Showing papers in "Journal of Lightwave Technology in 1987"

Coupled-mode theory of optical waveguides

Abstract: The coupled-mode theory of parallel waveguides is derived from a variational principle for the propagation constant of the waveguide-wave solution using a superposition of the uncoupled modes as a trial field. The nonorthogonality of modes as emphasized by Hardy and Streifer is part of this formalism as well. The coupling Coefficients agree with those of Hardy and Streifer derived for TE modes of loss-free guides. For TM modes the coupling coefficients differ slightly for the simpler trial solution and agree exactly for a different trial solution. The simpler trial solution gives results closer to the exact solution. Conventional coupled-mode theory emerges from orthonormalization.

Ultrawide-band long-wavelength p-i-n photodetectors

Abstract: We compare different designs for very high-speed (millimeter-wave) long-wavelength photodetectors, different materials for such detectors, and different ways of characterizing the speed of these devices. Experimental results are given, showing high-speed response with bandwidths beyond 50 GHz, impulse responses less than 10 ps, and detection sensitivities to 0.1 fJ in packaged devices. Discussed is the inherent bandwidth-efficiency limit in conventional p-i-n detectors, which is then compared to theoretical and experimental results for waveguide-geometry detectors.

Polarization independent coherent optical receiver

Abstract: This paper describes an optical heterodyne receiver for DPSK signals which can receive an optical signal having an arbitrary polarization state. This is achieved by splitting the received signal between two orthogonal polarization axes and processing the resulting two signals as in a conventional DPSK heterodyne receiver. The sum of the two demodulated signals provides a baseband signal independent of the polarization state of the received optical signal. When the receiver noise is dominated by the shot noise of the photodetectors, the receiver provides a BER of 10-9for an average number of 22 photon/bit. In comparison, a conventional optical heterodyne receiver requires under the same noise condition 20 photon/bit to achieve the same BER for a received optical signal polarized along the polarization axis of the local optical signal.

Protocols for very high-speed optical fiber local area networks using a passive star topology

Abstract: This paper deals with the problem of interconnection of many high-speed bursty traffic users via an optical passive star coupler. Each user can tune its laser over a range of wavelengths, thus resulting in a wavelength division multiplexed communication. The total number of wavelengths over which user tunability exists could be much smaller than the number of users. Therefore, some form of random access sharing and packet switching may be necessary. We propose several protocols that require each user to have a tunable receiver. The information on "where" and "when" to tune the laser is confined to a control (setup) channel that users tune to when in idle mode. An interconnection between two users lasting for the length of a data packet is set up on the control channel by the transmitting user who informs the receiving user where to tune in order to receive the data packet. No centralized control or coordination is required among the users. After analyzing each protocol, we present the throughput/ delay versus the offered traffic and the delay versus throughput in a sequence of plots. We show that in typical applications an average throughput of up to 0.95 can be achieved at a reasonable average delay using one of these protocols. In our benchmark examples we present an optical local area network (LAN) with a total throughput of 100- Gbit/s in which every user has access to a 1-Gbit/s data rate and the network can support over 1000 users. The protocols can be used in a) large LAN's that do not require a large capacity, b) small LAN's (1 kin) that require a large capacity and c) large LAN's (tens of kilometers) that require a rather large capacity.

Numerical analysis of planar optical waveguides using matrix approach

Abstract: We present here a simple matrix method for obtaining propagation characteristics, including losses for various modes of an arbitrarily graded planar waveguide structure which may have media of complex refractive indices. We show the applicability of the method for obtaining leakage losses and absorption losses, as well as for calculating beat length in directional couplers. The method involves straightforward 2 × 2 matrix multiplications, and does not require the solutions of any transcendental or differential equations.

Subcarrier multiplexing for multiple-access lightwave networks

Abstract: This paper describes the applicability of subcarrier multiplexing to lightwave multiple-access networks. It is shown how currently available microwave and lightwave components can be used, by using subcarrier multiplexing, to provide high-capacity networks. For example, the proposed multiple-access network can support 1024 users at a continuous bit rate of 1.5 Mbit/s, per user.

A coupled mode formulation by reciprocity and a variational principle

Abstract: A coupled mode formulation for parallel dielectric waveguides is presented via two methods: a reciprocity theorem and a variational principle. In the first method, a generalized reciprocity relation for two sets of field solutions (E^{(1)}, H^{(1)}) and (E^{(2)}, H^{(2)}) satisfying Maxwell's equation and the boundary conditions in two different media \epsilon^{(1)}(x,y) and \epsilon^{(2)}(x,y) , respectively, is derived. Based on the generalized reciprocity theorem, we then formulate the coupled mode equations. The second method using a variational principle is also presented for a general waveguide system which can be lossy. The results of the variational principle can also be shown to be identical to those from the reciprocity theorem. The exact relations governing the "conventional" and the new coupling coefficients are derived. It is shown analytically that our formulation satisfies the reciprocity theorem and power conservation exactly, while the conventional theory violates the power conservation and reciprocity theorem by as much as 55 percent and the Hardy-Streifer theory by 0.033 percent, for example.

Wavelength dispersion of Ti induced refractive index change in LiNbO 3 as a function of diffusion parameters

Abstract: Z -cut X -propagating, LiNbO 3 :Ti planar waveguides have been characterized over a wide range of diffusion conditions. Measurements of Ti concentration and refractive indexes have revealed Gaussian profiles. Their dependence with diffusion conditions have been studied. The relation, established at several wavelengths ( \lambda = 0.6328 \mu m, 1.1523 μm, 1.523 μm), between extraordinary and ordinary refractive index change \Deltan_{e,0}(z) and titanium concentration C(z) is found to be nonlinear and of the form: \Deltan_{e,0}(z) = A_{e,0}(C_{0},\lambda) (C(z))^{\alpha_{e,0}} While \alpha_{e,0} is a constant, the proportionality coefficient A_{e,0} depends not only on the wavelength λ, but also on the diffusion conditions, characterized by C 0 , the Ti surface concentration of the diffused guide. Such a nonlinearity of Ti diffusion in LiNbO 3 has been revealed thanks to a complete and wide range investigation on both indiffused Ti and index profiles.

Interactions of hydrogen and deuterium with silica optical fibers: A review

Abstract: This paper reviews all the interactions of hydrogen and deuterium with silica-based optical fibers. Included in the discussion are H 2 overtone absorption, OH formation, increased UV and IR absorption, radiation effects on H 2 -treated fibers, the gas-in-glass laser and applications, the reduction of OH absorption by isotope exchange OH → OD and other isotope-exchange related effects, and applications of isotope exchange and substitution for diagnostic purposes. Also included is a description of common sources of H 2 in materials used in fiber and cable manufacture, and countermeasures against hydrogen generation and intrusion into the fiber.

Computer simulation of high-bit-rate optical fiber transmission using single-frequency lasers

Abstract: Chirp-induced dispersion penalties in high-bit-rate optical fiber transmission are assessed using numerical integration of laser rate equations and a Fourier transform fiber dispersion routine. The roles of the imposed modulation waveform and laser design parameters are evaluated from computer generated eye diagrams and simple analytical observations. Consistent with experiment, we find device dependent optimum laser extinction ratios. In addition, we address the delicate balance between nonlinear chirp-induced dispersion penalties and the speed limitations imposed by linear current filtering on both the laser transmitter and the receiver. These considerations become increasingly important at higher bit rates such as 8 Gbit/s.

Analysis and evaluation of graded-index fiber lenses

Abstract: Graded-index multimode fibers are investigated for use as fiber-lenses. The performance of the fiber-lenses is based on the coupling efficiency between two single-mode fibers with fiber-lenses fused to their end faces. Coupling losses ranged from 0.1 to 1.6 dB for the various fiber-lenses. Expanded beam waists up to 39.5 μm were measured and a fiber separation of > 3.0 mm was possible while retaining the excess loss within the above range. Low loss coupling was observed with multiple-pitch ( > 3.0 mm long) VAD lenses. A theoretical analysis considers a ray matrix transformation of the complex beam parameter and predicts the coupling efficiency as a function of the relative transverse and axial displacements of the two fibers. A comparison to the corresponding measurements is made.

A new exact and efficient numerical matrix theory of complicated laser structures: properties of asymmetric phase-shifted DFB lasers

Abstract: A numerical matrix method is developed which permits the analysis of very complicated laser structures. It is applied to different laser structures including asymmetric phase-shifted DFB-lasers both with abrupt and extended phase-shift sections. Results for modal behavior, threshold gain differences and power distribution are presented.

Phase diversity techniques for coherent optical receivers

Abstract: In the present state of the art, coherent optical receivers most often operate in the heterodyne mode. Here a photodiode-amplifier combination having bandwidth greater than twice the bit rate ( B ) is needed: indeed bandwidths considerably greater than 2B are preferably employed to ease design of the bandpass filter needed for noise limitation, and to avoid demodulator penalties in some modulation schemes. For the high bit rate systems now coming into service (560 Mbit/s-2.4 Gbit/s), the optical receiver design requirements become more stringent for coherent heterodyne operation. The various modes of "zero IF" operation, however, require only baseband receiver module bandwidth. The options available are either homodyne (phase locked) operation, or phase diversity (multiport) techniques. In this paper, we compare these options, and show that phase diversity techniques are capable of good performance for high bit rate coherent receivers. In phase diversity operation, not only is phase locking avoided, but also the necessary frequency locking does not have high stability requirements. Furthermore, there are advantages in operating with a small frequency offset from zero (of the order of 1 percent of the bit rate). An experimental receiver has been operated at 320 and 680 Mbit/s, demodulating both amplitude shift keying (ASK) and differential phase shift keying (DPSK). Operation with FSK is also possible. Sensitivities so far achieved of -47.5 dBm (320-Mbit/s ASK) and -42 dBm (680- Mbit/s ASK) with limited local oscillator power are capable of substantial improvement when higher power local oscillators and lower noise receive modules become available. Demodulation of DPSK at 320 Mbit/s has also been achieved and shows a measured receiver sensitivity improvement of over 4 dB over ASK at the same bit rate and local oscillator power. These practical results show clearly that phase diversity is a very realistic option for high bit rate systems.

Multielectrode distributed feedback laser for pure frequency modulation and chirping suppressed amplitude modulation

Abstract: A new concept for operation of distributed feedback lasers with multielectrodes is proposed and its capability for amplitude or frequency modulation is demonstrated. The device has electrically separated electrodes so that carrier density distribution along the laser cavity can be controlled artificially by adjusting the current distribution for each electrode. The lasing frequency can be controlled by changing the current ratio applied to the electrodes. Frequency modulation experiments disclose that neither frequency modulation efficiency nor phase delay depend on modulation frequency. It turned out that the frequency shift under modulation showed blue shift or red shift depending on bias current distribution and the position of the modulation applied electrode. Using these characteristics, chirping suppressed amplitude modulation and frequency modulation with constant output power are realized.

Directional couplers made of nonidentical asymmetric slabs. Part II: Grating-assisted couplers

Abstract: In this second part of the paper we discuss TE and TM mode directional couplers made of nonsynchronous, nonidentical asymmetric slab waveguides. Coupling is accomplished with the help of a diffraction grating that is placed on either of the two guides on the side facing the opposite slab. The grating couples the compound modes of the complete slab structure to each other. However, since the two slabs are nonsynchronous, the compound modes resemble closely the modes of each slab in isolation. We also provide approximate expressions that result from approximating the compound modes with the modes of the individual slabs. The accuracy of these approximations is estimated by comparison with the exact results.

Large signal nonlinear distortion prediction for a single-mode laser diode under microwave intensity modulation

Abstract: The large-signal nonlinear distortions from a directly-modulated single-mode GaAlAs laser diode are closely predicted by using a large-signal equivalent circuit model. Criteria for determining intrinsic parameter values are described. The simulations are done in the time domain and then transformed to the frequency domain by FFT. Second harmonics, two-tone third-order intermodulation, multicarrier intermodulation, and intermodulation due to two arbitrarily separated tones have all been simulated and match well with corresponding measured results.

System characteristics of direct modulated and externally modulated RF fiber-optic links

Abstract: RF fiber-optic links have numerous applications to microwave systems. To fully exploit their usefulness, and RF system designer must understand their properties in terms of the performance parameters that are used to describe the terminal properties of other RF components such as loss, signal-to-noise, linearity, and dynamics. This review paper details the performance of direct and external modulation fiber-optic links in terms of those parameters. Specific examples of a 4.1-4.7 GHz direct modulation link and a 2.0-12.0 GHz external modulation link are used.

Mode conversion in optical fibers with monotonically increasing core radius

Abstract: In this paper we discuss mode conversion in a straight fiber which maintains its circular cross section but whose radius a(z) increases monotonically with the length coordinate z so that it passes from the single-mode to the multimode regime. Our principal concern is with step-index fibers which are treated in the scalar approximation. We study conversion of power from the incident dominant mode to other core and cladding modes for several functions a(z) . The results of our calculations show clearly that the dominant mode is able to adapt itself to the changing fiber radius provided the change is gradual. For comparison, we also consider a fiber with an infinitely extended radial parabolic-index profile as an approximation to graded index fibers. We show that it too exhibits mode conversion similar to that of the step-index fiber, provided that the comparison is made on the basis of corresponding mode spot sizes instead of actual core radii.

Multichannel coherent optical communications systems

Abstract: Balanced coherent receivers perform substantially better than single-detector receivers in multichannel optical fiber FDM communications systems since the balanced approach eliminates the direct-detection and signal-cross-signal interference. The permissible channel spacing D depends on the intermediate frequency f IF , on the bit rate R b , and on the modulation/demodulation format. In particular, D increases by 2 Hz for every 1-Hz increase of the f IF . The signal-to-interference ratio SIR, as defined in the text, provides a simple measure of the amount of the interference generated by undesired channels. The criterion SIR = 30 dB is selected in this paper and leads to the following minimum channel spacings: for heterodyne systems, 3.8R_{b} for FSK, 9.5R_{b} for ASK, and 12.4R_{b} for PSK; for homodyne systems, 7.5R_{b} for ASK and 10.5R_{b} for PSK. Simultaneous transmission of several channels generates an excess shot noise studied here for the first time. If the local oscillator power is 40 dB above the received signal power and 2000 channels are transmitted without optical prefiltering, the excess shot noise power penalty is less than 1 dB.

Monolithic integration of InGaAsP/InP distributed feedback laser and electroabsorption modulator by vapor phase epitaxy

Abstract: Monolithic integration of a 1.55-μm InGaAsP/InP distributed feedback (DFB) laser and an electroabsorption (EA) modulator was studied. The difference between the lasing photon energy and the bandgap energy of the modulator waveguide was designed to be 30-40 meV, taking into account the linewidth-enhancement factor and the zero-bias absorption loss. The integrated devices were grown by three-step vapor phase epitaxy (VPE). The CW threshold current at 20°C of the DFB laser part with a buried heterostructure was 30-60 mA and the breakdown voltage of the modulator part with a strip-loaded stripe geometry was 20-40 V, and these values indicated satisfactory crystal quality in the VPE epitaxial layers. The operating voltage of the modulator to give on:off ratios of 10:1 and 100:1 was 1.5- 4 V and 2.5-6.5 V, respectively, depending on the length in the range 200-500 \mu m. A 3-dB bandwidth of about 2.5 GHz and a linewidth-enhancement factor of about 1.6 were obtained for the integrated modulator.

Directional couplers made of nonidentical asymmetric slabs. Part I: Synchronous couplers

Abstract: We discuss TE and TM mode directional couplers made of nonidentical asymmetric slab waveguides. Approximate expressions are provided for the coupling coefficients of synchronous (no grating) couplers and their accuracy is checked by comparison with exact solutions that are based on solving the guided mode problem of the total structure consisting of the two slabs considered to be a single waveguide.

The performance of optical phase-locked loops in the presence of nonnegligible loop propagation delay

Abstract: The optical phase-locked loop is analyzed taking into account shot noise, phase noise, and loop propagation delay. The degradation of loop phase error due to propagation delay is evaluated in terms of the delay bandwidth product \omega_{n} \cdot \tau_{D} . This product was found to have a maximum value of 0.736 for absolute loop stability. The resulting effect on a Costas loop system optimized for zero time delay is discussed. It is found that in order to maintain a 10-9BER system performance with \xi = 1/2^{0.5}, R = 0.85 A/W, P_{DATA} = -59.2 dBm, and a 1-MHz beat linewidth, the delay time must be kept below 1.8 ns. If the beat linewidth increases to 15 MHz this figure drops to 0.12 ns.

Reformulation of the coupled-mode theory of multiwaveguide systems

Abstract: We show that by proper reformulation the coupled-mode theory of Hardy and Streifer can be reconciled with that of Haus et al based on a variational principle. The new formulation has the merit of leading to simpler coupled-mode equations while giving marginally more accurate results.

Multigigabit-per-second avalanche photodiode lightwave receivers

Abstract: High-speed avalanche photodiodes and high-sensitivity receivers are vital components for future multigigabit-per-second lightwave transmission systems. We review theoretical and experimental performance of high-speed III-V avalanche photodiodes, and also that of multigigabit-per-second lightwave receivers using FET and bi-polar amplifiers. Particular attention is given to APD gain-bandwidth product, and to its effect on high-speed receiver sensitivity. Comparisons between measured receiver sensitivities and calculated performance are presented for bit rates up to 8 Gbit/s.

ASK multiport optical homodyne receivers

Abstract: Several types of ASK multiport homodyne receivers are investigated, and the impact of the phase noise and of the shot noise on these receivers is analyzed. The simplest structure is the conventional multiport receiver with a matched filter in each branch. This structure can tolerate \DeltavT [ \deltav is the laser finewidth and T is the bit duration) of several percent with a small power penalty (3.6 percent for 1-dB penalty and 5.2 percent for 2-dB penalty). Optimization of branch filters of conventional multiport receivers does not help when the linewidth (and the penalty) is small but does improve the receiver performance for larger linewidths. The most important point of the paper is the novel wide-band filter-rectifier-narrow-band filter (WIRNA) structure, proposed and investigated here for the first time for optical communication systems. It is shown that the optimized WIRNA homodyne receivers are extremely robust with respect to the phase noise: the WIRNA tolerable value of \DeltavT is 3.6 percent for 1-dB penalty and more than 50 percent for 2-dB penalty. Thus, the WIRNA structure opens, for the first time, the possibility of constructing homodyne receivers operating at several hundred megabits per second with conventional DFB lasers without complicated external cavities. Under no-phase-noise conditions, all the multiport receivers investigated here have the same performance, which is identical to that of heterodyne ASK receivers. In addition, the optimized WIRNA receivers can tolerate tapproximately) the same laser linewidth as the heterodyne ASK receivers. Thus, the main difference between the WIRNA multiport homodyne and heterodyne receivers is that the former shifts the processing to a lower frequency range, in return for a more complicated implementation. This difference makes the WIRNA multiport homodyne receivers particularly attractive at high (say, several gigabit per second) bit rates.

Modulation and detection characteristics of optical continuous phase FSK transmission system

Abstract: The modulation and differential detection characteristics of optical CPFSK transmission systems are investigated both theoretically and experimentally. The error rate expressions of differentially detected CPFSK are derived by considering phase noise of LD's. It is clear that the linewidth requirement is less than 0.68 m percent of the bit rate, where m is modulation index. The performances of CPFSK are then experimentally presented at 400 Mbit/s using external optical feedback DFB LD's as the optical source. A beat spectral linewidth of less than 200 kHz for the transmitter and local oscillator LD's is achieved. The frequency response nonuniformity of frequency modulation efficiency is compensated by electrical circuits within 3 dB and 60°. To reduce IF thermal noise, a resonance-type preamplifier is used, with a 4.8 pA/ \sqrt{Hz} average input noise current density, and a receiver sensitivity 1.3 dB better than the conventional preamplifier. Differential detection of the 400-Mbit/s CPFSK modulation is performed. The generation of CPFSK is confirmed by good correlation between the output spectrum and theory. The average received optical power at a 10-9bit error rate is -49.9 dBm which improves direct detection by 10.3 dB. No additional power penalties due to 290-km transmission exist.

A fiber-optic interferometric seismometer

Abstract: A fiber-optic interferometric sensor has been developed which consists of a seismic mass of 520 gm supported by two rubber mandrels, each wound with a single layer of single-mode optical fiber 6.5 m long. One end of each fiber is cleaved to enhance reflection. The other ends are interconnected via a fiber-to-fiber 3-dB coupler, forming a Michelson interferometer. When the case of the sensor is displaced, the fiber around one mandrel extends in length while the other contracts. The resulting "push-pull" mechanical operation of the sensor allows both legs of the interferometer to be active, providing good common mode rejection of spurious effects, as a reference leg is not required. This, together with the fact that the light traverses each leg of a Michelson interferometer twice due to reflection, provides the sensor with four times the sensitivity of a conventionally constructed interferometric sensor. Sensitivities of 8500 rad of optical phase shift per micrometer of case displacement have been measured above the mass-spring resonance, where the sensor operates as a seismometer. Below resonance the sensor operates as an accelerometer with a measured sensitivity of 10 500 rad/g, the highest reported to date. Including both thermodynamic and demodulator noise sources ( \approx 10 \mu rad/ \sqrt{Hz} ), below resonance the sensor has a detection threshold of 1 ng/ \sqrt{Hz} , a 20- dB improvement over the best existing conventional low noise vibration sensors.

Time-domain addressing of remote fiber-optic interferometric sensor arrays

Abstract: This paper describes and analyzes a particular application of high duty-cycle time-division multiplexing to the separation and identification of signals from an interferometric sensor array. Using the method discussed here, the coherence length of the laser is no longer a severe design constraint. Also, the source phase-induced intensity noise which limits some other multiplexing methods may be overcome, leading to a higher sensitivity. The arrays of all-passive remote sensors exhibit minimal crosstalk between sensors, and have downlead insensitivity. A synthetic heterodyne demodulation technique prevents environmentally induced signal fading. Analysis includes coupling ratios for all directional couplers in the system, signal and noise spectra, minimum detectable phase shift, and the effect of ac coupling on noise and crosstalk. An experimental all-fiber implementation of a two sensor array has yielded a measured sensitivity of approximately 10 μrad/ \sqrt{Hz} over a range of signal frequencies, and a crosstalk level of better than 55 dB.

Intensity effects on the stimulated four photon spectra generated by picosecond pulses in optical fibers

Abstract: The intensity dependence of stimulated four photon mixing (SFPM) spectra generated in 15 m of a 4-mode optical fiber by 25- ps pulses has been investigated. Despite the shortness of pulses, the SFPM conversion was highly efficient due to the intrinsic phase matching condition. In addition to usual features of SFPM spectra generated by nanosecond pump pulses, picosecond SFPM spectra were broadened by self phase modulation (SPM) and cross phase modulation (XPM). At the highest pump powers, intensity saturated frequency continua, arising from the combined effects of SFPM, stimulated Raman scattering (SRS), SPM, and XPM were generated all over the visible spectrum.

Optical FDM transmission technique

Abstract: This paper surveys the present state of optical frequency-division multiplexing (optical FDM) technologies. Utilizing a broad optical frequency bandwidth up to several hundred terahertz, optical FDM is expected to find applications in large-capacity trunking and local distribution networks. The present state of the related technologies and the future prospects for these applications are discussed.