012). [CrossRef]  

5. J. Yu, M.-F. Huang, D. Qian, L. Chen, and G.-K. Chang, “Centralized lightwave WDM-PON employing 16-QAM intensity modulated OFDM downstream and OOK modulated upstream signals,” IEEE Photon. Technol. Lett. 20(18), 1545–1547 (2008). [CrossRef]  

6. W. Chow, C. H. Yeh, C. H. Wang, F. Y. Shih, and S. Chi, “Signal remodulation of OFDM-QAM for long reach carrier distributed passive optical networks,” IEEE Photon. Technol. Lett. 21(11), 715–717 (2009). [CrossRef]  

7. Y.-C. Chi, Y.-C. Li, H.-Y. Wang, P.-C. Peng, H.-H. Lu, and G.-R. Lin, “Optical 16-QAM-52-OFDM transmission at 4 Gbit/s by directly modulating a coherently injection-locked colorless laser diode,” Opt. Express 20(18), 20071–20077 (2012). [CrossRef]   [PubMed]  

8. J. M. Tang, P. M. Lane, and K. A. Shore, “High-speed transmission of adaptively modulated optical OFDM signals over multimode fibers using directly modulated DFBs,” J. Lightwave Technol. 24(1), 429–441 (2006). [CrossRef]  

9. T. Tanaka, M. Nishihara, T. Takahara, L. Li, Z. Tao, and J. C. Rasmussen, “50 Gbps Class Transmission in Single Mode Fiber using Discrete Multi-tone Modulation with 10G Directly Modulated Laser,” in Optical Fiber Communication / National Fiber Optic Engineers Conference (OFC/NFOEC), (Optical Society of America, Los Angeles, California, 2012) Paper OTh4G.3. [CrossRef]  

10. K. Jung, S. K. Shin, C.-H. Lee, and Y. C. Chung, “Wavelength-division-multiplexed passive optical network based on spectrum-slicing techniques,” IEEE Photon. Technol. Lett. 10(9), 1334–1336 (1998). [CrossRef]  

11. G. Maier, M. Martinelli, A. Pattavina, and E. Salvadori, “Design and cost performance of the multistage WDM-PON access networks,” J. Lightwave Technol. 18(2), 125–143 (2000). [CrossRef]  

12. W. R. Lee, M. Y. Park, S. H. Cho, J. Lee, C. Kim, G. Jeong, and B. W. Kim, “Bidirectional WDM-PON based on gain-saturated reflective semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 17(11), 2460–2462 (2005). [CrossRef]  

13. G.-R. Lin, T.-K. Cheng, Y.-C. Chi, G.-C. Lin, H.-L. Wang, and Y.-H. Lin, “200-GHz and 50-GHz AWG channelized linewidth dependent transmission of weak-resonant-cavity FPLD injection-locked by spectrally sliced ASE,” Opt. Express 17(20), 17739–17746 (2009). [CrossRef]   [PubMed]  

14. T. Duong, N. Genay, P. Chanclou, B. Charbonnier, A. Pizzinat, and R. Brenot, “Experimental demonstration of 10 Gbit/s upstream transmission by remote modulation of 1 GHz RSOA using Adaptively Modulated Optical OFDM for WDM-PON single fiber architecture” in European Conference on Optical Communication (ECOC), (Institution of Engineering and Technology, Brussels, Belgium,) pp. 39–49. [CrossRef]  

15. R. P. Giddings, E. Hugues-Salas, X. Q. Jin, J. L. Wei, and J. M. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gbit/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. 22(11), 745–747 (2010). [CrossRef]  

16. H. Yeh, C. W. Chow, Y. F. Wu, and H. Y. Chen, “Demonstrations of 10 and 40Gbps upstream transmissions using 1.2 GHz RSOA-based ONU in long-reach access networks,” Opt. Fiber Technol. 18(2), 63–67 (2012). [CrossRef]  

17. Z. Xu, Y.-J. Wen, W.-D. Zhong, C.-J. Chae, X.-F. Cheng, Y. Wang, C. Lu, and J. Shankar, “High-speed WDM-PON using CW injection-locked Fabry-Pérot laser diodes,” Opt. Express 15(6), 2953–2962 (2007). [CrossRef]   [PubMed]  

18. C.-L. Tseng, C.-K. Liu, J.-J. Jou, W.-Y. Lin, C.-W. Shih, S.-C. Lin, S.-L. Lee, and G. Keiser, “Bidirectional transmission using tunable fiber lasers and injection-locked Fabry-Pérot laser diodes for WDM access networks,” IEEE Photon. Technol. Lett. 20(10), 794–796 (2008). [CrossRef]  

19. G.-R. Lin, H.-L. Wang, G.-C. Lin, Y.-H. Huang, Y.-H. Lin, and T.-K. Cheng, “Comparison on injection-locked Fabry–Perot laser diode with front-facet reflectivity of 1% and 30% for optical data transmission in WDM-PON system,” J. Lightwave Technol. 27(14), 2779–2785 (2009). [CrossRef]  

20. C.-H. Yeh, C.-W. Chow, H.-Y. Chen, J.-Y. Sung, and Y.-L. Liu, “Demonstration of using injection-locked Fabry-Perot laser diode for 10 Gbit/s 16-QAM OFDM WDM-PON,” Electron. Lett. 48(15), 940–942 (2012). [CrossRef]  

21. Z. Xu, Y. Yeo, X. Cheng, and E. Kurniawan, “20-Gb/s injection locked FP-LD in a wavelength-divisionmultiplexing OFDM-PON,” in Proc. Optical Fiber Communication Conference (2012), Los Angeles, USA, Paper OW4B.3. [CrossRef]  

22. H.-Y. Chen, C.-H. Yeh, C.-W. Chow, J.-Y. Sung, Y.-L. Liu, and J. Chen, “Investigation of using injection locked Fabry–Perot laser diode with 10% front-facet reflectivity for short-reach to long-reach upstream PON access,” IEEE Photon. J. 5(3), 7901208 (2013). [CrossRef]  

23. Y.-S. Liao, H.-C. Kuo, Y.-J. Chen, and G.-R. Lin, “Side-mode transmission diagnosis of a multichannel selectable injection-locked Fabry-Perot Laser Diode with anti-reflection coated front facet,” Opt. Express 17(6), 4859–4867 (2009). [CrossRef]   [PubMed]  

24. G.-R. Lin, Y.-S. Liao, Y.-C. Chi, H.-C. Kuo, G.-C. Lin, H.-L. Wang, and Y.-J. Chen, “Long-cavity Fabry–Perot laser amplifier transmitter with enhanced injection-locking bandwidth for WDM-PON application,” J. Lightwave Technol. 28(20), 2925–2932 (2010). [CrossRef]  

25. W.-D. Xiong, W.-D. Zhong, and H. Kim, “A broadcast-capable WDM-PON based on polarization-sensitive Weak-resonant-cavity Fabry–Perot laser diodes,” J. Lightwave Technol. 30(3), 355–361 (2012). [CrossRef]  

26. I.-C. Lu, C.-C. Wei, W.-J. Jiang, H.-Y. Chen, Y.-C. Chi, Y.-C. Li, D.-Z. Hsu, G.-R. Lin, and J. Chen, “20-Gbps WDM-PON transmissions employing weak-resonant-cavity FPLD with OFDM and SC-FDE modulation formats,” Opt. Express 21(7), 8622–8629 (2013). [CrossRef]   [PubMed]  

27. M.-C. Cheng, Y.-C. Chi, Y.-C. Li, C.-T. Tsai, and G.-R. Lin, “Suppressing the relaxation oscillation noise of injection-locked WRC-FPLD for directly modulated OFDM transmission,” Opt. Express 22(13), 15724–15736 (2014). [CrossRef]   [PubMed]  

28. T.-T. Shih, P.-H. Tseng, Y.-Y. Lai, and W.-H. Cheng, “Compact TO-CAN header with bandwidth excess 40 GHz,” J. Lightwave Technol. 29(17), 2538–2544 (2011). [CrossRef]  

29. T.-T. Shih, P.-H. Tseng, Y.-Y. Lai, and W.-H. Cheng, “A 25 Gbit/s transmitter optical sub-assembly package employing cost-effective TO-CAN materials and processes,” J. Lightwave Technol. 30(6), 834–840 (2012). [CrossRef]  

30. Y.-C. Chi, Y.-C. Li, and G.-R. Lin, “Specific jacket SMA-Connected TO-Can package FPLD transmitter with direct modulation bandwidth beyond 6 GHz for 256-QAM single or multi subcarrier OOFDM up to 15 Gbit/s,” J. Lightwave Technol. 31(1), 1079–1087 (2013). [CrossRef]  

31. R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18(6), 976–983 (1982). [CrossRef]  

32. H. Mogensen, Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron. 21, 784–793 (1985).

33. K. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron. 39(10), 1196–1204 (2003). [CrossRef]  

34. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1997), Chap. 5.

35. Y.-C. Li, Y.-C. Chi, M.-C. Cheng, I.-C. Lu, J. Chen, and G.-R. Lin, “Coherently wavelength injection-locking a 600-μm long cavity colorless laser diode for 16-QAM OFDM at 12 Gbit/s over 25-km SMF,” Opt. Express 21(14), 16722–16735 (2013). [CrossRef]   [PubMed]  

36. J. Lu, K. B. Letaief, J. C.-I. Chuang, and M. L. Liou, “M-PSK and M-QAM BER computation using signal-space concepts,” IEEE Trans. Commun. 47(2), 181–184 (1999). [CrossRef]  

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1 The pictures and illustrations of the 10-GHz TO-56-can packaged WRC-FPLD.
Fig. 2
Fig. 2 The 10-GHz TO-56-can/jacket-SMA packaged WRC-FPLD with the self-designed temperature control system.
Fig. 3
Fig. 3 The testing bench of the injection-locked WRC-FPLD for transmitting the QAM OFDM data delivered by the AWG (a) without and (b) with pre-amplifier. AWG: arbitrary waveform generator, DSO: digital signal oscilloscope, SMF: single mode fiber. PD: photodetector, Amp: amplifier, TL: tunable laser.
Fig. 4
Fig. 4 (a) The frequency response of the WRC-FPLD with low-speed TO-can package (black dashed line) and 10 GHz TO-can package (red solid line). Inset: The RF spectrum of the 16-QAM OFDM data with various bandwidth carried by the WRC-FPLD, and (b) the simulated frequency responses of the WRC-FPLD obtained at different injection powers.
Fig. 5
Fig. 5 (a) The measured frequency responses of the injection-locked WRC-FPLD with 4-GHz and 10-GHz TO-can packages, and the RIN spectra of the 10-GHz TO-can packaged and injection-locked WRC-FPLD at different (b) injection powers and (c) bias currents.
Fig. 6
Fig. 6 (b) The constellation plots of the 16-QAM OFDM data received at free-running and injection-locking cases and (a) the BERs of the 16-QAM OFDM data at raw data rate of 20-36 Gbit/s transmitted by the WRC-FPLD at different injection-locking powers.
Fig. 7
Fig. 7 The measured frequency response, RIN and SNR behaviors for 20-Gbit/s (upper) and 36-Gbit/s (lower) transmissions with injection powers ranged from −12 to −3 dBm (left) and from −3 to 3 dBm (right).
Fig. 8
Fig. 8 The 3D contour of the received BER for (a) 32 Gbit/s and (b) 36 Gbit/s 16-QAM OFDM transmissions at different bias currents and injection powers.
Fig. 9
Fig. 9 (a) BER vs. receiving power of the injection-locked WRC-FPLD output under back-to-back transmission and (b) the BER vs. raw data rate of the 16-QAM OFDM data after back-to-back and 25-km transmissions.
Fig. 10
Fig. 10 Upper: the (i) original and (ii) pre-amplified 16-QAM OFDM based direct modulation setup for the colorless WRC-FPLD. Lower: the BER of the 16-QAM OFDM data with and without pre-amplification carried by the injection-locked WRC-FPLD vs. receiving power after back-to-back and 25-km transmissions.
Fig. 11
Fig. 11 The 3D contour of the received BER for 36 Gbit/s 16-QAM OFDM transmission without and with pre-amplification.
Fig. 12
Fig. 12 (a) BER performance of the pre-amplified 16-QAM OFDM data at 20-36 Gbit/s transmitted by the injection-locked WRC-FPLD and (b) the corresponding power penalty.
Fig. 13
Fig. 13 BER performance of the pre-amplified 64-QAM OFDM data with bandwidth ranged from 5 to 8 GHz.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

dN(t) dt = η i I(t) q N(t) τ s v g gS(t), dϕ(t) dt = 1 2 αΓ v g gκ ( S inj S(t) ) 1/2 sin(Δϕ(t))Δ w inj , dS(t) dt =Γ v g gS(t) S(t) τ p +2κ ( S inj S(t) ) 1/2 cos(Δϕ(t)),
ϕ B = sin 1 ( Δ ω inj κ 1+ α 2 S B S inj ) tan 1 α= tan 1 α cos( ϕ B )= 1 1 α 2
jωn(ω)= η i i(ω) q n(ω) τ s v g [ g B s(ω)+g' S B n(ω)+g'n(ω)s(ω) ], jωs(ω)=Γ v g [ g B s(ω)+g' S B n(ω)+g'n(ω)s(ω) ] s(ω) τ p + κ 1+ α 2 S inj S B [ s(ω) S B ]),
H(ω)= s(ω) i(ω) = η i Γ v g g' S B qV { ω 2 +jω( 1 τ s + v g g' S B κ 1+ α 2 S inj S B )+[ v g g' S B τ p κ 1+ α 2 S inj S B ( 1 τ s + v g g' S B ) ] } ,
RIN= 16 (Δν) ST { η i Γ v g g' q ( I B I th ' )+ κ 1+ α 2 S inj S B [ η i Γ v g g' τ p q ( I B I th ' )+ 1 τ s ] } 2 τ ΔN 2 + 2hC λ P 0 [ η 0 ( I B + I th ' ) ( I B I th ' ) +(1 η 0 ) ],
BER= 2(1 1 M ){ erfc[ 3SNR 2(M1) ]+erfc[ 3 3SNR 2(M1) ] } log 2 M ,
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.