Emission characteristics from dipoles with fixed positions inFabry-Perot cavities

Spectral characteristics of emission from Fabry-Perot cavities containing dipoles with fixed positions are calculated. It is shown that the emission characteristics can have a sensitive dependence on the precise location of the dipoles. When the dipoles have a fixed position the usual analysis of the emission in terms of the cavity transmission characteristics becomes invalid. Interference effects which lead to the spectral characteristics are then determined by the details of the interaction between the cavity reflectors and the spontaneous wavepackets emitted from the excited dipoles. Typical measured emission which resembles cavity transmission spectra actually results from averaging over many dipole positions. For dipole locations close to a cavity reflector, that is within the first-order coherence length of the spontaneous emission, total emission into all cavity modes can be either increased or decreased depending on the precise dipole location. An example of the dipole localization effects is given in the experimental emission characteristics from a semiconductor Fabry-Perot cavity     

Calculation of the mode suppression ratio in Fabry-Perot, DBR, andexternal cavity lasers

The mode-suppression ratio of Fabry-Perot, distributed Bragg reflector, and external-cavity lasers, both with and without gratings, is calculated using a linear amplifier mode. It is shown that the apparently anomalous behavior of long external cavity structures can be explained using this simple model, provided that the dependence of the spontaneous emission factor on longitudinal mode spacing is included. Practical expressions relating the static mode suppression ratio to laser device parameters are given     

Noise in an AlGaAs semiconductor laser amplifier

The noise characteristics in a Fabry-Perot (FP) cavity type semiconductor laser amplifier, biased at just below its oscillation threshold current, have been studied theoretically and experimentally. Quantum mechanical multimode rate equations containing a Langevin shot noise source and an input signal term were numerically solved for an exponential band-tail model with nok-selection rule. Noise power calculated using this rate equation was compared with a simpler photon statistic master equation method. The experimental results on noise power for an AlGaAs laser amplifier are in reasonable agreement with the two different theoretical predictions. Dominant noise powers in a semiconductor laser amplifier are beat noise powers between signal and spontaneous emission, and between spontaneous emission components. Noise characteristics in a Fabry-Perot cavity type laser amplifier can be improved both by the reduction of the facet mirror reflectivities and by use of an asymmetric cavity configuration with low-input and high-output mirror reflectivities. Two beat noise powers are expressed in simple analytic form by introducing an equivalent noise bandwidth and an excess noise coefficient as figures of merit in an optical amplifier.     

Noise in an AlGaAs Semiconductor Laser Amplifier

The noise characteristics in a Fabry-Perot (FP) cavity type semiconductor laser amplifier, biased at just below its oscillation thresh-old current, have been studied theoretically and experimentally. Quantum mechanical multimode rate equations containing a Langevin shot noise source and an input signal term were numerically solved for an exponential band-tail model with no k-selection rule. Noise power calculated using this rate equation was compared with a simpler photon statistic master equation method. The experimental results on noise power for an AlGaAs laser amplifier are in reasonable agreement with the two different theoretical predictions. Dominant noise powers in a semiconductor laser amplifier are beat noise powers between signal and spontaneous emission, and between spontaneous emission components. Noise characteristics in a Fabry-Perot cavity type laser amplifier can be improved both by the reduction of the facet mirror reflectivities and by use of an asymmetric cavity configuration with low-input and high-output mirror reflectivities. Two beat noise powers are expressed in simple analytic form by introducing an equivalent noise bandwidth and an excess noise coefficient as figures of merit in an optical amplifier.     

Trapped radiation in injection lasers

The effect of trapped radiation on the stimulated emission threshold and power in injection lasers is investigated theoretically and experimentally. The density of trapped radiation is determined by the relation between the gain and the loss coefficients for this radiation in the active region. The last value depends upon treatment of the cavity sidewalls and laser diode geometry. The absorption of spontaneous emission in the active diode region provides for an additional optical excitation of the crystal and can result in a decrease of threshold current. The GaAs laser diodes with Fabry-Perot cavities and four-ended resonators were studied. The lasing threshold for the axial modes is increased with the diode width and that for the nonaxial radiating modes is decreased with it. The luminescence spectra from the cavity ends and sidewalls are investigated as a function of diode length and current density. It is shown that the gained luminescence can be an essential source of energy losses in injection lasers and leads to limitations of dimensions of laser diodes with planar p-n-junctions. Various methods for suppression of harmful radiation and for increase of the stimulated emission power in injection lasers are discussed.     

Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers

A theory of spontaneous emission noise is presented based on classical electromagnetic theory. Unlike conventional theories of laser noise, this presentation is valid for open resonators. A local Langevin force is added to the wave equation to account for spontaneous emission. A general expression is found relating the diffusion coefficient of this force to the imaginary part of the dielectric function. The fields of lasers and amplifiers are found by solving the wave equation by the Green's function method. The lasing mode is a resonant state associated with a pole in Green's function. In this way, noise in lasers and amplifiers is treated by a unified approach that is valid for either gain guiding or index guiding. The Langevin rate equations for the laser are derived. The theory is illustrated with applications to traveling wave and Fabry-Perot amplifiers and Fabry-Perot lasers. Several new results are found: optical amplifier noise increases inversely with quantum efficiency; spontaneous emission into the lasing mode is enhanced in lasers with low facet reflectivities; and the linewidth of a Fabry-Perot laser with a passive section decreases as the square of the fraction of the cavity optical length that is active.     

半导体激光器的微腔结构调制及其脉码在光纤中的传输

采用腔量子电动力学(QED)方法,定量讨论了平面结构微腔半导体激光器的自发发射特征物理量随腔结构的变化规律.在微腔半导体激光器自发发射因子调制、自发发射寿命调制以及一些实验依据的基础上,提出了微腔结构调制方法.数值模拟了其脉码在光纤中的传输图形.结果表明,微腔结构调制方法在提高脉码比特率方面优于同参数下的电流调制方法.     

Characteristics of a semiconductor laser with external feedback

The theoretical analysis of the compound cavity of a semiconductor laser with external optical feedback is conducted. For large optical feedback, the output power from the laser and its oscillation frequency differ from those for small optical feedback. From the rate equations of the compound cavity, the conditions of the laser oscillation are derived in the presence of large optical feedback The dependencies of the output power and the laser oscillation frequency on the external-cavity length are investigated. Some new results involving laser oscillation depending on the external-cavity length are presented. The experimental results are compared with theoretical predictions. The dependence of the laser oscillation on the external-cavity length is qualitatively explained in the present model     

玻璃微球荧光的腔量子电动力学增强效应

报道了腔量子电动力学效应对高钡玻璃微球荧光光谱的影响,利用Mie散射的共振峰位计算公式,对测量的光谱进行了分析,估算了自发辐射速率的量子电动力学效应的增强因子,实验证实其增强幅度超过676倍。     

The linewidth of a mode-locked semiconductor laser caused by spontaneous emission: Experimental comparison to single-mode operation

We experimentally compare the linewidth of the individual modes of an extended cavity semiconductor laser when it operates mode locked and when it operates single mode. We find that the linewidths under these two operating conditions have the same inverse dependence on the average power. Therefore, the coherence length of the mode-locked source is the same as that of the single-mode source despite lower power per mode, much broader total bandwidth, and much higher spontaneous emission noise level in the mode-locked source. It can be inferred from our data that the electric fields of over 1000 consecutive mode-locked pulses are correlated.     

Self-calibrated interferometric-intensity-based optical fibersensors

This paper presents self-calibrated interferometric-intensity-based optical fiber sensors, which combine for the first time fiber interferometry and intensity-based devices into a single sensor system. The sensor involves an extrinsic Fabry-Perot (FP) interferometric cavity. The broadband light returned from the FP cavity is split into two channels in such a way that one channel has a coherence length much longer than the doubled air-gap separation in the sensor so the FP generates effective interference, while the coherence length in the other channel is so short that no effective interference takes place. As a result, the optical signal in the channel with a long coherence length yields information about the FP cavity length while the signal in the other channel is proportional only to the source power, fiber attenuation, and other optical loss factors in the optical path. To eliminate fringe direction ambiguity and relative measurement limitations associated with interferometric sensors, the sensor is designed such that it is operated over the linear range between a valley and a peak of one interference fringe in the first channel. Moreover, the ratiometric signal-processing method is applied for the signals in the two channels to obtain self-calibrating measurement to compensate for all unwanted factors, including source power variations and fiber bending losses. Various pressure and temperature sensors based on the self-calibrated interferometric/intensity-based scheme are designed, fabricated, and tested. Experimental results show that a resolution as high as 0.02% of full scale can be obtained for both the pressure and temperature measurements     

Effects of nonlinear gain on mode-hopping in semiconductor laserdiodes

A systematic and comprehensive analysis of longitudinal mode-hopping, due to nonlinear gain, and its influence on the design criteria of transverse-mode-controlled semiconductor laser diodes are presented. An existing nonlinear model, which was derived using a density matrix formalism, has been extended in this paper to generate the nonlinear gain coefficient matrix. Properties of the nonlinear gain coefficient matrix, which describes the interaction among cavity modes, are discussed. Using the new nonlinear gain in the steady-state multimode rate equations, conventional Fabry-Perot (FP) and short cavity Fabry-Perot (SFP) semiconductor laser diodes have been numerically simulated. Design issues such as cavity length, cavity volume, facet reflectivity, spontaneous emission factor, mode wavelength, intraband relaxation time, linewidth enhancement factor, and laser structure are also discussed. It is shown that increasing the injection current causes the lasing mode to jump to longer wavelengths. Furthermore, increasing the spontaneous emission factor reduces the dynamic range of laser operation without mode-hopping, and vice versa for short cavity. It has been also shown that the carrier density in the active region shifts to higher values (i.e., experiences a kink) at the onset of mode-hopping. Finally, the total modal gain (linear and nonlinear) competes as the injection current increases     

Multiplexed optical fiber sensors using a single Fabry-Perotresonator for phase modulation

This paper describes the use of different optical return paths in a single Fabry-Perot phase modulator to perform coherence division multiplexing, and a combination of coherence and frequency division multiplexing of Fabry-Perot interferometric optical fiber sensors. A path-matched differential interferometry (PMDI) using low finesse Fabry-Perot sensors, one moderate finesse Fabry-Perot read-out resonator, and a broadband light source consisting of amplified spontaneous emission (ASE) from an erbium-doped fiber amplifier (EDFA) is used to illustrate the idea. The first, second and third order of multiple paths in a single Fabry-Perot read-out resonator are used to path-match three Fabry-Perot sensors. These three orders of path-matches provide a single, double and triple depth of modulation (phase-change) when the read-out is used as an optical phase modulator, and therefore provide a single, double and triple carrier frequency when serrodyne demodulation is used. The use of a single moderate finesse read-out Fabry-Perot resonator to simultaneously path-match coherence multiplexed sensors reduces the complexity of the optical system. Experiments and modeling are used to show the existence of the first, second, and third order of interference path-match conditions, and to determine the read-out configuration that enhances the visibility of the higher order path-match conditions. Using the multiple return paths in a single PZT-based Fabry-Perot read-out interferometer and serrodyne demodulation, several multiplexing schemes are investigated, and their relative merits discussed     

A quantum amplifier model for predicting temporal variations in theoutput power from a semiconductor laser on a picosecond time scale

A new model for simulating temporal fluctuations in the power emitted by a semiconductor laser is described. Light in the cavity is assumed to circulate in the form of traveling photon packets, in which the photon number fluctuates due to the processes of spontaneous emission, stimulated emission, absorption, scattering, and reflection. The dipole dephasing time T plays a critical role in modeling the interaction of the photon packets and gain medium. The Monte Carlo method is used to simulate the temporal behavior of a continuously pumped Fabry-Perot laser. The laser output power is found to exhibit periodic fluctuations at the cavity transit time frequency (longitudinal mode beat frequency). The amplitude of these fluctuations, as well as the relaxation oscillation, which occurs at a much lower frequency, is strongly influenced by the magnitude of T. The results of these simulations are related to the temporal behavior expected from a conventional FP laser     

Characteristics of AlGaAs Fabry-Perot cavity type laser amplifiers

Signal gain, saturation power, and noise bandwidth, which are important parameters determining preamplifier and linear repeater system performance [1], were measured for an AlGaAs Fabry-Perot cavity type laser amplifier. The unsaturated signal gain increases with the pumping level and a maximum signal gain as high as 27 dB is obtained near oscillation threshold. The saturation output power, at which the signal gain is decreased from the unsaturated value by 3 dB, is -6 to -8 dBm. The beat noise powers between signal and spontaneous emission components were measured. The error rate characteristics of an AlGaAs laser preamplifier and Si photodiode scheme were studied at a data rate of 100 Mbits/s. The experimental results on noise powers and error rate performance are in reasonable agreement with the theoretical analysis given in an accompanying paper [1].     

Theory of timing jitter in actively mode-locked lasers

An analysis of the pulse-to-pulse timing jitter in an actively mode-locked laser is presented. The model includes spontaneous emission noise, mode-locker driver phase noise, and cavity length detuning. Analytical expressions for the laser pulse train phase noise spectrum, the intensity power spectrum, and the RMS timing jitter are given. The timing fluctuations are characterized by a time constant proportional to the cavity round-trip time times the number of locked modes squared divided by the modulation depth. The contribution from the mode-locker driver phase noise will dominate unless high-stability RF sources are used. The residual timing jitter due to spontaneous emission noise is very sensitive to cavity detuning     

Spectral characteristics of external-cavity controlled semiconductor lasers

Experiments with an external-cavity semiconductor laser indicate that single-frequency oscillation may be obtained in an injection laser when the gain is temporally and spatially stabilized within the active region. Using an originally multimode laser diode as the gain medium, the external-cavity laser oscillates stably in the fundamental spatial mode and in a single longitudinal mode with a frequency which is tunable over a 10 nm spectral range. The rms frequency jitter of the unstabilized laser is 500 kHz. These mode characteristics suggest that spatially inhomogeneous gain saturation is significant only in the lateral direction in the active region of a stripe-geometry double-heterostructure laser diode. A quantitative analysis of the spontaneous emission in the spectral vicinity of the lasing mode shows no evidence of spectral hole burning, with a 0.5 percent upper limit to the depth of the hole burned in the gain spectrum by a lasing mode power of 5 mW.     

Two-stage Fabry-Perot filters as demultiplexers in optical FDMALANs

A high-finesse optical filter can be constructed by cascading two moderate-finesse Fabry-Perot filters of different free spectral ranges. Methods for controlling the undesirable interactions within the interfilter cavity are studied. In particular, the use of an isolator, an attenuator, or a length of fiber longer than the coherence length of the light sources used is considered. The use of a three-mirror filter, which avoids the offending cavity altogether, is also considered. The implications on the number of potential users of optical frequency-division multiple-access (FDMA), local-area networks (LANs) are also addressed     

Optical fiber Fabry-Perot cavities and recirculating delay lines astunable microwave filters

The radio frequency or microwave responses of single-mode fiber Fabry-Perot cavities and recirculating delay lines are studied. It is shown that fiber Fabry-Perot cavities may be used as bandpass filters and the recirculating delay lines as bandstop filters at radio or microwave frequencies. These electric filters are tunable by electrooptic effects since the bandpass or bandstop characteristic changes when the cavity or the delay line length is varied by a few tenths of an optical wavelength. The ultimate limit on speed of tuning is set by the coherence time of the light source. The dependence of the filter responses on the spectral purity of light is studied. Examples are given to illustrate the tunability of these electric filters. The availability of various components required to build the tunable RF or microwave filters is reviewed     

Spectral characteristics of high-power 1.5 μm broad-bandsuperluminescent fiber sources

The spectral variation of spontaneous emission from erbium-doped single-mode fibers is studied with the aim of producing high-power (more than 5 mW), broadband (in excess of 10 nm) amplified spontaneous emission sources for fiber gyroscope applications. In particular, the evolution of spectral shape and center wavelength with fiber length and output power in the previously unstudied high-power regime where saturation effects dominate is demonstrated. A visibility curve for a potential twin-peaked nonresonant erbium-doped fiber gyroscope source with a short (210 μm) coherence length is also presented