Multi-Dimensional Formats and Transceiver Architectures for Direct Detection With Analysis on Inter-Polarization Phase Modulation

In this paper, we numerically demonstrate the advantage of utilizing continuous amplitude and phase modulation in super-oscillation focusing lens design. Numerical results show that compared with simple binary amplitude modulation, continuous amplitude and phase modulation can greatly improve the super-oscillation focusing performance by increasing the central lobe intensity and the ratio of its energy to the total energy, reducing the sidelobe intensity, and substantially extending the field of view. Our study also reveals the role of phase distribution in reducing the spatial frequency bandwidth of the super-oscillation optical field on the focal plane. Based on continuous amplitude and binary phase modulation, a lens was designed with double layer metal slit array for wavelength of 4.6 µm. COMSOL is used to carry out the 2D simulation. The lens focal length is 40.18λ and the focal spot FWHM is 0.308λ. Two largest sidelobes are located right next to the central lobe with intensity about 40% of the central lobe intensity. Except for the two sidelobes, other sidelobes have intensity less than 25% of the central lobe intensity, which leads to a clear field of view on the whole focal plane.

The performance of optical inter‐satellite communications using microwave photonics technologies employing intensity modulation with direct detection (IMDD) and phase modulation (PM) with interferometric detection are investigated and demonstrated with a numerical example. The theoretical model considering the saturated gain and amplifier spontaneous emission noise of optical booster amplifier and optical preamplifier is constructed for both architectures. Furthermore, the authors compare the performance of PM with interferometric detection to optimum biased IMDD in terms of radio frequency (RF) gain, RF noise figure and compression dynamic range (CDR). The numerical results show that the PM with interferometric detection can achieve better RF gain, RF noise figure and CDR than the optimum biased IMDD link as the laser output power is lower than 14.34, 12.45 and 4.2 dBm, respectively.

Phase modulation with an analytic signal, which is a Gaussian random process, is examined in order to determine the amount of spectrum conservation that may be achieved by using single-sideband phase modulation (SSB-PM) rather than conventional phase modulation (PM). The autocorrelation function is derived and found to be an analytic signal in terms of the autocorrelation function of the actual modulating signal and its Hilbert transform. When the modulating signal strength is very low, the sideband spectral distribution is the same as that of the actual modulating signal or single-sideband amplitude modulation. As the modulating signal mean-square value is increased, the sideband spectrum broadens and approaches a Gaussian shape. The average power output of an SSB-PM system increases exponentially with input modulating signal strength, while the carrier power remains constant. For the same modulating signal mean-square value, a greater fraction of power is in the one sideband of an SSB-PM system than in the two sidebands of conventional PM. Single-sideband phase or frequency modulation always effectuates spectrum conservation in the continuum when it is compared with conventional phase or frequency modulation on the basis of equal relative sideband power. A Fourier transform computer program is used to generate SSB-PM spectral distributions with varying modulating signal mean-square values, when the modulating signal spectrum is a low-pass rectangular spectrum, a narrowband pass spectrum, and the shape of an average voice spectrum. These examples illustrate the power series formulation of the output spectrum as well as the theoretical analysis of bandwidth.

A longitudinal binary phase modulator (LBPM) based on the KTa 1‐x Nb x O 3 (KTN) crystal is proposed for laser speckle reduction. The actuation voltages are applied by two series of transparent electrodes consisted of interdigitated fingers. By sequentially changing the phase modulation depth of the LBPM pixel during the detector integration time, speckle reduction can be achieved. Due to the large Kerr coefficient of the KTN crystal, the LBPM is expected to work at low voltage levels.

We propose a dual modulation scheme that integrates phase and intensity modulation, enabled by a directly modulated laser (DML) and an electro-absorption modulator (EAM). Unlike conventional intensity modulation schemes, we employ the frequency chirp of the DML for phase modulation through the time integral. The EAM is utilized for intensity modulation due to its advantages in frequency chirp and extinction ratio performance. To address the phase distortion induced by chromatic dispersion (CD) and bandwidth constraints, we derive a phase damage formula and propose a modified equalization algorithm based on the second-order Volterra equalizer (VE), which can effectively mitigate the differential phase interference. We experimentally validate the feasibility of generating, transmitting, and recovering the dual-modulation signals with high spectral efficiency (SE). Results indicate that compared with the traditional single-stage modulation schemes that employ only a DML or an electro-absorption modulated laser (EML), the dual modulation scheme achieves the maximum transmission rate of 84 Gb/s. Moreover, after applying the second-order VE, the system exhibits strong robustness to variations in DML chirp values, eliminating the need for precise measurement of DML chirp parameters. Additionally, the bit error rate (BER) for BtB and 25-km SSMF transmission exhibits negligible differences. The proposed dual modulation scheme enhances the transmission rate and SE and ensures high compatibility with existing passive optical networks (PONs), providing a cost-effective solution for next-generation optical access networks.

A chromatic dispersion (CD) compensation scheme for analog optical link is introduced and experimentally demonstrated based on parallel modulators module, which composes of electro-optic phase and intensity modulators. The dispersion-induced power fading is adequately compensated over operational bandwidth of 0-18 GHz using our scheme. CD-tolerant transmission over 24.45-km single mode fiber has been achieved. Crucial parameters such as gain and spur free dynamic range (SDFR) are also analyzed to evaluate the CD effect on the analog optical links. Compared with conventional links based on double-sideband (DSB) intensity modulation, the proposed scheme with hybrid modulation improves the link gain and SFDR up to 35 dB and 33 dB· Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2/3</sup> , respectively.

We report on the operation and performance of a novel electrooptic polarization scrambler that is capable of generating any desired combination of optical phase and polarization modulation. The scrambler comprises a dual-drive Mach-Zehnder-type intensity modulator on lithium niobate and an external microoptic polarization splitter which combines the two complementary outputs of the integrated-optic intensity modulator in orthogonal polarization states. The modulation indexes of the sinusoidal phase and polarization modulation in the output light can be varied independently of each other via the amplitudes and phases of the two drive voltages to the Mach-Zehnder modulator. The scrambler has a 3-dB modulation bandwidth of 14 GHz and operates in the 1.5-1.6-/spl mu/m wavelength range with an overall fiber-to-fiber insertion loss of less than 5 dB. At 5 GHz modulation frequency and electric drive powers between 390-2030 mW, we demonstrate phase-chirped and chirp-free depolarization with a residual degree of polarization of less than 0.02 and continuously variable phase modulation to 2.3-rad peak phase deviation.

We introduce a three-dimensional modulation format using a Stokes-vector direct-detection system, where a pulse amplitude modulation (PAM) signal is polarization multiplexed with a quadrature amplitude modulation (QAM) signal. The phase reference of the PAM signal enables the retrieval of the phase information of the QAM signal using a Stokes vector receiver (SVR). A dual-polarization in-phase–quadrature modulator is employed to generate QAM-PAM optical signals with chromatic dispersion precompensation. We show direct detection of dual-polarization 16QAM-PAM2 and 16QAM-PAM4 signals delivering 280 and 336 Gb/s (net bit rate 233 and 280 Gb/s) below the soft-decision forward error correction threshold of 2 $\times$ 10 $^{-2}$ at 320 and 80 km, respectively. In addition, we study system performance at different modulation formats and symbol rates. Our findings indicate that increasing the order of modulation formats of the QAM signal is better than increasing that of the PAM signal to achieve the same bit rate. Finally, the performance of a 56 Gbaud 16QAM signal with PAM2 modulation on one polarization and a 56 Gbaud 16QAM signal with a pilot carrier on the orthogonal polarization detected with an SVR is experimentally investigated.

We presented a concept of converged coexistence (CC) access network and generate, and test model is demonstrated for optimization of channel launch power PTODN in the distribution network which subsequently confirm power budget class of NG-PON2 in this paper. Multiplexing of wavelength and time (TWDM) technology is incorporated for multichannel NG-PON2 configurations for 5G, internet-of-things (IoT) applications, and fiber-to-the-x (FTTX) services. CC NG-PON2 symmetric configuration supporting 2.5 and 10 Gbps channels are analyzed and compared in the sight of channel nonlinear impairments includes Kerr-effect (γ) spanning from self phase modulation (SPM) and cross-phase modulation (CPM), chromatic dispersion (CD), and four wave mixing (FWM) in worst-case scenario. Intensity modulation (IM) technique incorporated before multiplexing the D/S channels by coexisting element (CEx) and coupled to wavelength routed (WR) optical distribution network (ODN). U/S channels are routed using wavelength select (WS) ODN. ODN is implemented using G.652 non zero dispersion shift (NZ-DSF) single-mode (SM) fiber. Multi-channel spectrum envelope propagating in either direction is optimized to PTODN = 3/5/7/9 dBm and 4 dBm, respectively. The theoretical modeling and simulative results confirms the proposed network configuration supports incremental receiver sensitivity (Rxs) as −42.19/−42/−39.75/−37.97 dBm and −35.45/−35.38/−33.45/0.38/−42 dBm for λ1 2.5 Gbps and λ8 10 Gbps TWDM and PtP WDM channels, respectively, for all-class networks supporting splitter configuration ratio of 640 at 50 km mitigating effect of channel nonlinearities like CD, SPM, cross-phase modulation (XPM), and FWM for λ8 10 Gbps channel.

Acoustic holography underpins the number of modern acoustics applications. The usage of multi-focal acoustic holograms with phased array transducers (PATs) in ultrasonic tactile displays and acoustic levitation are increasing, and achieving a high-quality hologram are of significant interest. Inspired by the latest optical hologram optimizer, we developed a novel acoustic hologram optimizer for PATs called Diff-PAT [T. Fushimi, K. Yamamoto, and Y. Ochiai, “Acoustic hologram optimisation using automatic differentiation”]. Diff-PAT is based on a gradient-descent algorithm and automatic differentiation. The performance of Diff-PAT was numerically evaluated using three array configurations and it achieved superior accuracy over the conventional optimizers. For example, when two focal points are generated with 196 ultrasonic (40 kHz) transducers; the state of art optimizer (with phase and amplitude modulation) based on Eigensolver has an average error of 4.07 % where Diff-PAT (with only phase modulation) achieve average error of 0.0174%. These results show that amplitude and phase modulation may not be necessary for PATs to be successful. Furthermore, we demonstrate the versatility of Diff-PAT by applying it to binary acoustic holograms, simultaneous modulation of acoustic amplitude and phase at the target plane, and phase plates. [Work supported by Pixie Dust Technologies, Inc., Diff-PAT is patent pending (JP2020-167367A).]

High-speed PAM-4 is a promising way for future low-cost short-reach fibre communications. However, for 1550 nm transmission with the lowest attenuation for standard single-mode fibre (SSMF), the fibre dispersion-induced inter-symbol interference (ISI) becomes non-linear in direct detection. Dispersion pre-compensation at the transmitter side is necessary to avoid such non-linear ISI. Different from previous methods to generate the vector signal from dispersion pre-compensation using IQ modulators, in this study a digital dispersion pre-compensation (DDPC) scheme based on an intensity modulator (IM) plus a phase modulator (PM) is studied. Taking into account the digital-to-analogue converter (DAC) bandwidth limit on the vector signal generation, anti-aliasing filtering on both the magnitude signal and the phase signal should be applied. The error rate performance of the IM-PM based DDPC scheme is analysed in detail using numerical simulations. For 50 Gb/s PAM-4 transmission at 1550 nm over SSMF, over 50 km fibre transmission can be supported if the two DACs have enough bandwidth larger than 17.5 GHz. If the DAC bandwidth is limited to 15 GHz, it is also possible to transmit over 20 km SSMF. Meanwhile, it is verified that practical 5-bit DAC resolution is enough for the IM-PM based DDPC scheme to work for a wide range of SSMF lengths.

A nonlinear circuit with periodic operation, such as a mixer and oscillator, can be modeled as a linear periodic time‐varying circuit by assuming a small‐signal input and output. This paper presents a method by which the transfer function of such a periodic time‐varying circuit can be decomposed into phase and amplitude modulation components. Assuming a small input, the phase modulation component can be interpreted as a result of narrow‐band phase modulation with a small modulation index. Thus, it suffices to consider only the first sideband. As regards the spectrum of the amplitude modulated signal, it suffices to consider only the first sideband, regardless of the modulation index. Thus, the two spectra corresponding to the upper and lower sidebands around the carrier are decomposed into narrow‐band phase and amplitude modulation components, and the transfer function can be decomposed into phase and amplitude modulation components. By this method, it becomes possible to decompose the noise of the mixer and the oscillator into the amplitude noise and the phase, or to simulate AM‐PM conversion. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(7): 29–37, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1105

Laser phase noise conversion to intensity noise due to fiber chromatic dispersion is analyzed by deriving the noise power spectral density. Theory predicts that the phase-modulation-amplitude-modulation conversion noise is a principal limiting factor of the gigabit-per-second nonregenerative transmission using an external modulator when the linewidth of the laser transmitter is above several tens of megahertz and the total chromatic dispersion of fibers exceeds several thousand picoseconds per nanometer. This fact is confirmed by the 2.4-Gb/s transmission experiments using multiple inline Er-doped fiber amplifiers. The system penalty due to this noise in the intensity modulation and direct detection (IM-DD) optical transmission using an external modulator is evaluated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

For the first time, we experimentally demonstrate a 400-Gb/s [4×100-Gb/s wavelength-division multiplexing (WDM)] pulse-amplitude-modulation-4 (PAM-4) transmission based on free space optics (FSO) utilizing the polarization modulation (PolM) and direct detection (DD) scheme. Each WDM channel comprises a polarization modulator, a polarizing beam splitter (PBS), and two photodetectors (PDs). Four wavelengths each carrying a 100-Gb/s PAM-4 signal (aggregate 400 Gb/s) are transmitted over the free space. At the receiver side, the PBS separates the two orthogonal polarizations, and then, the two polarized signals are detected by two PDs. Then, the two detected signals are combined by a subtractor, followed by digital signal processing (DSP). The PolM-DD system can achieve higher data rate while maintaining the required forward-error-correction (FEC) threshold compared with intensity modulation and direct detection (IM-DD) scheme. Moreover, owing to the stable polarization state in the free space and the mitigation of the common mode noise by the subtraction, the PolM-DD system provides enhanced tolerance to the amplitude fluctuations attributable to weather turbulence, which makes it more reliable than the conventional IM-DD FSO system. To the best of our knowledge, this is the first experimental demonstration of a 400-Gb/s FSO system using the PolM-DD scheme with the transmission distance of 1.2 m.

The performance of intensity modulation (IM) with direct detection (DD) transmission systems is enhanced through a novel combination of multidimensional coding, Nyquist pulse shaping, and electronic dispersion compensation (EDC) at the transmitter using a finite impulse response (FIR) filter. A 24- dimensional (24D) extended Golay binary code effectively transforms each incoming 12-bit message into a 24-bit codeword, achieving a coding efficiency of 0.5 bits per symbol for a 56 Gb/s on-off keying (OOK) transmission over 80 km of single mode fiber. While this encoding process introduces a 50% overhead, the required bandwidth is maintained at 56 GHz through doubling the symbol rate and the application of Nyquist pulse shaping with a raised cosine (RC) profile and a roll-off factor of zero, resulting in a flat power spectral density. This flat distribution contrasts with standard OOK transmission at 56 Gb/s with a roll-off factor of 1.0, where signal power is predominantly concentrated in the lower frequency range. One of the key advantages of the 24D Golay code is its substantial error correction capability. However, the benefits of this multidimensional coding and Nyquist pulse shaping extend beyond error correction. It is shown that, while both the proposed and standard OOK methods exhibit comparable performance in a white Gaussian noise channel at back-to-back, they differ significantly under frequency selective power fading conditions caused by the interplay of chromatic dispersion (CD) and direct detection. The misalignment between the frequency notches introduced by the FIR pre-EDC and those inherent in the channel response, especially severe at lower frequencies, favors transmission schemes with a flat power spectral density, like the 24D Golay-coded Nyquist pulses.