Mikel Arteaga - Academia.edu (original) (raw)

Papers by Mikel Arteaga

Research paper thumbnail of Parametric investigation of polarization properties of VCSELs subject to optical feedback from extremely-short-external-cavity

Finds and Results from the Swedish Cyprus Expedition: A Gender Perspective at the Medelhavsmuseet, 2004

Research paper thumbnail of Polarization control and stabilization of VCSELs by means of optical feedback from an extremely short external cavity

2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, 2007

ABSTRACT

Research paper thumbnail of Experimental Evidence of Coherence Resonance in a Time-Delayed Bistable System

Physical Review Letters, 2007

We report on the experimental observation of coherence resonance in a bistable system with delay.... more We report on the experimental observation of coherence resonance in a bistable system with delay. Our system consists of a vertical-cavity surface-emitting laser subject to time-delayed optical feedback simultaneously from a long and from an extremely short external cavity. Coherence resonance is experimentally proven by analysis of the residence time distribution of the polarization mode-hopping regime and of the signal to noise ratio in the power spectrum.

Research paper thumbnail of Investigation of polarization properties of VCELs subject to optical feedback from an extremely short external cavity

Finds and Results from the Swedish Cyprus Expedition: A Gender Perspective at the Medelhavsmuseet, 2006

A two modes rate equation model for vertical-cavity surface-emitting lasers (VCSELs) subject to o... more A two modes rate equation model for vertical-cavity surface-emitting lasers (VCSELs) subject to optical feedback from an extremely short external cavity (ESEC) is presented. By making use of it we develop a map of bistability to investigate the parametric dependence of polarization properties of VCSELs in such configuration, finding out a periodic dependence of the polarization switching (PS) currents on the ESEC length. By increasing the external mirror reflectivity we can make this periodic dependence stronger and strongly asymmetric providing the possibility to prevent PS for any injection current achieving polarization stabilization in VCSELs. Further numerical simulations with isotropic and non isotropic feedback show how parameters as the compression coefficients, the frequency splitting between the linearly polarized (LP) modes, the differential gain and the top mirror reflection coefficient, affect the map of bistability.

Research paper thumbnail of Extremely short external cavity VCSELs: a new way to achieve polarization control and stabilization

Research paper thumbnail of Panajotov aot2011

Research paper thumbnail of <title>Experimental study of transverse mode dynamics in vertical-cavity surface-emitting lasers under current modulation</title>

Semiconductor Lasers and Laser Dynamics III, 2008

Research paper thumbnail of <title>Optical feedback from extremely short external cavity in VCSEL</title>

Micro-Optics, VCSELs, and Photonic Interconnects, 2004

ABSTRACT Vertical-cavity surface-emitting lasers (VCSELs) have now entered the stage of implement... more ABSTRACT Vertical-cavity surface-emitting lasers (VCSELs) have now entered the stage of implementation in optical devices and networks. Besides the number of properties superior to EEL, VCSELs have the drawback of less stabilized polarization. As any semiconductor laser, VCSELs are sensitive to Optical Feedback (OF) due to parasitic reflections inevitable in practical applications. Here we experimentally and numerically investigate the spectral and polarization properties of VCSELs subject to polarization insensitive optical feedback from an extremely short external cavity -ESEC (few microns). We observe that the total output power and the wavelength of laser emission are sinusoidally, in-phase modulated with the external cavity (EC) length and with a period equal to half the wavelength of the VCSEL. Moreover the currents at which the switches between the two linearly polarized (LP) modes happen and the hysteresis width are also sinusoidally modulated with the same period. When biasing the VCSEL at the switching current polarization switching between two orthogonal linearly polarized states happens at different EC lengths. This polarization switching happens through a hysteresis when decreasing and increasing the EC length. We have also develop a two modes rate equation model that proves and explains the changes of all VCSEL characteristics observed in the experimental part, showing very good agreement with the experimental results.

Research paper thumbnail of Study of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity

CLEO/Europe. 2005 Conference on Lasers and Electro-Optics Europe, 2005., 2005

ABSTRACT In this paper, we present a rate equation model for VCSELs subject to optical feedback f... more ABSTRACT In this paper, we present a rate equation model for VCSELs subject to optical feedback from an extremely short external cavity (ESEC) to develop a map of bystability. This allows us to investigate the parametric dependence of polarization properties of VCSELs in ESEC configuration, finding out a strong periodic dependence of the polarisation switching (PS) current on the external cavity length. By increasing the external mirror reflectivity we can make this periodic dependence not only stronger but also asymmetric providing the possibility of preventing PS for any injection current, which constitutes a new way to achieve polarization stabilization in VCSELs.

Research paper thumbnail of Integrated Optoelectronic Devices 2004

Photonic crystal fibers (PCFs) are normally holey fibers, made of silica glass, which is opaque i... more Photonic crystal fibers (PCFs) are normally holey fibers, made of silica glass, which is opaque in the mid- and far-infrared spectral range 3-20 μm. We have fabricated novel PCFs by multiple extrusions of silver halide (AgClxBr1-x) crystalline materials, which are highly transparent in this spectral range. These PCFs are composed of two solid materials: the core consists of pure AgBr (n=2.16), and the cladding includes small diameter fiberoptic elements, made of AgCl (n=1.98). These AgCl fiberoptic elements are arranged in two concentric hexagonal rings around the core. This structure gives rise to a cladding region of lower refractive index, thus ensuring total internal reflection. Flexible PCFs of outer diameter 1mm and length of about 1m were fabricated, and their optical properties were measured. Measurements of numerical aperture, laser power transmission and evanescent wave spectroscopy indicated that the PCFs behave like a core-clad structure. There was a good agreement betwe...

Research paper thumbnail of Coherence resonance in a time-delayed bistable system

Research paper thumbnail of Chaotic polarization dynamics and chaos synchronization in VCSELs

2009 IEEE/LEOS Winter Topicals Meeting Series, 2009

We review our recent results related to nonlinear polarization dynamics and chaos in VCSELs. The ... more We review our recent results related to nonlinear polarization dynamics and chaos in VCSELs. The possibility to generate multimode chaos motivates the study of chaos synchronization in coupled VCSELs and its application for secure communications.

Research paper thumbnail of <title>Semiconductor lasers for quantum sensing</title>

Quantum Sensing and Nanophotonic Devices, 2004

Semiconductor lasers can be used simultaneously as optical sources and optical sensors, as they a... more Semiconductor lasers can be used simultaneously as optical sources and optical sensors, as they are extremely sensitive to a small amount of coherent optical feedback. We present a survey on experimental results on optical feedback in semiconductor lasers and on different approaches to describe its effect on the laser properties. We show that for long and moderate long external cavities

Research paper thumbnail of Double cavity feedback and experimental observation of coherence resonance

2008 10th Anniversary International Conference on Transparent Optical Networks, 2008

We first discuss the effect of isotropic optical feedback from an extremely short external cavity... more We first discuss the effect of isotropic optical feedback from an extremely short external cavity (ESEC) (K. Petermann, 1195, K. Hsu, et al., 1998) on the emission properties of vertical-cavity surface-emitting lasers (VCSELs). When changing the external cavity length a modulation of the total power and the wavelength emitted by the VCSEL is observed with a period of half the

Research paper thumbnail of Light polarization fingerprints on nonlinear dynamics of vertical-cavity surface-emitting lasers

Opto-Electronics Review, 2008

In this paper we summarize the recent results on nonlinear dynamics of vertical-cavity surface-em... more In this paper we summarize the recent results on nonlinear dynamics of vertical-cavity surface-emitting lasers (VCSELs) which are bearing the fingerprints of the particular polarization properties of VCSELs. Due to the surface emission and cylindrical symmetry, VCSELs lack strong polarization anisotropy and may undergo polarization switching and polarization mode-hopping. This provides new specificities to the rich nonlinear dynamics induced in VCSELs by an external perturbation. We unveil both experimentally and theoretically these new specificities for the case of optical feedback, optical injection, and unidirectional synchronization between VCSELs.

Research paper thumbnail of Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback

Optical Engineering, 2006

ABSTRACT

Research paper thumbnail of Spectral properties of edge-emitting semiconductor laser subject to optical feedback from extremely short external cavity

Optical and Quantum Electronics, 2008

We experimentally and theoretically study the impact of optical feedback from an extremely short ... more We experimentally and theoretically study the impact of optical feedback from an extremely short external cavity (tens of µm) on the spectral behavior of edge emitting lasers (EELs). We are able to investigate a broad range of external cavity lengths and feedback strengths, by using a nanometer precision movable mirror attached to a fiber facet. A discrete modulation of the wavelength of operation is observed and its amplitude depends on the external cavity length and the external mirror reflectivity. We show that it is possible to optimize the tuning range of such a discrete wavelength tunable laser with respect to the external cavity and laser parameters.

Research paper thumbnail of Investigation of Polarization Properties of VCSELs Subject to Optical Feedback From an Extremely Short External Cavity—Part I: Theoretical Analysis

IEEE Journal of Quantum Electronics, 2006

A two modes rate equation model for vertical-cavity surface-emitting lasers (VCSELs) subject to o... more A two modes rate equation model for vertical-cavity surface-emitting lasers (VCSELs) subject to optical feedback from an extremely short external cavity (ESEC) is presented. By making use of it we develop a map of bistability to investigate the parametric dependence of polarization properties of VCSELs in such configuration, finding out a periodic dependence of the polarization switching (PS) currents on the ESEC length. By increasing the external mirror reflectivity we can make this periodic dependence stronger and strongly asymmetric providing the possibility to prevent PS for any injection current achieving polarization stabilization in VCSELs. Further numerical simulations with isotropic and non isotropic feedback show how parameters as the compression coefficients, the frequency splitting between the linearly polarized (LP) modes, the differential gain and the top mirror reflection coefficient, affect the map of bistability.

Research paper thumbnail of Nonlinear dynamics of vertical-cavity surface-emitting lasers

IEEE Journal of Quantum Electronics, 1999

The dependence of the transient response of a vertical-cavity surface-emitting laser (VCSEL) on i... more The dependence of the transient response of a vertical-cavity surface-emitting laser (VCSEL) on its aperture size is investigated subject to direct current modulation and external optical feedback. It is shown that lasers with small aperture size suppress higher order bifurcations and chaos even under large-signal modulation and external optical feedback. Furthermore, the noise characteristics of VCSEL's under the influence of external optical feedback are studied via the calculation of relative intensity noise. It is found that the level of external optical feedback for the onset of coherence collapse is high for devices with small aperture size. On the other hand, the smallsignal response of lasers is also analyzed through the calculation of third-order harmonic distortion. It is shown that harmonic distortion is minimized in small devices. Therefore, VCSEL's with small aperture size have better immunity to irregular response under direct current modulation and external optical feedback.

Research paper thumbnail of Optical feedback in vertical-cavity surface-emitting lasers

IEEE Journal of Quantum Electronics, 2001

Optical feedback in a vertical-cavity surface-emitting laser due to a fiber facet of varying posi... more Optical feedback in a vertical-cavity surface-emitting laser due to a fiber facet of varying position is studied in experiment and theory. Measured spectra and light-current curves show periodic variations in resonant wavelength, threshold current, differential quantum efficiency, and output power as a function of fiber position. Theoretical results were obtained using a 2 2 vector propagation matrix method which models the laser and fiber in a single structure and shows good agreement with experimental results. A novel method for determining the linewidth enhancement factor by analyzing the wavelength variation as a function of fiber position is presented and a value of = 2.8 was obtained. Index Terms-Linewidth enhancement factor, optical feedback, optical fiber, vertical-cavity surface-emitting laser. I. INTRODUCTION I N THE last decade, progress in the development of verticalcavity surface-emitting lasers (VCSEL) has emerged to benefit fiber-optic communication systems due to excellent VCSEL performance characteristics and advantages in manufacturing and testing over their edge-emitting counterparts. VCSELs typically consist of a multi-quantum-well active region surrounded by top and bottom distributed Bragg reflectors (DBRs) which create the resonant cavity. The incorporation of oxide apertures for index-guided VCSEL design [1], [2] has allowed for lower threshold currents, higher powers, and single-mode operation. When coupling laser light into glass optical fiber for optical communication systems, the presence of the fiber facet can create optical feedback in the laser cavity and change the operational characteristics of the laser. Optical feedback is generally considered to be detrimental to the performance of lasers because, under certain conditions, feedback can cause significant changes in spectrum [3], [4], power instabilities [5]-[7], relative intensity noise [8], [9], and polarization switching [10], [11]. An important and practical case to consider is that of fiber-induced feedback where the fiber facet is positioned to within less than two microns of the VCSEL. Heinrich et al. [12] showed experimentally that fiber feedback could have a significant effect on the spectrum and output power of multimode VCSELs. Law et al. [5] predicted power variations in VCSELs due to varying Manuscript received May 4, 2001.

Research paper thumbnail of Parametric investigation of polarization properties of VCSELs subject to optical feedback from extremely-short-external-cavity

Finds and Results from the Swedish Cyprus Expedition: A Gender Perspective at the Medelhavsmuseet, 2004

Research paper thumbnail of Polarization control and stabilization of VCSELs by means of optical feedback from an extremely short external cavity

2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, 2007

ABSTRACT

Research paper thumbnail of Experimental Evidence of Coherence Resonance in a Time-Delayed Bistable System

Physical Review Letters, 2007

We report on the experimental observation of coherence resonance in a bistable system with delay.... more We report on the experimental observation of coherence resonance in a bistable system with delay. Our system consists of a vertical-cavity surface-emitting laser subject to time-delayed optical feedback simultaneously from a long and from an extremely short external cavity. Coherence resonance is experimentally proven by analysis of the residence time distribution of the polarization mode-hopping regime and of the signal to noise ratio in the power spectrum.

Research paper thumbnail of Investigation of polarization properties of VCELs subject to optical feedback from an extremely short external cavity

Finds and Results from the Swedish Cyprus Expedition: A Gender Perspective at the Medelhavsmuseet, 2006

A two modes rate equation model for vertical-cavity surface-emitting lasers (VCSELs) subject to o... more A two modes rate equation model for vertical-cavity surface-emitting lasers (VCSELs) subject to optical feedback from an extremely short external cavity (ESEC) is presented. By making use of it we develop a map of bistability to investigate the parametric dependence of polarization properties of VCSELs in such configuration, finding out a periodic dependence of the polarization switching (PS) currents on the ESEC length. By increasing the external mirror reflectivity we can make this periodic dependence stronger and strongly asymmetric providing the possibility to prevent PS for any injection current achieving polarization stabilization in VCSELs. Further numerical simulations with isotropic and non isotropic feedback show how parameters as the compression coefficients, the frequency splitting between the linearly polarized (LP) modes, the differential gain and the top mirror reflection coefficient, affect the map of bistability.

Research paper thumbnail of Extremely short external cavity VCSELs: a new way to achieve polarization control and stabilization

Research paper thumbnail of Panajotov aot2011

Research paper thumbnail of <title>Experimental study of transverse mode dynamics in vertical-cavity surface-emitting lasers under current modulation</title>

Semiconductor Lasers and Laser Dynamics III, 2008

Research paper thumbnail of <title>Optical feedback from extremely short external cavity in VCSEL</title>

Micro-Optics, VCSELs, and Photonic Interconnects, 2004

ABSTRACT Vertical-cavity surface-emitting lasers (VCSELs) have now entered the stage of implement... more ABSTRACT Vertical-cavity surface-emitting lasers (VCSELs) have now entered the stage of implementation in optical devices and networks. Besides the number of properties superior to EEL, VCSELs have the drawback of less stabilized polarization. As any semiconductor laser, VCSELs are sensitive to Optical Feedback (OF) due to parasitic reflections inevitable in practical applications. Here we experimentally and numerically investigate the spectral and polarization properties of VCSELs subject to polarization insensitive optical feedback from an extremely short external cavity -ESEC (few microns). We observe that the total output power and the wavelength of laser emission are sinusoidally, in-phase modulated with the external cavity (EC) length and with a period equal to half the wavelength of the VCSEL. Moreover the currents at which the switches between the two linearly polarized (LP) modes happen and the hysteresis width are also sinusoidally modulated with the same period. When biasing the VCSEL at the switching current polarization switching between two orthogonal linearly polarized states happens at different EC lengths. This polarization switching happens through a hysteresis when decreasing and increasing the EC length. We have also develop a two modes rate equation model that proves and explains the changes of all VCSEL characteristics observed in the experimental part, showing very good agreement with the experimental results.

Research paper thumbnail of Study of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity

CLEO/Europe. 2005 Conference on Lasers and Electro-Optics Europe, 2005., 2005

ABSTRACT In this paper, we present a rate equation model for VCSELs subject to optical feedback f... more ABSTRACT In this paper, we present a rate equation model for VCSELs subject to optical feedback from an extremely short external cavity (ESEC) to develop a map of bystability. This allows us to investigate the parametric dependence of polarization properties of VCSELs in ESEC configuration, finding out a strong periodic dependence of the polarisation switching (PS) current on the external cavity length. By increasing the external mirror reflectivity we can make this periodic dependence not only stronger but also asymmetric providing the possibility of preventing PS for any injection current, which constitutes a new way to achieve polarization stabilization in VCSELs.

Research paper thumbnail of Integrated Optoelectronic Devices 2004

Photonic crystal fibers (PCFs) are normally holey fibers, made of silica glass, which is opaque i... more Photonic crystal fibers (PCFs) are normally holey fibers, made of silica glass, which is opaque in the mid- and far-infrared spectral range 3-20 μm. We have fabricated novel PCFs by multiple extrusions of silver halide (AgClxBr1-x) crystalline materials, which are highly transparent in this spectral range. These PCFs are composed of two solid materials: the core consists of pure AgBr (n=2.16), and the cladding includes small diameter fiberoptic elements, made of AgCl (n=1.98). These AgCl fiberoptic elements are arranged in two concentric hexagonal rings around the core. This structure gives rise to a cladding region of lower refractive index, thus ensuring total internal reflection. Flexible PCFs of outer diameter 1mm and length of about 1m were fabricated, and their optical properties were measured. Measurements of numerical aperture, laser power transmission and evanescent wave spectroscopy indicated that the PCFs behave like a core-clad structure. There was a good agreement betwe...

Research paper thumbnail of Coherence resonance in a time-delayed bistable system

Research paper thumbnail of Chaotic polarization dynamics and chaos synchronization in VCSELs

2009 IEEE/LEOS Winter Topicals Meeting Series, 2009

We review our recent results related to nonlinear polarization dynamics and chaos in VCSELs. The ... more We review our recent results related to nonlinear polarization dynamics and chaos in VCSELs. The possibility to generate multimode chaos motivates the study of chaos synchronization in coupled VCSELs and its application for secure communications.

Research paper thumbnail of <title>Semiconductor lasers for quantum sensing</title>

Quantum Sensing and Nanophotonic Devices, 2004

Semiconductor lasers can be used simultaneously as optical sources and optical sensors, as they a... more Semiconductor lasers can be used simultaneously as optical sources and optical sensors, as they are extremely sensitive to a small amount of coherent optical feedback. We present a survey on experimental results on optical feedback in semiconductor lasers and on different approaches to describe its effect on the laser properties. We show that for long and moderate long external cavities

Research paper thumbnail of Double cavity feedback and experimental observation of coherence resonance

2008 10th Anniversary International Conference on Transparent Optical Networks, 2008

We first discuss the effect of isotropic optical feedback from an extremely short external cavity... more We first discuss the effect of isotropic optical feedback from an extremely short external cavity (ESEC) (K. Petermann, 1195, K. Hsu, et al., 1998) on the emission properties of vertical-cavity surface-emitting lasers (VCSELs). When changing the external cavity length a modulation of the total power and the wavelength emitted by the VCSEL is observed with a period of half the

Research paper thumbnail of Light polarization fingerprints on nonlinear dynamics of vertical-cavity surface-emitting lasers

Opto-Electronics Review, 2008

In this paper we summarize the recent results on nonlinear dynamics of vertical-cavity surface-em... more In this paper we summarize the recent results on nonlinear dynamics of vertical-cavity surface-emitting lasers (VCSELs) which are bearing the fingerprints of the particular polarization properties of VCSELs. Due to the surface emission and cylindrical symmetry, VCSELs lack strong polarization anisotropy and may undergo polarization switching and polarization mode-hopping. This provides new specificities to the rich nonlinear dynamics induced in VCSELs by an external perturbation. We unveil both experimentally and theoretically these new specificities for the case of optical feedback, optical injection, and unidirectional synchronization between VCSELs.

Research paper thumbnail of Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback

Optical Engineering, 2006

ABSTRACT

Research paper thumbnail of Spectral properties of edge-emitting semiconductor laser subject to optical feedback from extremely short external cavity

Optical and Quantum Electronics, 2008

We experimentally and theoretically study the impact of optical feedback from an extremely short ... more We experimentally and theoretically study the impact of optical feedback from an extremely short external cavity (tens of µm) on the spectral behavior of edge emitting lasers (EELs). We are able to investigate a broad range of external cavity lengths and feedback strengths, by using a nanometer precision movable mirror attached to a fiber facet. A discrete modulation of the wavelength of operation is observed and its amplitude depends on the external cavity length and the external mirror reflectivity. We show that it is possible to optimize the tuning range of such a discrete wavelength tunable laser with respect to the external cavity and laser parameters.

Research paper thumbnail of Investigation of Polarization Properties of VCSELs Subject to Optical Feedback From an Extremely Short External Cavity—Part I: Theoretical Analysis

IEEE Journal of Quantum Electronics, 2006

A two modes rate equation model for vertical-cavity surface-emitting lasers (VCSELs) subject to o... more A two modes rate equation model for vertical-cavity surface-emitting lasers (VCSELs) subject to optical feedback from an extremely short external cavity (ESEC) is presented. By making use of it we develop a map of bistability to investigate the parametric dependence of polarization properties of VCSELs in such configuration, finding out a periodic dependence of the polarization switching (PS) currents on the ESEC length. By increasing the external mirror reflectivity we can make this periodic dependence stronger and strongly asymmetric providing the possibility to prevent PS for any injection current achieving polarization stabilization in VCSELs. Further numerical simulations with isotropic and non isotropic feedback show how parameters as the compression coefficients, the frequency splitting between the linearly polarized (LP) modes, the differential gain and the top mirror reflection coefficient, affect the map of bistability.

Research paper thumbnail of Nonlinear dynamics of vertical-cavity surface-emitting lasers

IEEE Journal of Quantum Electronics, 1999

The dependence of the transient response of a vertical-cavity surface-emitting laser (VCSEL) on i... more The dependence of the transient response of a vertical-cavity surface-emitting laser (VCSEL) on its aperture size is investigated subject to direct current modulation and external optical feedback. It is shown that lasers with small aperture size suppress higher order bifurcations and chaos even under large-signal modulation and external optical feedback. Furthermore, the noise characteristics of VCSEL's under the influence of external optical feedback are studied via the calculation of relative intensity noise. It is found that the level of external optical feedback for the onset of coherence collapse is high for devices with small aperture size. On the other hand, the smallsignal response of lasers is also analyzed through the calculation of third-order harmonic distortion. It is shown that harmonic distortion is minimized in small devices. Therefore, VCSEL's with small aperture size have better immunity to irregular response under direct current modulation and external optical feedback.

Research paper thumbnail of Optical feedback in vertical-cavity surface-emitting lasers

IEEE Journal of Quantum Electronics, 2001

Optical feedback in a vertical-cavity surface-emitting laser due to a fiber facet of varying posi... more Optical feedback in a vertical-cavity surface-emitting laser due to a fiber facet of varying position is studied in experiment and theory. Measured spectra and light-current curves show periodic variations in resonant wavelength, threshold current, differential quantum efficiency, and output power as a function of fiber position. Theoretical results were obtained using a 2 2 vector propagation matrix method which models the laser and fiber in a single structure and shows good agreement with experimental results. A novel method for determining the linewidth enhancement factor by analyzing the wavelength variation as a function of fiber position is presented and a value of = 2.8 was obtained. Index Terms-Linewidth enhancement factor, optical feedback, optical fiber, vertical-cavity surface-emitting laser. I. INTRODUCTION I N THE last decade, progress in the development of verticalcavity surface-emitting lasers (VCSEL) has emerged to benefit fiber-optic communication systems due to excellent VCSEL performance characteristics and advantages in manufacturing and testing over their edge-emitting counterparts. VCSELs typically consist of a multi-quantum-well active region surrounded by top and bottom distributed Bragg reflectors (DBRs) which create the resonant cavity. The incorporation of oxide apertures for index-guided VCSEL design [1], [2] has allowed for lower threshold currents, higher powers, and single-mode operation. When coupling laser light into glass optical fiber for optical communication systems, the presence of the fiber facet can create optical feedback in the laser cavity and change the operational characteristics of the laser. Optical feedback is generally considered to be detrimental to the performance of lasers because, under certain conditions, feedback can cause significant changes in spectrum [3], [4], power instabilities [5]-[7], relative intensity noise [8], [9], and polarization switching [10], [11]. An important and practical case to consider is that of fiber-induced feedback where the fiber facet is positioned to within less than two microns of the VCSEL. Heinrich et al. [12] showed experimentally that fiber feedback could have a significant effect on the spectrum and output power of multimode VCSELs. Law et al. [5] predicted power variations in VCSELs due to varying Manuscript received May 4, 2001.