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Daan Lenstra

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I am Emeritus Professor of Theoretical Physics, presently affiliated with Eindhoven University of Technology, Institute of Photonic Integration. My specialty is dynamics and stability of semiconductor lasers.

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Villetaneuse

Sebastien Forget

Stefano Toffanin

Mount Holyoke College

Université Sorbonne Paris Nord / Sorbonne Paris Nord University

Bernard Geffroy

Muhammad H Sazzad

The University of New South Wales

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Papers by Daan Lenstra

Simple Theory of Spectral Evolution in an Organic Laser Diode

HAL (Le Centre pour la Communication Scientifique Directe), Mar 4, 2023

The spectrum of the light emitted by a microcavity OLED is strongly time dependent on the nanosec... more The spectrum of the light emitted by a microcavity OLED is strongly time dependent on the nanosecond timescale after switch-on of the pump mechanism. This is one reason why convincing confirmation of laser operation in such device is difficult. The simple theory here presented is helpful in interpreting observed light-emission behavior. One important finding is that the occurrence in the optical spectrum of a narrow Lorentzian on top of a spontaneousemission pedestal is no guarantee for observed laser operation. Another finding is that reabsorbtion by the singlet excitons leads to the highest gain when the cavity is detuned to the red side of the emission spectrum. This is confirmed by experimental observations on an optically pumped organic laser diode.

Semiconductor Laser Dynamics

Design, Fabrication and Validation of Mixed Order Distributed Feed-Back Organic Diode Laser Cavity

Photonics

In the context of the quest for the organic laser diode, we address a key challenge to design and... more In the context of the quest for the organic laser diode, we address a key challenge to design and fabricate high-quality factor cavities compatible with electrical excitation of organic semiconductors. More precisely, we present the design of DFB micro-cavities for integration in organic laser diodes and their validation under optical pumping. To design high-quality factor mixed-order DFB micro-cavities, we consider the half- and quarter-wavelength multilayered system and use the optical waveguide analysis to quantify the effective indices of the high and low indices, and the matrix transfer method to calculate the reflectances. Matrices of DFB micro-cavities made from different doses and different grating periods were fabricated. We then identified those showing laser emission under optical pumping as an indication of optimal matching of their resonance wavelength with respect to the electroluminescence peak of the organic gain material. Potential applications of organic laser diod...

First-Passage-Time Analysis of the Pulse-Timing Statistics in a Two-Section Semiconductor Laser under Excitable and Noisy Conditions

Photonics

A two-section semiconductor laser can exhibit excitability for certain parameter settings. When u... more A two-section semiconductor laser can exhibit excitability for certain parameter settings. When used as a photonic spiking neuron, it is relevant to investigate its sensitivity to noise due to, e.g., spontaneous emission. Under excitable conditions, the system emits irregularly timed noise-triggered pulses. Their statistics is analyzed in terms of a first-passage time distribution for the fluctuating intensity to reach the threshold for excitable response. Two analytic approximations valid for short and long times, respectively, are derived which very well explain measured and simulated pulse-repetition time distributions. This provides physical insight into the noise-triggered spiking mechanism.

Monolithically Integrated Widely Tunable Coupled Cavity Laser Source for Gas Sensing Applications around 2.0μm Wavelength

Advanced Photonics 2015, 2015

Intermediate-depth seismicity in the subducting Philippine Sea slab beneath Kyushu island shows a... more

Bound Modes in Dielectric Microcavities

We demonstrate how exactly bound cavity modes can be realized in dielectric structures other than... more We demonstrate how exactly bound cavity modes can be realized in dielectric structures other than 3d photonic crystals. For a microcavity consisting of crossed anisotropic layers, we derive the cavity resonance frequencies, and spontaneous emission rates. For a dielectric structure with dissipative loss and central layer with gain, the beta factor of direct spontaneous emission into a cavity mode and the laser threshold is calculated.

Organic Diode Laser Dynamics: Rate-Equation Model, Reabsorption, Validation and Threshold Predictions

Photonics, 2021

We present and analyze a simple model based on six rate equations for an electrically pumped orga... more We present and analyze a simple model based on six rate equations for an electrically pumped organic diode laser. The model applies to organic host-guest systems and includes Stoke-shifted reabsorption in a self-consistent manner. With the validated model for the Alq3:DCM host-guest system, we predict the threshold for short-pulse laser operation. We predict laser operation characterized by damped relaxation oscillations in the GHz regime and several orders of magnitude linewidth narrowing. Prospect for CW steady-state laser operation is discussed.

02 10 17 1 v 1 2 4 O ct 2 00 2 Bound Modes in Dielectric Microcavities

We demonstrate how exactly bound cavity modes can be realize d in dielectric structures other tha... more We demonstrate how exactly bound cavity modes can be realize d in dielectric structures other than 3d photonic crystals. For a microcavity consisting of crossed ani sotropic layers, we derive the cavity resonance frequencies, and spontaneous emission rates. For a dielectric structure with dissipative loss and central layer with gain, theβ factor of direct spontaneous emission into a cavity mode and the laser threshold is calculated.

First-Passage-Time Distributions in a Bistable Two-Mode Laser

Coherence and Quantum Optics V, 1984

The statistical properties of a two-mode laser can be described by a four-dimensional Fokker-Plan... more The statistical properties of a two-mode laser can be described by a four-dimensional Fokker-Planck (FP) equation for the real and imaginary parts of the weakly time dependent field amplitudes.1 It has been shown in the rather special case in which the only asymmetry between the modes was in their net linear gain while there was no dispersion, that this equation can be reduced to a one-dimensional FP-equation for the intensity of one of the modes,2,3 which led to certain predictions that have been confirmed by experiment.4 A similar way of approach, that is, reducing the description of the statistical behavior of a field to the analysis of a one-dimensional FP-equation, was followed in the problem of the mean first-passage time in optical bistability.5 In the present contribution we will deal with the first-passage-time (FPT) problem in a bistable two-mode laser without making any of the above mentioned restrictions concerning the symmetry of the modes or the absence of dispersion. The method employed as well as the results obtained are applicable to a wide class of bistable lasers, including homogeneously broadened ring lasers3. single-mode lasers exhibiting polarization bistabilityb6 and single-mode lasers operating under weak external optical feedback conditions7. Moreover, they will be relevant in other contexts too, such as in optical bistability.

Analogies in Optics and Micro Electronics || Aharonov-Bohm Oscillations and Non-Local Electronic Conduction

In a mesoscopic (size smaller than the electron phase coherence length Lφ ∼ 1µm) disordered metal... more In a mesoscopic (size smaller than the electron phase coherence length Lφ ∼ 1µm) disordered metal film or Si-MOSFET inversion layer, the ensemble averaging of the interference between scattered electron waves is incomplete. The tuning of the electron phase by the Aharonov-Bohm effect causes sample-specific magneto conductance fluctuations with rms amplitude Gun = e2/h. For a mesoscopic loop, the fluctuations are replaced by oscillations with flux period h/e. In the macroscopic regime, only the interference in the backscatterina direction survives and causes the weak electron localization. In a long cylinder (diameter ∼ Lφ), the coherent backscattering induces magneto conductance oscillations with flux period h/2e.

On the Analogy Between Electrons and Light

Coherence and Quantum Optics VI, 1989

Many typically quantummechanical concepts have equivalent notions in the context of electromagnet... more Many typically quantummechanical concepts have equivalent notions in the context of electromagnetic waves and especially in coherent optics. The correspondence between these two areas in physics is related to the fact that both are governed by wave equations. The miniaturization of devices in solid state physics has led to new phenomena in which coherent propagation and interference of electrons play significant, if not dominant roles1This will undoubtedly stimulate the analogy thinking in terms of analogies between electrons and light. Many quantummechanical phenomena underlying the performance of presently made submicron systems have optical analogies which may experimentally be realized in relatively easy ways2In view of the enormous progress made in optical engineering devices since the availability of lasers as coherent light sources we are facing, among other things, the fascinating possibility of performing “visible” quantummechanics on a macroscopic scale with rather simple set ups.

Optical level crossings

We discuss the behavior of two coupled optical modes, specializing to the case of a clockwise and... more We discuss the behavior of two coupled optical modes, specializing to the case of a clockwise and a counter-clockwise wave in an optical ring with backscattering. Generally the coupling constant is complex-valued; the limiting cases of conservative and dissipative coupling are emphasized. When lifting the polarization degeneracy we deal with four optical modes, coupled by backscattering and birefringence. We also consider an active i.e. oscillating optical ring: this corresponds to adding a nonlinear mode-coupling and leads to a description of frequency-locking in a ring laser gyro. Finally we address the analogy between optical and electronic mode coupling in ring-type and lattice-type configurations (“band structures”). Here we emphasize dynamic effects and discuss the merits and limitations of optical modeling of phenomena such as Bloch oscillations and Zener tunneling.

Suppressed Relaxation-Oscillation Dynamics in a DFB laser Monolithically Integrated with Weak Optical Feedback

CLEO: 2015, 2015

<title>Polarization-dependent amplification in planar waveguides</title>

Physics and Simulation of Optoelectronic Devices IV, 1996

ABSTRACT

Experimental stability diagram of a diode laser subject to weak phase-conjugate feedback from a rubidium vapor cell

by Daan Lenstra and Alexis FISCHER

IEEE Journal of Quantum Electronics, 1999

Special Issue “Semiconductor Laser Dynamics: Fundamentals and Applications”

Photonics

With the advent of integrated photonics, a crucial role is played by semiconductor diode lasers (... more With the advent of integrated photonics, a crucial role is played by semiconductor diode lasers (SDLs) as coherent light sources. Old paradigms of semiconductor laser dynamics, like optical injection, external feedback and the coupling of lasers, regained relevance when SDLs were integrated on photonic chips. This Special Issue presents a collection of seven invited feature papers and 11 contributed papers reporting on recent advances in semiconductor laser dynamics.

Synchronization of Mutually Delay-Coupled Quantum Cascade Lasers with Distinct Pump Strengths

Photonics

The rate equations for two delay-coupled quantum cascade lasers are investigated analytically in ... more The rate equations for two delay-coupled quantum cascade lasers are investigated analytically in the limit of weak coupling and small frequency detuning. We mathematically derive two coupled Adler delay differential equations for the phases of the two electrical fields and show that these equations are no longer valid if the ratio of the two pump parameters is below a critical power of the coupling constant. We analyze this particular case and derive new equations for a single optically injected laser where the delay is no longer present in the arguments of the dependent variables. Our analysis is motivated by the observations of Bogris et al. (IEEE J. Sel. Top. Quant. El. 23, 1500107 (2017)), who found better sensing performance using two coupled quantum cascade lasers when one laser was operating close to the threshold.

Saturation-induced polarization preferences in two-mode oscillating gas lasers

Physica B+C

Nonlinear Dynamics of Semiconductor Lasers

Quantum and Semiclassical Optics: Journal of the European Optical Society Part B

Bifurcations of relaxation oscillations in an optically injected diode laser

Quantum and Semiclassical Optics: Journal of the European Optical Society Part B

Simple Theory of Spectral Evolution in an Organic Laser Diode

HAL (Le Centre pour la Communication Scientifique Directe), Mar 4, 2023

The spectrum of the light emitted by a microcavity OLED is strongly time dependent on the nanosec... more The spectrum of the light emitted by a microcavity OLED is strongly time dependent on the nanosecond timescale after switch-on of the pump mechanism. This is one reason why convincing confirmation of laser operation in such device is difficult. The simple theory here presented is helpful in interpreting observed light-emission behavior. One important finding is that the occurrence in the optical spectrum of a narrow Lorentzian on top of a spontaneousemission pedestal is no guarantee for observed laser operation. Another finding is that reabsorbtion by the singlet excitons leads to the highest gain when the cavity is detuned to the red side of the emission spectrum. This is confirmed by experimental observations on an optically pumped organic laser diode.

Semiconductor Laser Dynamics

Design, Fabrication and Validation of Mixed Order Distributed Feed-Back Organic Diode Laser Cavity

Photonics

In the context of the quest for the organic laser diode, we address a key challenge to design and... more In the context of the quest for the organic laser diode, we address a key challenge to design and fabricate high-quality factor cavities compatible with electrical excitation of organic semiconductors. More precisely, we present the design of DFB micro-cavities for integration in organic laser diodes and their validation under optical pumping. To design high-quality factor mixed-order DFB micro-cavities, we consider the half- and quarter-wavelength multilayered system and use the optical waveguide analysis to quantify the effective indices of the high and low indices, and the matrix transfer method to calculate the reflectances. Matrices of DFB micro-cavities made from different doses and different grating periods were fabricated. We then identified those showing laser emission under optical pumping as an indication of optimal matching of their resonance wavelength with respect to the electroluminescence peak of the organic gain material. Potential applications of organic laser diod...

First-Passage-Time Analysis of the Pulse-Timing Statistics in a Two-Section Semiconductor Laser under Excitable and Noisy Conditions

Photonics

A two-section semiconductor laser can exhibit excitability for certain parameter settings. When u... more A two-section semiconductor laser can exhibit excitability for certain parameter settings. When used as a photonic spiking neuron, it is relevant to investigate its sensitivity to noise due to, e.g., spontaneous emission. Under excitable conditions, the system emits irregularly timed noise-triggered pulses. Their statistics is analyzed in terms of a first-passage time distribution for the fluctuating intensity to reach the threshold for excitable response. Two analytic approximations valid for short and long times, respectively, are derived which very well explain measured and simulated pulse-repetition time distributions. This provides physical insight into the noise-triggered spiking mechanism.

Monolithically Integrated Widely Tunable Coupled Cavity Laser Source for Gas Sensing Applications around 2.0μm Wavelength

Advanced Photonics 2015, 2015

Intermediate-depth seismicity in the subducting Philippine Sea slab beneath Kyushu island shows a... more

Bound Modes in Dielectric Microcavities

We demonstrate how exactly bound cavity modes can be realized in dielectric structures other than... more We demonstrate how exactly bound cavity modes can be realized in dielectric structures other than 3d photonic crystals. For a microcavity consisting of crossed anisotropic layers, we derive the cavity resonance frequencies, and spontaneous emission rates. For a dielectric structure with dissipative loss and central layer with gain, the beta factor of direct spontaneous emission into a cavity mode and the laser threshold is calculated.

Organic Diode Laser Dynamics: Rate-Equation Model, Reabsorption, Validation and Threshold Predictions

Photonics, 2021

We present and analyze a simple model based on six rate equations for an electrically pumped orga... more We present and analyze a simple model based on six rate equations for an electrically pumped organic diode laser. The model applies to organic host-guest systems and includes Stoke-shifted reabsorption in a self-consistent manner. With the validated model for the Alq3:DCM host-guest system, we predict the threshold for short-pulse laser operation. We predict laser operation characterized by damped relaxation oscillations in the GHz regime and several orders of magnitude linewidth narrowing. Prospect for CW steady-state laser operation is discussed.

02 10 17 1 v 1 2 4 O ct 2 00 2 Bound Modes in Dielectric Microcavities

We demonstrate how exactly bound cavity modes can be realize d in dielectric structures other tha... more We demonstrate how exactly bound cavity modes can be realize d in dielectric structures other than 3d photonic crystals. For a microcavity consisting of crossed ani sotropic layers, we derive the cavity resonance frequencies, and spontaneous emission rates. For a dielectric structure with dissipative loss and central layer with gain, theβ factor of direct spontaneous emission into a cavity mode and the laser threshold is calculated.

First-Passage-Time Distributions in a Bistable Two-Mode Laser

Coherence and Quantum Optics V, 1984

The statistical properties of a two-mode laser can be described by a four-dimensional Fokker-Plan... more The statistical properties of a two-mode laser can be described by a four-dimensional Fokker-Planck (FP) equation for the real and imaginary parts of the weakly time dependent field amplitudes.1 It has been shown in the rather special case in which the only asymmetry between the modes was in their net linear gain while there was no dispersion, that this equation can be reduced to a one-dimensional FP-equation for the intensity of one of the modes,2,3 which led to certain predictions that have been confirmed by experiment.4 A similar way of approach, that is, reducing the description of the statistical behavior of a field to the analysis of a one-dimensional FP-equation, was followed in the problem of the mean first-passage time in optical bistability.5 In the present contribution we will deal with the first-passage-time (FPT) problem in a bistable two-mode laser without making any of the above mentioned restrictions concerning the symmetry of the modes or the absence of dispersion. The method employed as well as the results obtained are applicable to a wide class of bistable lasers, including homogeneously broadened ring lasers3. single-mode lasers exhibiting polarization bistabilityb6 and single-mode lasers operating under weak external optical feedback conditions7. Moreover, they will be relevant in other contexts too, such as in optical bistability.

Analogies in Optics and Micro Electronics || Aharonov-Bohm Oscillations and Non-Local Electronic Conduction

In a mesoscopic (size smaller than the electron phase coherence length Lφ ∼ 1µm) disordered metal... more In a mesoscopic (size smaller than the electron phase coherence length Lφ ∼ 1µm) disordered metal film or Si-MOSFET inversion layer, the ensemble averaging of the interference between scattered electron waves is incomplete. The tuning of the electron phase by the Aharonov-Bohm effect causes sample-specific magneto conductance fluctuations with rms amplitude Gun = e2/h. For a mesoscopic loop, the fluctuations are replaced by oscillations with flux period h/e. In the macroscopic regime, only the interference in the backscatterina direction survives and causes the weak electron localization. In a long cylinder (diameter ∼ Lφ), the coherent backscattering induces magneto conductance oscillations with flux period h/2e.

On the Analogy Between Electrons and Light

Coherence and Quantum Optics VI, 1989

Many typically quantummechanical concepts have equivalent notions in the context of electromagnet... more Many typically quantummechanical concepts have equivalent notions in the context of electromagnetic waves and especially in coherent optics. The correspondence between these two areas in physics is related to the fact that both are governed by wave equations. The miniaturization of devices in solid state physics has led to new phenomena in which coherent propagation and interference of electrons play significant, if not dominant roles1This will undoubtedly stimulate the analogy thinking in terms of analogies between electrons and light. Many quantummechanical phenomena underlying the performance of presently made submicron systems have optical analogies which may experimentally be realized in relatively easy ways2In view of the enormous progress made in optical engineering devices since the availability of lasers as coherent light sources we are facing, among other things, the fascinating possibility of performing “visible” quantummechanics on a macroscopic scale with rather simple set ups.

Optical level crossings

We discuss the behavior of two coupled optical modes, specializing to the case of a clockwise and... more We discuss the behavior of two coupled optical modes, specializing to the case of a clockwise and a counter-clockwise wave in an optical ring with backscattering. Generally the coupling constant is complex-valued; the limiting cases of conservative and dissipative coupling are emphasized. When lifting the polarization degeneracy we deal with four optical modes, coupled by backscattering and birefringence. We also consider an active i.e. oscillating optical ring: this corresponds to adding a nonlinear mode-coupling and leads to a description of frequency-locking in a ring laser gyro. Finally we address the analogy between optical and electronic mode coupling in ring-type and lattice-type configurations (“band structures”). Here we emphasize dynamic effects and discuss the merits and limitations of optical modeling of phenomena such as Bloch oscillations and Zener tunneling.

Suppressed Relaxation-Oscillation Dynamics in a DFB laser Monolithically Integrated with Weak Optical Feedback

CLEO: 2015, 2015

<title>Polarization-dependent amplification in planar waveguides</title>

Physics and Simulation of Optoelectronic Devices IV, 1996

ABSTRACT

Experimental stability diagram of a diode laser subject to weak phase-conjugate feedback from a rubidium vapor cell

by Daan Lenstra and Alexis FISCHER

IEEE Journal of Quantum Electronics, 1999

Special Issue “Semiconductor Laser Dynamics: Fundamentals and Applications”

Photonics

With the advent of integrated photonics, a crucial role is played by semiconductor diode lasers (... more With the advent of integrated photonics, a crucial role is played by semiconductor diode lasers (SDLs) as coherent light sources. Old paradigms of semiconductor laser dynamics, like optical injection, external feedback and the coupling of lasers, regained relevance when SDLs were integrated on photonic chips. This Special Issue presents a collection of seven invited feature papers and 11 contributed papers reporting on recent advances in semiconductor laser dynamics.

Synchronization of Mutually Delay-Coupled Quantum Cascade Lasers with Distinct Pump Strengths

Photonics

The rate equations for two delay-coupled quantum cascade lasers are investigated analytically in ... more The rate equations for two delay-coupled quantum cascade lasers are investigated analytically in the limit of weak coupling and small frequency detuning. We mathematically derive two coupled Adler delay differential equations for the phases of the two electrical fields and show that these equations are no longer valid if the ratio of the two pump parameters is below a critical power of the coupling constant. We analyze this particular case and derive new equations for a single optically injected laser where the delay is no longer present in the arguments of the dependent variables. Our analysis is motivated by the observations of Bogris et al. (IEEE J. Sel. Top. Quant. El. 23, 1500107 (2017)), who found better sensing performance using two coupled quantum cascade lasers when one laser was operating close to the threshold.

Saturation-induced polarization preferences in two-mode oscillating gas lasers

Physica B+C

Nonlinear Dynamics of Semiconductor Lasers

Quantum and Semiclassical Optics: Journal of the European Optical Society Part B

Bifurcations of relaxation oscillations in an optically injected diode laser

Quantum and Semiclassical Optics: Journal of the European Optical Society Part B