Fundamental Thermal Noise in Distributed Feedback Fiber Lasers

A detailed analysis of fundamental thermal frequency noise in distributed feedback fiber lasers (DFB FL) is presented. An expression relating the laser frequency noise spectrum to the spectrum of thermal (temperature) fluctuations in the fiber, accounting for the nontrivial DFB FL mode shape, is derived. A new expression for the thermal fluctuation spectrum of single-mode optical fiber is derived which predicts high-frequency thermal noise 3 dB higher than previously published results. Theoretical predictions are compared against experimental measurements for a well characterized DFB FL. Anomalous 1/f noise at low frequency is discussed     

A DFB Fiber Laser Sensor System with Ultra-High Resolution and Its Noise Analysis

A distributed feedback fiber laser （DFB FL） sensor system with ultra-high resolution is described. The sensor is made by writing distributed feedback structures into a high gain active fiber, and the system employs an unbalanced Michelson interferometer to translate laser wavelength shifts induced by weak measurands into phase shifts. A digital phase generated carrier demodulation scheme is introduced to achieve ultra-high resolution interrogation. A detailed noise analysis of the system is presented, and it is shown that the system resolution is limited by the frequency noise of the DFB FL.     

Performance limitations of high-power DFB fiber lasers

In this letter, we experimentally study several different configurations of high-power single-frequency sources based on distributed-feedback fiber laser (DFB FL). In particular, we have compared two schemes in terms of pumping efficiency, relative intensity noise (RIN) and optical signal-to-noise ratio (OSNR): directly pumped DFB FLs pumped by a high-power fiber-based pump source (stand-alone DFB FL) and a combination of a DFB FL and a power amplifier (amplified DFB FL). At the output powers below 40 mW, a stand-alone DFB FL has the highest OSNR (> 63 dB) and the lowest RIN (< -165 dB/Hz). The net efficiency of a stand-alone DFB FL can be doubled by using an amplified DFB FL at the expense of degraded OSNR and RIN. It is also shown that RIN below -160 dB/Hz and OSNR > 60 dB can be achieved by an amplified DFB with output power greater than 1 W.     

Fiber-reflection-induced impairments in lightwave AM-VSB CATVsystems

Impairments due to multiple fiber reflections are evaluated for amplitude-modulated (AM) vestigial-side-band (VSB) lightwave cable TV (CATV) systems using directly modulated distributed feedback (DFB) lasers or externally modulated diode-pumped YAG laser transmitters. For DFB lasers, the spectral broadening caused by laser chirp results in a Gaussian optical spectrum with a width near 5 GHz. Square-law detection of multipath signals from two -30-dB reflections results in an effective intensity noise near -150 dB/Hz. For externally modulated YAG lasers, the same multiple reflections result in interference that cannot be described by an effective RIN. Although the total interference power is comparable to that of the DFB lasers, the signal and interference are highly correlated. As a result of this correlation, multipath interference for YAG-based systems cannot be measured using the standard test procedure with unmodulated carriers     

Effect of nonuniform laser FM response on the performance ofmultichannel heterodyne FSK systems using optical amplifiers

A theoretical analysis is provided to evaluate the performance of optical frequency division multiplexed systems taking into considerations the combined effect of receiver noise, laser phase noise and nonuniform FM response characteristic of a practical DFB laser. To overcome the effect of nonuniform frequency modulation characteristic of semiconductor lasers, two different linecoding schemes are used for the laser driving signal. The crosstalk penalty due to the combined effect of nonuniform FM response and phase noise of lasers is evaluated. The improvement in receiver sensitivity due to optical preamplifier is also estimated. The computed results show that the performance of the system is highly degraded due to the effect of laser nonuniform fm response and can be reduced substantially by using linecoding. Further, there is considerable improvement in receiver sensitivity due to the use of an optical preamplifier in the absence of phase noise. In the presence of phase noise there is a reduction in receiver sensitivity     

DFB laser with attached external intensity modulator

A theoretical study is made of the frequency pulling effect exerted on a distributed feedback (DFB) laser by an external amplitude modulator that is directly attached to it. The modulator consists of a piece of waveguide whose loss is modulated by means of an externally applied voltage. The modulator affects the laser due to residual reflections from its far end which appear as a variable effective reflectivity to the output end of the DFB laser. Modulation affects the magnitude as well as the phase of the effective reflection coefficient presented to the laser due to the coupling of the real and imaginary parts of the effective refractive index of the modulator waveguide. The tuning problem is formulated as an eigenvalue equation for the DFB laser in the presence of an externally attached lossy cavity     

Transfer-matrix formulation of spontaneous emission noise of DFBsemiconductor lasers

A unified formulation of the spontaneous emission noise in semiconductor DFB (distributed feedback) lasers is presented by using a transfer-matrix approach. Analytical expressions for the noise power per unit frequency bandwidth below threshold and the spontaneous emission rate into the lasing mode are obtained based on the Green's function method. Three DFB laser structures are analyzed: (1) a standard DFB structure with facet reflectivities, (2) a multisection DFB structure composed of n sections which models a phase-shifted DFB laser and a multielectrode (tunable) DFB laser, and (3) a periodic layered DFB structure which models a surface-emitting DFB laser. It is shown that the spontaneous emission noise of a complicated DFB laser structure can be calculated easily by the transfer matrix of each section of the structure and its derivative to frequency     

A Michelson interferometer with balanced detection for thecharacterization of modulation and noise properties of semiconductorlasers

A Michelson interferometer with balanced detection, built to study semiconductor lasers, is analyzed. The quantum noise due to vacuum fluctuations, coupling losses, detector quantum efficiency, and spatial mode mismatches are included in the analysis. The limits for frequency noise detection and the sensitivity of the interferometer are examined. It is observed that under ordinary measurement conditions the frequency noise can only be measured up to slightly above the cavity bandwidth of the laser. Comprehensive measurement procedures are proposed, and experimental results showing the frequency modulation response, measured from 10 kHz to 8 GHz, of a three-section distributed feedback (DFB) laser and the frequency noise spectra, measured from 30 MHz to 8 GHz, of a two-section distributed Bragg reflector (DBR) laser are presented. These results reveal new cavity detuning effects in the noise characteristics of tunable DBR lasers     

Experimental and theoretical investigations of coherent OFDR withsemiconductor laser sources

Experimental and theoretical investigations of coherent optical-frequency-domain reflectometry using semiconductor laser sources are presented. Good agreement was found between the analysis of the signal-to-noise ratio due to the phase noise and the experimental results. The sensitivity limit due to the quantum noise is also described. Limitations due to the nonlinearity in the optical frequency sweep produced by the thermal-response time of the laser and mode hopping are investigated and compared with experimental results. Two interferometric methods to characterize the thermal-response time of the laser and their implementations are described. The effects of mode hopping in the optical-frequency sweep are compared to numerical simulations. A simple formula to predict the position of spurious peaks due to mode hopping are presented. A spatial resolution of 400 μm over 10 cm was obtained by correcting the nonlinearity in the optical-frequency sweep by using an auxiliary interferometer. The Rayleigh backscattering was observed for the first time over more than 400 m of fiber using a DFB laser coupled to an external cavity     

Static, dynamic, and noise analysis of multisection DFB lasersusing frequency-domain transmission line model

A novel frequency-domain transmission line model for multisection distributed feedback (DFB) lasers is developed. The characteristic impedances of active periodic structures are derived. A multisection DFB laser is described as a transmission line network, with each section represented by a transmission lint segment with a corresponding characteristic impedance. Static, dynamic, and noise analysis of multisection DFB lasers is demonstrated. The reflections at the junctions between sections are evaluated more accurately. The resonant condition of the equivalent transmission line network, instead of cumbersome Wronskian, is used to reformulate the rate equations. The diffusion coefficient of Langevin noise terms of any two different positions is solved for the first time, resulting in a more accurate noise analysis of multisection semiconductor lasers. Analytical expressions of the dynamic responses and noise properties of multisection DFB semiconductor lasers are derived     

Numerical simulation of intensity and phase noise from extracted parameters for CW DFB lasers

A self-consistent numerical approach is demonstrated to analyze intensity and phase noise from experimentally extracted parameters for a continuous-wave distributed feedback (DFB) laser. The approach takes into account the intrinsic fluctuations of the photon number, carrier number, and phase. Values for the parameters appearing in the rate equations are extracted from the measured relative intensity noise spectra and linewidth of the laser. The simulation of the frequency spectra of intensity and phase noise of the DFB laser are performed by fast Fourier transform and exhibit good agreement with experimental results. The model presented here can readily be extended for the purpose of system simulations.     

Large-signal spurious-free dynamic range due to static and dynamicclipping in direct and external modulation systems

Large-signal spurious-free dynamic range (SFDR) is useful in an optical system with a high intensity noise level, which can be due to optical reflections or optical beat interference, and with large modulating signals to achieve sufficient carrier-to-noise ratio (CNR). A closed-form analysis on large-signal SFDR due to static and dynamic clipping for direct and external modulation systems is presented in this paper. The analysis can be applied to laser diodes (LDs) and external modulators with arbitrary transfer functions. We have used the analysis to predict the theoretical upper-bound for large-signal SFDR due to static clipping in an ideal LD and external modulators with various linearization techniques. We have also used the analysis to predict the dynamic-clipping-induced nonlinear distortions (NLDs) in a weakly clipped LD, and confirm that dynamic clipping is more important to consider than static clipping when weak LD clipping takes place. Large-signal SFDRs in practical LDs and external modulators were also compared. The validity of our analysis is confirmed through computer simulation and actual measurement of clipping-induced NLDs in a typical CATV-quality DFB LD     

Noise properties of semiconductor lasers due to optical feedback

It has been recognized for some time that reflections back into the cavity of an injection laser from a mechanically unstable external mirror cause noise in the output of the laser (reflection noise). In this paper, noise measurements are presented for index-guided lasers as functions of the output power, the degree of optical isolation and external cavity length (5-15 cm), while current modulation (using 2-4 mA at 50-200 MHz) has been used to reduce the noise levels by as much as 20 dB. It is demonstrated that the mechanism of noise reduction by modulation is the frequency modulation of the laser's spectrum and its interaction with the modes of the external cavity. It is shown that using an optical isolator can give a relative intensity noise of -110 dB while using modulation in addition can reduce this to -125 dB; the bandwidth performance of optical storage systems is discussed in terms of these two schemes.     

Theoretical analysis of external optical feedback on DFB semiconductor lasers

The effect of external optical feedback on resonant frequency, threshold gain, and spectral linewidth of distributed feedback (DFB) semiconductor lasers is theoretically analyzed. The analysis applies to any type of laser cavity formed by a corrugated waveguide limited by partially reflecting facets. It is shown that the sensitivity to optical feedback on a facet is closely related to the power emitted through this facet. Numerical results on wavelength selectivity and on sensitivity to optical feedback are given for conventional DFB lasers having an AR-coated facet and for quarter-wave-shifted (QWS) DFB lasers with AR-coatings on both facets. Both laser types are found to be more sensitive to optical feedback on their AR-coated facet than Fabry-Perot lasers for lowkL. On the other hand, QWS-DFB lasers are found to be relatively insensitive to optical feedback for largekL.     

Intensity noise characteristics of erbium-doped distributed-feedback fiber lasers

We present an experimental and theoretical investigation into the low-frequency intensity noise characteristics of erbium-doped distributed feedback (DFB) fiber lasers. The intensity noise characteristics of six nonidentical erbium-doped DFB fiber lasers are presented along with the characteristics of the grating and doped fibers. An analytical model has been used to predict the intensity noise generated in a linear fiber laser and explain the observed noise characteristics. Overall we find good agreement between our analytical model and observations. In particular, we find the intensity noise at frequencies close to the relaxation oscillation frequency significantly elevated due to excess noise from either spontaneous emission or cavity loss modulation. These results can be used to optimize the fiber laser design for sensor applications.     

Criterion of external feedback sensitivity in index-coupled andgain-coupled DFB semiconductor lasers to be free from excess intensitynoise

Sensitivities of index-coupled as well as gain-coupled DFB semiconductor lasers to external optical feedback are theoretically investigated in this work. The conditions of getting free operation from excess intensity noise in these two types of DFB lasers are obtained. It is found that the sensitivity of external feedback for these two types of DFB laser depends significantly on the structure such as the internal grating, the facet reflection, and the phase relation between the grating and the facet. The condition of making a DFB laser less sensitive to external optical feedback is to adjust the lasing wavelength to the Bragg wavelength in both index-coupled and gain-coupled structures. A phase-adjusting mechanism such as the λ/4 shift region in the index-coupled structure is effective to avoid the external feedback     

Simple and Accurate Optical Frequency Domain Ranging Using Off-the-Shelf DFB Lasers Subject to Frequency-Shifted Optical Feedback

It is demonstrated that accurate distance measurement may be effected using a commercially available distributed feedback (DFB) semiconductor laser subject to frequency-shifted optical feedback. A simple experimental arrangement is employed wherein a chirped frequency comb is generated in an external cavity DFB laser using an intracavity acoustic-optic modulator. The frequency comb generates a beat frequency which is proportional to the path difference of a target and reference arm. An estimate of the accuracy and resolution of the measurement is given.     

用于布里渊分布式光纤传感的光学锁频系统

报道了一种用于布里渊分布式光纤传感器(DOFS)的高稳定光学锁频系统。一台波长为1550nm的半导体分布反馈(DFB)激光器作为主激光器用于光纤传感探测,另一台同样的激光器作为从激光器,采用光学锁相的方法将其与主激光器进行频率跟踪,使主激光器与从激光器频率差恒定为11GHz。利用该光源搭建基于自发布里渊的分布式光纤传感系统(BOTDR),可以有效地实现宽带移频,使得探测解调频率降低到百兆赫兹量级,大大降低了探测的噪声,并且降低了BOTDR系统成本。结果表明,采用此光源方案的频率波动范围为±1MHz。     

Amplified-spontaneous-emission spectrum of the radiation field in surface-emitting DFB lasers

In this paper, the authors calculate the amplified-spontaneous-emission spectrum of the radiation field in surface-emitting distributed feedback (DFB) lasers. The response of the laser cavity to the Langevin noise source in the frequency domain is obtained using the newly developed Green's functions for the slowly varying amplitudes of the guided waves. The authors show that the power spectra from the surface and the edge are different, and this discrepancy is due to excitation of the radiation field by the interference between the counter-propagating waves inside the cavity. This feature can be properly exploited in the design of surface-emitting DFB lasers for optical communications.     

Analysis of external optical feedback on distributed-feedbacksemiconductor lasers above threshold

An analysis of external optical feedback based on distributed-feedback (DFB) semiconductor lasers above threshold is presented. It is based on a numerical model taking into account the longitudinal spatial hole burning (SHB) effect, which has been recently known to be an important phenomenon for DFB lasers above threshold. Numerical results for a typical index-coupled quarter-wave-shifted (QWS) DFB laser with a moderate coupling coefficient (κL=3) are given. It was found that the SHB effect can affect the sensitivity to feedback for DFB lasers above threshold