The dependence of carrier lifetime on spectral width in multimode semiconductor lasers

Comprehensive measurements of the dependence of the carrier lifetime, eye pattern, and power penalty on the spectral width in multimode semiconductor lasers for a gigabit lightwave transmission system are presented. The results show that the carrier lifetime, eye pattern, and power penalty caused by mode partition noise (MPN) are strongly dependent on the source spectral width. The lasers with shorter carrier lifetimes exhibit a narrow spectral width, and hence show less MPN, a better eye opening, and a lower power penalty. A theoretical calculation of the MPN-induced power penalty is in good agreement with the measured system penalties. The likely cause for narrow spectral width with shorter carrier lifetime of the lasers is due to the smaller linewidth enhancement factor a caused by a higher doping concentration in the lasers.     

Dynamic behavior of fundamental-mode stabilized VCSELs using a shallow surface relief

An extensive theoretical study was performed on the dynamic behavior of 850-nm-wavelength oxide-confined fundamental-mode stabilized vertical-cavity surface-emitting lasers (VCSELs), using a shallow surface relief. The surface relief is used to provide lower mirror loss for the fundamental mode, thus acting as a mode discriminator. In this way, single-mode operation at high power levels can be obtained. We utilized a comprehensive model that includes the detailed epitaxial layer structure and device geometry when calculating the optical fields and that accurately accounts for the dynamic effects of carrier density and temperature on the modal distributions. Modulation response, eye diagrams, bit error rate (BER), and relative intensity noise (RIN) were simulated and compared to the performance of VCSELs without a mode discriminator, i.e., conventional multimode VCSELs. The fundamental-mode stabilized VCSELs are associated with a higher out-coupling, which lowers the relaxation oscillation frequency and damping, and strong spatial hole burning, which induces a low-frequency roll-off in the modulation response and contributes to the damping of the relaxation oscillation at low bias. However, their dynamics is fully competitive with conventional multimode VCSELs at both 2.5 and 10 Gb/s although they exhibit a slightly higher eye closure. We only found a 0.5-dB power penalty in the BER. The RIN is enhanced, with a peak that is about 10-15 dB higher, caused by the lower damping of the relaxation oscillation. It should be noted that in the comparison we assume that all modes are equally captured from the multimode VCSEL. A mode-selective loss can severely degrade its performance.     

Practicability of determining the modal power distribution by measured near and far fields

Under certain assumptions the modal power distribution in optical multimode fibers can be derived from either the near- or the far-field. We measured both intensities and compared the calculated mode spectra. From these results, it becomes clear which assumptions are necessary and how to control them. The influence on the modal power distribution by leaky modes and some error sources such as the profile exponent, the fiber end quality, and misalignments are shown.     

Mode Coupling in Plastic Optical Fiber Enables 40-Gb/s Performance

We report 40-Gb/s capability of 50-mum core plastic optical fiber using differential modal delay measurements and power penalty due to intersymbol interference computations. The results are explained via a comprehensive multimode fiber model that includes mode coupling (MC) and differential modal attenuation (DMA). We show that strong MC can enable 40-Gb/s transmission for reach in excess of 100 m even in the presence of irregularities in the refractive index profile that prevent 10-Gb/s performance without MC. Furthermore, we show that DMA effects are negligible and that the mode power distributions are not a good indicator of bandwidth.     

Simulation and measurement of radiation loss at multimode fibermacrobends

A ray-tracing model for simulating light propagation in bent multimode fibers is described. The model takes modal effects into account. Calculations of the bend loss using this model are compared with measurements. Reasonable agreement with measured bend losses is obtained by including a realistic modal power distribution (MPD) in the simulation. For situations in which the power per mode in each principle mode group is constant, the simulations predict fractional loss curves as a function of the normalized group number m/M that are independent of wavelength. These curves can be used to predict bend losses in other constant radius bends as long as the MPD is known. The emission pattern of the radiated light has been calculated and qualitative agreement with the measured pattern found. It is suspected that the differences between simulation and experiment might be explained if the exact shape of the fiber in the bend were known and taken into account     

Effect of carrier lifetime on mode partition noise in multimodesemiconductor lasers

The dependence of mode partition noise (MPN), and its association with the eye diagram and power penalty, on carrier lifetime in 1.3 μm InGaAsP multimode semiconductor lasers for a 1.2 Gbit/s lightwave transmission system was investigated. It was found that lasers with shorter carrier lifetimes showed less MPN, and hence, a better eye opening and a lower power penalty, than the lasers with longer carrier lifetimes. The significant dependence of MPN, eye opening, and power penalty on carrier lifetime in multimode semiconductor lasers suggests that the carrier lifetime of the laser, which depends on the laser design, can be used as an important parameter for characterizing the performance of high-speed lightwave transmission systems     

Modal structure analysis for a class of axially symmetricflat-topped laser beams

A recently proposed algorithm for the determination of the modal power distribution inside a stable multimode laser cavity is applied to the case of a flat-topped transverse intensity beam profile. We show that such a technique leads to closed-form expressions for the modal weights and for the M² factor of the output beam. Comparisons with experimental results present in literature are also reported     

Characterization of source power distributions in multimode fiber by a splice offset technique

Using a splice loss versus transverse offset technique in conjunction with a modal splice loss model, the power distribution created by a number of lasers and LED's in multimode fiber has been determined as a function of mode number. This technique provides a convenient way to characterize sources and to determine the mode power distribution they produce in multimode graded-index fibers.     

High-speed digital modulation characteristics of oxide-confined vertical-cavity surface-emitting lasers-numerical simulations consistent with experimental results

The vertical-cavity surface-emitting laser (VCSEL) is a preferred light source for short-distance high-speed fiber-optic communication links. We simulate the digital modulation behavior of typical oxide-confined VCSELs under realistic working conditions with a comprehensive model that includes the detailed geometry when calculating the optical fields and that accurately accounts for the dynamic effects of carrier density and temperature on the modal distributions. The intrinsic output characteristics of single- and multimode VCSELs were studied as functions of bias and modulation depth under a 2/sup 7/-1 pseudorandom bit sequence current modulation at 2 and 10 Gb/s. The data were used to create numerical eye diagrams that show, e.g., the significant impact of the bit pattern history and the noise on the timing jitter in both single- and multimode VCSELs. For the single-mode VCSEL, the choice of the bias current and modulation depth was less critical due to its higher damping of the relaxation oscillations. The simulated VCSELs were fabricated and experimentally evaluated. The measured eye diagrams showed the same characteristic features as those in the simulations.     

Analysis of vertical-cavity surface-emitting laser multimodebehavior

This paper investigates problems associated with multimode oscillation in vertical-cavity surface-emitting lasers (VCSELs). The multimode rate equations for transverse mode were formulated. These equations take into account carrier diffusion and gain nonuniformity in the lateral direction. It was shown that multimode transverse mode excitation is due to carrier spatial hole burning, but many factors affect the number of lasing modes. The role of gain nonuniformity distribution, carrier diffusion, and modal loss compared with mirror loss in a cavity were demonstrated by numerical solution of the multimode rate equations     

Reliability of a new method for measurements of modal power distribution in optical fibres with application to mode scrambler testing

An experimental investigation about the reliability of an attractive method recently proposed for modal power distribution measurements in multimode fibres is performed. The method is shown to work also in some common cases when the hypotheses of validity are not rigorously fulfilled. Finally, an illustrative application to the testing of mode scramblers is presented.     

Calculating the performance of optical communication systems withmodal noise by saddlepoint method

Modal noise disturbs the received power of optical receivers. It arises in multimode fiber systems and can be modeled by a gamma distribution. In our system, the number of secondary electrons is amplified by an avalanche photodiode (APD) and further corrupted by the thermal noise of the subsequent linear amplifier. The degradation to the system caused by modal noises is considered along with the signal dependent shot noise and the circuit generated thermal noise. The error probabilities are computed by using the saddlepoint method under the influence of various degrees of modal noise. Methods for searching for the threshold and the optimum APD gain are also presented     

Spatial investigation of transverse mode turn-on dynamics in VCSELs

Data transmission experiments with single-mode as well as multimode 850-nm vertical-cavity surface-emitting lasers (VCSELs) are carried out from a near-field point of view. Special attention is paid to important quantities like on/off-ratio and bit error rate (BER). A single-mode VCSEL oscillating on the fundamental LP₀₁ mode shows no change in eye opening, on/off-ratio, and BER at different lateral fiber coupling positions. In the case of a multimode VCSEL oscillating both on the LP₀₁ mode and LP₁₁ donut mode, we observe a significant lateral change in the on/off-ratio, which plays an important role in BER measurements     

Influence of core diameter on the 3-dB bandwidth of graded-indexoptical fibers

The frequency response and bandwidth of multimode silica glass fibers are investigated in this paper. The theoretical model incorporates both wavelength and modal effects including power coupling from random microbends. The 3-dB bandwidth is examined through the study of the fiber transfer function which introduces the wavelength and modal effects as two separate filter functions. The formal derivation of the chromatic transfer function is analytical. On the other hand, the modal bandwidth is obtained by numerically solving the power flow equation in the frequency domain using the Crank-Nicholson method. As an application, the transfer function is illustrated and subsequently discussed with special focus spent on analyzing the influence of the fiber size in combination with the launching conditions. We show in particular that the larger the core, the greater the bandwidth potential of the fiber when operated under selective mode excitation. Some measurements are also carried out and excellent agreement between this model and data is achieved     

Bandwidth and modal noise effects in fused-head-end multimode fiberpassive components

Passive multimode fiber components, particularly 1-to-2 splitters/couplers, manufactured using the fused-head-end technique, are tested under network conditions. The mode power transfer matrix and its effects on the network are discussed. The modification of the pulse mode spectrum in the splitter is analyzed by studying the pulsewidth variation and the transmitted pulse power for components at the near and far end of a long length of fiber. The modal noise generated in such passive fiber components is determined, and the modal noise ratio (MNR) and the modal noise susceptibility (MNS) are introduced as figures of merit characterizing modal noise sources and multimode fiber passive components, respectively     

Body Conformal Antennas for Superficial Hyperthermia: The Impact of Bending Contact Flexible Microstrip Applicators on Their Electromagnetic Behavior

Hyperthermia is a powerful radiosensitizer for treatment of superficial tumors. This requires body conformal antennas with a power distribution as homogeneous as possible over the skin area. The contact flexible microstrip applicators (CFMA) operating at 434 MHz exist in several sizes, including the large size 3H and 5H. This paper investigates the behavior of the electromagnetic fields for the 3H and 5H CFMA in both flat and curved configurations, and the impact on performance parameters like the penetration depth (PD) and the effective heating depth (EHD). The underlying theory behind the electromagnetic behavior in curved situations is presented as well as numerical simulations of both flat and curved configurations. The results are compared to measurements of the electromagnetic field distributions in a cylindrical patient model. Due to their large size multimode solutions may exist, and our results confirm their existence. These multimode solutions affect both the power distribution and PD/EHD, with a dependence on applicator curvature. Therefore, the performance parameters like PD and EHD need to be carefully assessed when bending large size CFMA applicators to conform to the patient body. This conclusion also holds for other types of large size surface current applicators.      

Minimum pulse broadening in multimode fibers with index imperfections

Minimum pulse broadening of multimode graded-index fibers is investigated theoretically. Exact solutions of the rms pulse-width σ for a fiber with a power-law index profile is obtained by using the integral expression of group delay time based the multilayer approximation. It is shown that the minimum value of σ and the optimum α for the power-law index profile calculated by the multi-layer approximation in the steady-state modal power distribution are nearly equal to the well-known WKB solution. Next,sigma_{min}and the corresponding αoptare evaluated for certain index imperfections such as a central index dip and sinusoidal index ripple along a radial direction. The results offer the possibility to avoid the bandwidth degradation due to an inevitably generated index tipple in an MCVD graded-index fiber.     

Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers

An analytical calculation of relative intensity noise spectra of weakly index-guided vertical-cavity surface-emitting lasers (VCSELs) in a multimode regime is performed. We obtain analytical expressions that incorporate the spatial dependence of electrical field and carrier density profiles. Expressions are derived for single-mode and two-transverse-mode operation. Our analysis shows that single-mode noise spectrum depends on the spatial mode profile through a modal effective volume. Two-mode noise spectra also incorporate the dependence on the degree of spatial overlapping between the modes. Two resonance peaks appear in the noise spectra of the individual modes and total power of the two-mode VCSEL. We analytically show that those peaks appear at frequencies that correspond to the relaxation oscillation frequencies of the multimode laser. Simple analytical expressions are also derived for noise spectra at zero frequency.     

Determination of mode power distribution in a parabolic-index optical fibers: Theory and application

A novel measurement method for determining mode power distribution in a multimode parabolic-index fiber is developed. Using this method, the mode power distributions are obtained in terms of the principal mode number by numerically processing the measured Fraunhofer diffraction patterns of the near-field patterns on an output fiber endface. As an example, differential mode attenuation of a multimode parabolic-index fiber is measured. It is confirmed experimentally that the method is practically applicable to the mode power distribution measurements in a parabolic-index fiber.     

Dispersion in optical fibres with stairlike refractive-index profiles

In multimode circularly symmetric fibres whose index distribution is a stairlike approximation of an optimum profile, the modal dispersion increases as the number of steps decreases. For a fibre with ?n/n=0.02 and a core radius of 40 ?m, numerical calculations based on wave optics show that the r.m.s. impulse response width at ?=1 ?m increases from 0.075 ns/km for the smooth optimum profile to 0.23 ns/km for 40 steps of equal areas. Thus an important conclusion of the analysis is that one should avoid introducing steps in the refractive-index profile of fibres for optimum results.