We propose a method to generate physical random numbers based on intermittent optical chaos. Intermittent chaotic output is produced in a semiconductor laser subjected to optical feedback embedded in a photonic integrated circuit. This dynamics is characterized by a temporal waveform organized in a succession of laminar regions of low amplitude and bursts of high amplitude. The temporal randomness ruling the alternation of successive laminar regions and bursts is used as an entropy source to generate sequences of random bits. We compare the performances of the exclusive OR and reverse methods implemented in the bit generation process and evaluate the quality of the random bits with the Rabbit test of TestU01 for different bit sequences lengths.

Synchronization properties of chaotic dynamics in two mutually coupled semiconductor lasers with optical feedback embedded in a photonic integrated circuit are investigated from the point of view of their dynamical content. A phenomenon in which the two lasers can show qualitatively different synchronization properties according to the frequency range of investigation and their nonlinear dynamics is identified and termed dynamics-dependent synchronization. In-phase synchronization is observed for original signals and antiphase synchronization is observed for low-pass filtered signals in the case where one of the lasers shows chaotic oscillations while the other laser exhibits low-frequency fluctuations dynamics. The experimental conditions causing the synchronization states to vary according to the considered frequency interval are studied and the key roles of asymmetric coupling strength and injection currents are clarified.

We report a comprehensive experimental investigation of the nonlinear dynamics yielded in five photonic integrated circuits, each consisting of a semiconductor laser with optical feedback from a short external cavity. The external cavity lengths are different for each laser and range from 1.3 to 10.3 mm, allowing analysis of the dependence of the dynamical scenario on the feedback delay time. We draw two-dimensional bifurcation diagrams and study the relative predominance of the different dynamics exhibited in each laser when the feedback strength and the laser injection current are varied. We identify that, in the commonly termed short cavity regime, small variations of the external cavity length can result in totally different dynamical distributions, suggesting the possibility to use the feedback delay time as a means to control laser behaviors.

We demonstrate a random bit streaming system that uses a chaotic laser as its physical entropy source. By performing real-time bit manipulation for bias reduction, we were able to provide the memory of a personal computer with a constant supply of ready-to-use physical random bits at a throughput of up to 4 Gbps. We pay special attention to the end-toend entropy source model describing how the entropy from physical sources is converted into bit entropy. We confirmed the statistical quality of the generated random bits by revealing the pass rate of the NIST SP800-22 test suite to be 65 % to 75 %, which is commonly considered acceptable for a reliable random bit generator. We also confirmed the stable operation of our random bit steaming system with long-term bias monitoring.

Random number generators are essential for applications in information security and numerical simulations. Most optical-chaos-based random number generators produce random bit sequences by offline post-processing with large optical components. We demonstrate a real-time hardware implementation of a fast physical random number generator with a photonic integrated circuit and a field programmable gate array (FPGA) electronic board. We generate 1-Tbit random bit sequences and evaluate their statistical randomness using NIST Special Publication 800-22 and TestU01. All of the BigCrush tests in TestU01 are passed using 410-Gbit random bit sequences. A maximum real-time generation rate of 21.1 Gb/s is achieved for random bit sequences in binary format stored in a computer, which can be directly used for applications involving secret keys in cryptography and random seeds in large-scale numerical simulations.

In this report, we propose a ring resonator with one port for surface normal input/output attached with another ring resonator. A resonance generated by one of the ring resonators is used for sensing and that by the other as a reference. The device characteristics were examined using the FDTD simulation.

We experimentally investigate an intermittent route to chaos in a photonic integrated circuit consisting of a semiconductor laser with time-delayed optical feedback from a short external cavity. The transition from a period-doubling dynamics to a fully-developed chaos reveals a stage intermittently exhibiting these two dynamics. We unveil the bifurcation mechanism underlying this route to chaos by using the Lang-Kobayashi model and demonstrate that the process is based on a phenomenon of attractor expansion initiated by a particular distribution of the local Lyapunov exponents. We emphasize on the crucial importance of the distribution of the steady-state solutions introduced by the time-delayed feedback on the existence of this intermittent dynamics. (C) 2016 Optical Society of America

We experimentally investigate an intermittent route to chaos in a photonic integrated circuit consisting of a semiconductor laser with time-delayed optical feedback from a short external cavity. The transition from a period-doubling dynamics to a fully-developed chaos reveals a stage intermittently exhibiting these two dynamics. We unveil the bifurcation mechanism underlying this route to chaos by using the Lang-Kobayashi model and demonstrate that the process is based on a phenomenon of attractor expansion initiated by a particular distribution of the local Lyapunov exponents. We emphasize on the crucial importance of the distribution of the steady-state solutions introduced by the time-delayed feedback on the existence of this intermittent dynamics. (C) 2016 Optical Society of America

An asymmetric resonant cavity can be used to form a path that is much longer than the cavity size. We demonstrate this capability for a deformed microdisk equipped with two linear waveguides, by constructing a multiply reflected periodic orbit that is confined by total internal reflection within the deformed microdisk and outcoupled by the two linear waveguides. Resonant mode analysis reveals that the modes corresponding to the periodic orbit are characterized by high-quality factors. From measured spectral and far-field data, we confirm that the fabricated devices can form a path about 9.3 times longer than the average diameter of the deformed microdisk.

© 2016 American Physical Society.An asymmetric resonant cavity can be used to form a path that is much longer than the cavity size. We demonstrate this capability for a deformed microdisk equipped with two linear waveguides, by constructing a multiply reflected periodic orbit that is confined by total internal reflection within the deformed microdisk and outcoupled by the two linear waveguides. Resonant mode analysis reveals that the modes corresponding to the periodic orbit are characterized by high-quality factors. From measured spectral and far-field data, we confirm that the fabricated devices can form a path about 9.3 times longer than the average diameter of the deformed microdisk.

We report an experimental investigation on the spectra of fully chaotic and nonchaotic microcavity lasers under continuous-wave operating conditions. It is found that fully chaotic microcavity lasers operate in single mode, whereas nonchaotic microcavity lasers operate in multimode. The suppression of multimode lasing for fully chaotic microcavity lasers is explained by large spatial overlaps of the resonance wave functions that spread throughout the two-dimensional cavity due to the ergodicity of chaotic ray orbits.

We report experimentally on the bifurcation cascade leading to the appearance of self-pulsation in a photonic integrated circuit in which a laser diode is subjected to delayed optical feedback. We study the evolution of the self-pulsing frequency with the increase of both the feedback strength and the injection current. Experimental observations show good qualitative accordance with numerical results carried out with the Lang-Kobayashi rate equation model. We explain the mechanism underlying the self-pulsations by a phenomenon of beating between successive pairs of external cavity modes and antimodes.

This paper reviews an approach to secret-key distribution based on the bounded observability (BO) model. First, the information-theoretic framework of secret-key agreement from a correlated random source is reviewed. Next, the BO model is introduced. In the context of this model, the BO condition is presented as a necessary and sufficient condition for the possibility of secret-key distribution. This condition describes limits on the information obtained by observation of a random object, and models the practical difficulty of completely observing random physical phenomena. Finally, an implementation of secret-key distribution based on BO in an optical fiber system is described.

This paper reviews an approach to secret-key distribution based on the bounded observability (BO) model. First, the information-theoretic framework of secret-key agreement from a correlated random source is reviewed. Next, the BO model is introduced. In the context of this model, the BO condition is presented as a necessary and sufficient condition for the possibility of secret-key distribution. This condition describes limits on the information obtained by observation of a random object, and models the practical difficulty of completely observing random physical phenomena. Finally, an implementation of secret-key distribution based on BO in an optical fiber system is described.

Based on the reformulation of the boundary integral equations recently derived by Creagh, Hamdin, and Tanner [J. Phys. A: Math. Theor. 46, 435203 (2013)] together with semiclassical (short wavelength) approximation, we theoretically show that low-loss resonances of a fully chaotic dielectric billiard can be related with ray dynamical orbits whose intensities are weighted by the Fresnel reflection and transmission coefficients. In addition, it is revealed that intensity localization spots observed in the phase-space representation of an individual resonance wave function are ray-dynamically correlated.

We investigated the polarization characteristics of emissions from two-dimensional microcavity laser diodes. For an unstrained single-quantum-well active layer structure, an argument based on the interband optical transition usually leads to the lasing of transverse electric (TE) rather than transverse magnetic (TM) modes. Indeed, we observed TE-polarized emissions for the excitation of modes quantized along a one-dimensional (Fabry-Perot) orbit. However, when selectively pumping modes quantized along a diamond-shaped ray orbit, we observed TM-polarized emissions. These unusual TM-polarized emissions can be explained by the fact that the incident angles of the diamond-shaped orbit are very close to the Brewster angle, making corresponding TE modes too leaky to be excited. This mode-dependent polarization leads us to propose a microcavity laser diode with the function of polarization switching.

We fabricated and tested a compact multipass GaAs optical cavity with a round-trip path length of approximately 3.7 mm. The optical light injected into the cavity was found to propagate along a stable ray trajectory. © OSA 2014.

We propose using an asymmetric resonant microcavity for the efficient generation of an optical path that is much longer than the diameter of the cavity. The path is formed along a star polygonal periodic orbit within the cavity, which is stable and confined by total internal reflection. We fabricated a semiconductor device based on this idea with an average diameter of 0.3 mm and achieved a path length of 2.79 mm experimentally. (C) 2014 AIP Publishing LLC.

We propose a compact chaotic laser device, which consists of a semiconductor laser and a two-dimensional (2D) external cavity for delayed optical feedback. The overall size of the device is within 230 mu m x 1mm. A long time delay sufficient for chaos generation can be achieved with the small area by the multiple reflections at the 2D cavity boundary, and the feedback strength is controlled by the injection current to the external cavity. We experimentally demonstrate that a variety of output properties, including chaotic output, can be selectively generated by controlling the injection current to the external cavity. (C) 2014 AIP Publishing LLC.

We generate random bit sequences from chaotic temporal waveforms by using photonic integrated circuits (PICs) with different external cavity lengths. We investigate the condition for generating random bits at different sampling rates of single-bit generation method with the PICs. We succeed in generating certified random bit sequences by using the PIC with 3, 4, 5, or 10-mm-long external cavity, whereas random bits cannot pass all the statistical tests of randomness when the PIC with 1 or 2 mm-long external cavity is used. (C) 2014 Optical Society of America

We fabricated and tested an unstrained GaAs single-quantum-well microlaser which has a two-dimensional cavity shape known as the Penrose unilluminable room. The cavity exhibits quasi-one-dimensional modes, namely axial, diamond-shaped, and V-shaped modes. In contrast to previous observations of TE-polarized emission in GaAs microlasers, we observed TM-polarized emission. We explain this observation as being the result of lasing of the diamond-shaped modes whose incident angle at the cavity interface is very close to the Brewster angle. (C)2014 Optical Society of America

Time-domain properties of the output from quasistadium-shaped microcavity semiconductor lasers are studied. Ring modes generating a bidirectional output are selectively excited by partial pumping. We observe a high anticorrelation between the two beams output from the ring modes. This can be considered as the generalization of alternate oscillations reported previously. We find that the outputs exhibit a robust slow modulation of 4-10 MHz, and explain it by the quasi-degeneracy of the resonator modes. © 2014 The Optical Society of Japan.

We experimentally and numerically show that single-wavelength emission can be stably observed for a fully chaotic microcavity laser with a stadium shape under continuous wave condition. The emission pattern is asymmetric with respect to the symmetry axes of the laser cavity, and it cannot be explained by a single cavity mode. On the basis of numerical analysis, we interpret such a lasing as the result of frequency-locking interaction among several low-loss cavity modes. Moreover, we experimentally investigate the optical spectral properties of the laser under pulsed-pumping condition, and discuss the pulse-width dependence on the number of lasing modes. © 2013 American Physical Society.

We performed ray dynamical simulations for a cavity having a two-dimensional shape known as the Penrose unilluminable room. The cavity is shown to have the potential to lase with a rich variety of resonator modes. © OSA 2013.

We propose a photonic integrated circuit with mutually-coupled semiconductor lasers for fast physical random number generation. The random bit sequences generated at 5.56 Gb/s pass statistical tests of randomness. © OSA 2013.

We present an experimental method for directly observing the amplification of microscopic intrinsic noise in a high-dimensional chaotic laser system, a laser with delayed feedback. In the experiment, the chaotic laser system is repeatedly switched from a stable lasing state to a chaotic state, and the time evolution of an ensemble of chaotic states starting from the same initial state is measured. It is experimentally demonstrated that intrinsic noises amplified by the chaotic dynamics are transformed into macroscopic fluctuating signals, and the probability density of the output light intensity actually converges to a natural invariant probability density in a strongly chaotic regime. Moreover, with the experimental method, we discuss the application of the chaotic laser systems to physical random bit generators. It is experimentally shown that the convergence to the invariant density plays an important role in nondeterministic random bit generation, which could be desirable for future ultimate secure communication systems. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4754872]

The Galton board is a classic example of the appearance of randomness and stochasticity. In the dynamical model of the Galton board, the macroscopic motion is governed by deterministic equations of motion, and predictability depends on uncertainty in the initial conditions and its evolution by the dynamics. In this sense the Galton board is similar to coin tossing. In this paper, we analyze a simple dynamical model which is inspired by the Galton board. Especially, we focus on the predictability, considering the relation between the uncertainty of initial states and the structure of basins of initial states that result in the same exit state. The model has basins with fractal basin structure, unlike the basins in coin tossing models which have only finite structure. Arbitrarily small uncertainty of initial conditions can cause unpredictability of final states if the initial conditions are chosen in fractal regions. In this sense, our model is in a different category from the coin tossing model. We examine the predictability of a small Galton board model from the viewpoint of the sensitivity and the statistical bias of final states. We show that it is possible to determine the radii of scatterers corresponding to a given predictability criterion, specified as a statistical bias, and a given uncertainty of initial conditions.

We propose a scheme for fast random number generation with bandwidth-enhanced chaotic semiconductor lasers. Chaotic laser intensity output and its time-delayed signal are sampled at 50 GigaSample per second and converted into eight-bit values. The order of the eight-bit samples of the time-delayed signal is reversed, and bitwise exclusive-or operation is executed between the bit-order-reversed samples and the original eight-bit samples. With this method, it is not necessary to eliminate any of the bits in eight-bit samples in order to obtain good-quality random bit sequences. The equivalent generation rate of 8 x 50 Gb/s is achieved in an experiment using bandwidth-enhanced chaotic semiconductor lasers.

We investigated the lasing modes of quasi-stadium laser diodes that have confocal cavity geometries, with stripe electrode contacts formed either along the cavity axis or a diamond-shaped trajectory. It was clearly demonstrated that by using narrow electrode contact patterns of 2 mu m width, the lowest-order axial and ring modes were excited selectively. On the other hand, the second-lowest-order axial and ring modes were excited by using broad electrode patterns of 14 mu m width. Experimentally obtained far-field patterns for lasers with broad and narrow electrode contact patterns agree very well with the simulation results obtained using an extended Fox-Li mode calculation method. (C) 2012 Optical Society of America

We theoretically show that completely stochastic fast physical random bit generation at a rate of more than one gigabit per second can be realized by using lasers with optical delayed feedback which creates high-dimensional chaos of laser light outputs. The theory is based on the mixing property of chaos, which transduces microscopic quantum noise of spontaneous emission in lasers into random transitions between discrete macroscopic states.

We propose a secure key distribution scheme based on correlated physical randomness in remote optical scramblers driven by common random light. The security of the scheme depends on the practical difficulty of completely observing random optical phenomena. We describe a particular realization using the synchronization of semiconductor lasers injected with common light of randomly varying phase. We experimentally demonstrate the feasibility of the scheme over a distance of 120 km.

We report physical random bit generation with on-chip chaos lasers. The design of the laser device is based on a theoretical model for non-deterministic random bit generation by amplification of microscopic noise. It is shown that the bit sequences generated at rates up to 2.08 gigabit per second (Gbit/s) pass a standard statistical test suite of randomness. (c) 2012 Published by Elsevier Ltd. Selection and/or Peer-review under responsibility of Takashi Hikihara and Tsutomu Kambe

We analyze the time for growth of bit entropy when generating nondeterministic bits using a chaotic semiconductor laser model. The mechanism for generating nondeterministic bits is modeled as a 1-bit sampling of the intensity of light output. Microscopic noise results in an ensemble of trajectories whose bit entropy increases with time. The time for the growth of bit entropy, called the memory time, depends on both noise strength and laser dynamics. It is shown that the average memory time decreases logarithmically with increase in noise strength. It is argued that the ratio of change in average memory time with change in logarithm of noise strength can be used to estimate the intrinsic dynamical entropy rate for this method of random bit generation. It is also shown that in this model the entropy rate corresponds to the maximum Lyapunov exponent.

We study emission from quasi-one-dimensional modes of an asymmetric resonant cavity that are associated with a stable periodic ray orbit confined inside the cavity by total internal reflection. It is numerically demonstrated that such modes exhibit directional emission, which is explained by chaos-assisted emission induced by dynamical tunneling. Fabricating semiconductor microlasers with an asymmetric resonant cavity, we experimentally demonstrate the selective excitation of the quasi-one-dimensional modes by employing the device structure to preferentially inject currents to these modes and observe directional emission in good accordance with the theoretical prediction based on chaos-assisted emission.

We experimentally show that a random optical pulse train can be generated by modulating a bistable semiconductor ring laser. When the ring laser is switched from the monostable to the bistable regime, it randomly selects one of two different stable unidirectional lasing modes, clockwise or counterclockwise modes. Non-deterministic random pulse sequences are generated by driving the switch parameter, the injection current, with a periodic pulse signal. The origin of the nondeterministic randomness is the amplified spontaneous emission noise coupled to the counter-propagating lasing modes. The statistical randomness properties are optimized by adjusting the relative strength of amplified spontaneous emission noise sources for the two lasing modes. It is also shown that it is possible to generate optical pulse sequences which pass a standard suite of statistical randomness tests. (C) 2011 Optical Society of America

We report a novel chaos semiconductor laser chip in which a distributed feedback (DFB) laser, two semiconductor optical amplifiers (SOAs) and a photodiode (PD) are monolithically integrated with a passive ring waveguide. The ring-type structure with the two separate SOAs achieves stronger delayed optical feedback compared to previous chaos laser chips which use linear waveguide and facet-reflection. The integrated PD allows efficient detection of the optical signal with low optical loss. A rich variety of dynamical behaviors and optical signals can be selectively generated via injection currents to the two separate SOAs. In particular, the strong optical feedback makes possible the generation of strong broadband optical chaos, with very flat spectrum of +/- 6.5 dB up to 10 GHz. The stability and quality of the chaotic mode is demonstrated using strict statistical tests of randomness applied to long binary sequences extracted by sampling the optical intensity signal. (c) 2011 Optical Society of America

It is shown that broadband chaos suitable for fast nondeterministic random-bit generation in small devices can be achieved in a semiconductor laser with a short external cavity. The design of the device is based on a theoretical model for nondeterministic random-bit generation by amplification of microscopic noise. Moreover, it is demonstrated that bit sequences passing common tests of statistical randomness at rates up to 2.08 Gbits/s can be generated using on-chip lasers with a monolithically integrated external cavity, amplifiers, and a photodetector.

We study the output from the modes described by the superposition of Gaussian beams confined in the quasistadium microcavities. We experimentally observe the deviation from Snell's law in the output when the incident angle of the Gaussian beam at the cavity interface is near the critical angle for total internal reflection, providing direct experimental evidence on the Fresnel filtering. The theory of the Fresnel filtering for a planar interface qualitatively reproduces experimental data, and a discussion is given on small deviation between the measured data and the theory. (C) 2011 Optical Society of America

The correspondence between ray and wave descriptions for twodimensional chaotic open billiards describing optical cavities is reviewed. Focusing on the stadium-shaped cavity, which is well-known for its fully chaotic ray dynamics, we show how ray chaos is manifested in emission patterns, or eigenfunctions of resonances (decaying eigenmodes). The flux phase-space distribution is introduced, which not only enables one to understand the relation between ray dynamics and emission directionality, but also provides a suitable stage to study the ray-wave correspondence. We observe intrinsic localization phenomenon in each resonance, which causes discrepancies with the ray description. Nonetheless, we demonstrate that the average of many low-loss resonances reproduces the ray description very well, where one can clearly observe that signature of ray chaos (i.e., long-term effects of stretching and folding) is embedded in resonance eigenfunctions. © 2011 Bentham Science Publishers Ltd.

We experimentally demonstrate random bit generation using multi-bit samples of bandwidth-enhanced chaos in semiconductor lasers. The bit generation rate of 75 Gigabit per second is achieved. FIO/ LS Technical Digest © 2011 OSA.

We fabricated and investigated two confocal quasi-stadium laser diodes: one has a narrow electrode contact pattern along its cavity axis and the other has a narrow electrode contact pattern along a diamond-shaped trajectory. The lowest-order axial and ring modes were selectively excited. The resonator modes of the laser diodes were calculated using the extended Fox-Li mode calculation method. Although some deformation of the far-field emission pattern was observed in experiments, the numerically calculated far-field emission patterns agree well with the experimentally observed far-field patterns.

We study the effect of dynamical tunneling on emission from ray-chaotic microcavities by introducing a suitably designed deformed disk cavity. We focus on its high quality factor modes strongly localized along a stable periodic ray orbit confined by total internal reflection. It is shown that dominant emission originates from the tunneling from the periodic ray orbit to chaotic ones; the latter eventually escape from the cavity refractively, resulting in directional emission that is unexpected from the geometry of the periodic orbit, but fully explained by unstable manifolds of chaotic ray dynamics. Experimentally performing selective excitation of those modes, we succeeded in observing the directional emission in good agreement with theoretical prediction. This provides decisive experimental evidence of dynamical tunneling in a ray-chaotic microcavity.

We experimentally demonstrate random bit generation using multi-bit samples of bandwidth-enhanced chaos in semiconductor lasers. Chaotic fluctuation of laser output is generated in a semiconductor laser with optical feedback and the chaotic output is injected into a second semiconductor laser to obtain a chaotic intensity signal with bandwidth enhanced up to 16 GHz. The chaotic signal is converted to an 8-bit digital signal by sampling with a digital oscilloscope at 12.5 Giga samples per second (GS/s). Random bits are generated by bitwise exclusive-OR operation on corresponding bits in samples of the chaotic signal and its time-delayed signal. Statistical tests verify the randomness of bit sequences obtained using 1 to 6 bits per sample, corresponding to fast random bit generation rates from 12.5 to 75 Gigabit per second (Gb/s) (= 6 bit x 12.5 GS/s). (C) 2010 Optical Society of America

The limaçon-shaped semiconductor microcavity is a ray-chaotic cavity sustaining low-loss modes with mostly unidirectional emission patterns. Investigating these modes systematically, we show that the modes correspond to ray description collectively rather than individually. In addition, we present experimental data on multimode lasing emission patterns that show high unidirectionality and closely agree with the ray description. The origin of this agreement is well explained by the collective correspondence mechanism. © 2009 The American Physical Society.

We report linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers with various length of passive waveguide. It is experimentally confirmed that the linewidth of the lasers is proportional to the square of the ratio of the length of active part of the cavity over the total length of the cavity. The lasers are applicable for communication and sensing devices, which need the narrow linewidth.

We investigated the effect of rapid thermal annealing from 700 °C to 950 °C on stacked InAs/GaAs quantum dots (QDs) covered with GaAs and In0.19Ga0.81As layers. Large blue-shift of the energy positions nearly 380 meV (1187 nm to 870 nm) have been observed in InGaAs capped samples together with improvement in the photoluminescence integrated intensity of more than five times. The strong narrowing of the photoluminescence line-width in both GaAs (as narrow as 8 meV) and InGaAs capped samples show an improvement of the size distribution of the QDs. In addition, a significant reduction of the energy spacing (ΔE2-1) between ground state and first excited state emissions were found in both GaAs and InGaAs capped quantum dots due to interface inter-diffusion induced by thermal treatment. The excited state filling experiments for InGaAs capped sample annealed at 950 °C exhibits quantum well like behavior where as, the GaAs capped sample shows a shoulder in high energy side might be due to first excited state of QDs. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

We have investigated the annealing-temperature dependence on photoluminescence (PL) properties of InAs quantum dots (QDs) fabricated on GaAs substrate. The annealing temperatures were varied from 700 to 1000°C. The observed PL spectra were drastically changed by changing the annealing temperature. The PL peaking-wavelength of non-annealed sample is around 1200 nm. However, the peaking-wavelength is drastically blue-shifted with increasing annealing temperature. The strongest PL intensity is observed from the sample annealed at 875°C. This PL intensity is more than seven fold compared with that of the non-annealed sample. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA.

We theoretically and numerically study the effect of backscattering on rotating ring lasers by employing the Maxwell-Bloch equations. We show that frequency shifts due to the Sagnac effect incorporating the effect of backscattering can be observed without lock-in phenomenon, if the strength of backscattering originating in the bumps of the refractive index is larger than a certain value. It is also shown that the experimental results corresponding to the theoretical ones can actually be obtained by using a semiconductor fiber-optic ring laser gyroscope.

We study spectral and far-field characteristics of lasing emission from stadium-shaped semiconductor (InGaAsP) microlasers. We demonstrate that the correspondence between a lasing far-field emission pattern and the result of a ray simulation becomes better as the number of lasing modes increases. This phenomenon is reproduced in the wave calculation of the cavity modes. © 2008 Optical Society of America.

We found alternate oscillations in AlGaAs/GaAs single-quantum-well quasistadium laser diodes (QSLDs). Unlike the alternate oscillations in conventional ring lasers, which are explained by interaction between two counterpropagating modes, the alternate oscillations in QSLDs arise from two nearly degenerate cavity modes due to its geometric structure. The lasing signals in QSLDs are directly obtained from the emitted beams which spread over the space without the use of waveguides. We also showed that the alternate oscillation frequencies decrease linearly as the amplitudes of the two different cavity modes increase.

We study light emission patterns from stadium-shaped semiconductor (GaAs) microcavity lasers theoretically and experimentally. Performing systematic wave calculations for passive cavity modes, we demonstrate that the averaging by low-loss modes, such as those realized in multimode lasing, generates an emission pattern in good agreement with the ray model's prediction. In addition, we show that the dependence of experimental far-field emission patterns on the aspect ratio of the stadium cavity is well reproduced by the ray model.

Optical and morphological properties of self-assembled InAs quantum dots (QDs) covered by InxGa1-xAs strain reducing layers (SRL) with different thicknesses (2. 4, 6 and Snm) and compositions (x-0.13, 0.1.8 and 0.30) were investigated. Photolumincscencc from InAs QDs shows the dependence on indium mole fraction and thickness of the overgrown InxGa 1-xAs SRL. Improvement in PL intensity and narrowing of PL width up to 26 meV occurred together with a red shift of up to 138 nm when the QDs were coved with 6 nm of In0.18Ga0.82As. Also, we found that when the total amount of InAs deposited to form the QDs and the SRL was larger than a critical value of around 6MLs, the surface roughness increased and the PL intensity decreased drastically. © IEICE 2008.

We report a theory and demonstration of lasing in several deformed microcavities which are rigorously known to be chaotic. We also discuss their applications to optical switching and sensing devices. © 2008 Optical Society of America.

We study spectral and far-field characteristics of lasing emission from stadium-shaped semiconductor microlasers. We demonstrate that the correspondence between far-field emission patterns and ray simulation results becomes better as the number of lasing modes increases. © 2008 Optical Society of America.

We detect the Earth's rotation rate using a semiconductor fiber optic gyroscope (S-FOG), which is an active ring laser gyroscope that consists of a semiconductor optical amplifier (SOA) and a fiber optic ring resonator. Four different optical fiber layouts with different scale factors in rotation rate measurement are configured and measured. Expected Sagnac beat signals proportional to the scale factors are observed. The maximum layout of S-FOG is extended over 10,898 m2, which, to our knowledge, is the largest active ring laser gyroscope ever built.

We fabricated Monza-shaped semiconductor microcavity lasers and evaluated their far-field characteristics. From the ray dynamical point of view, the Monza-shaped cavity belongs to a special class of fully chaotic cavities; its phase space is decomposed into two independent chaotic components, which yield two different emission patterns. In the present paper, we discuss which ensemble of ray trajectories (i.e., phase space measure) can reproduce far-field emission patterns observed in experiments. ©2008 IEEE.

The Sagnac effect in rotating microcavities is Studied theoretically and numerically. The frequency splitting due to the Sagnac effect Occurs as a threshold-like phenomenon for the angular velocity in a rotating microcavity. Above the threshold, the eigenfunctions of a rotating microcavity become rotating waves while they are standing waves below the threshold.

A semiconductor fiber-optic ring laser gyroscope (S-FOG) consists of a semiconductor optical amplifier (SOA) and optical fiber to form a ring cavity. The fiber ring cavity enables larger sizes and smaller scattering, while the SOA gain is shared by the clockwise (CW) and counterclockwise (CCW) propagating modes. When the S-FOG is rotated, a new beat signal called the Sagnac beat frequency is observed. We investigated the effect of the fiber ring cavity's length on detection characteristics. Detection sensitivity was not dependent on the number of laps of fiber ring cavity. However, when the cavity length became longer, the linewidth of Sagnac beat became narrower, and then accuracy of angular velocity detection improved. The relation between the linewidth Delta v of the Sagnac beat and cavity length P was proved to be Delta v approximate to p(-1.86).

We propose a novel method for extracting light beams from diamond-shaped total-internal reflection modes in two-dimensional microcavity laser diodes by the use of intracavity air gaps. By fabricating such a laser diode, we experimentally demonstrate that the direction and longitudinal mode spacing of the output beams are in good accordance with theoretical calculations. (c) 2007 Optical Society of America.

We obtained high-quality lowest-loss-mode lasing in quasi-stadium laser diodes having unstable resonators that consisted of two curved end mirrors and two straight sidewall mirrors. The laser diodes were fabricated by applying a reactive ion etching technique to a metal-organic chemical-vapor deposition-grown graded-index separate-confinement heterostructure single-quantum-well GaAs/AlGaAs structure. The electrode contact area of the laser diodes was formed along unstable periodic orbits, along which the optical beams are localized. Highly directional fan-out beams corresponding to the numerically obtained lowest loss mode were emitted from the end mirrors under CW operation at room temperature. (C) 2007 Optical Society of America.

We study theoretically and numerically the effect of rotation on resonant frequencies of microcavities in a rotating frame of reference. Cavity rotation causes the shifts of the resonant frequencies proportional to the rotation rate if it is larger than a certain value. Below the value, a region of rotation rate exists where there is no resulting the frequency shifts proportional to the rotation rate. We show that designing cavity symmetry as C-nv (n >= 3) can eliminate this region. (c) 2007 Optical Society of America.

Light emission from a dielectric cavity with a stadium shape is studied in both ray and wave models. For a passive cavity mode with low loss, a remarkable correspondence is found between the phase space representation of a quasibound wave function and its counterpart distribution in the ray model. This result provides additional and more direct evidence for good ray-wave correspondence in low-loss modes previously observed at the level of far-field emission pattern comparisons. © 2007 The American Physical Society.

We are conducting research to confirm the performance of a semiconductor fiber-optic ring laser gyroscope (S-FOG) featuring a semiconductor in its laser cavity. This S-FOG consists of a semiconductor optical amplifier (SOA) as a gain medium, a polarization-maintaining fiber to make a ring cavity, and a directional coupler to take part of the optical power out of the cavity. One of the advantages of the S-FOG is the adaptability of the laser cavity, which allows us to examine many cases of S-FOG applications easily. In the first case, we observed that the S-FOG generated Sagnac beat signals whose peak frequency was proportional to the rotation rate when it rotated. In the second case, we changed the area surrounded by the ring cavity (the fiber) and its perimeter and maintained a near-fixed oscillation wavelength of the ring laser. In this case, all of our experimental results were in good agreement with theoretical calculations, within a few percent. In the third case, we changed the oscillation wavelength and fixed the shape of the ring cavity. In this case, our results were also in good agreement with theoretical calculations. In the fourth case, we examined the Sagnac beat spectrum generated by the S-FOG in detail. The linewidth of the Sagnac beat spectrum increases as the area bounded by the optical path in the ring cavity becomes smaller, or as the length of the cavity becomes shorter. Our experimental results show that the S-FOG works as a gyro and that there exists practical potential for a semiconductor ring laser gyro.

We study light emission from a stadium-shaped optical cavity by ray and wave descriptions. A remarkable ray-wave correspondence is revealed by investigating phase space distributions that describe how the light is transmitted outside the cavity. © 2007 IEEE.

The Sagnac effect in rotating microcavities is studied theoretically and numerically. The frequency shift due to the Sagnac effect occurs as a threshold-like phenomenon for the angular velocity in a rotating microcavity Above the threshold, the eigenfunctions of a rotating microcavity become rotating waves while they arc standing waves below the threshold.

We study the effect of rotation on resonances of an optical cavity in an accelerated frame of reference. We show that, even when the resonant modes of an optical cavity are wave-chaotic, degenerate resonant frequency of those modes split into different frequencies due to the rotation of the cavity. The frequency difference is proportional to the rotation rate, although the splitting resonant modes are still wave-chaotic, which do not have any corresponding counter-propagating waves as well as ray-dynamical counterparts.

Multi-mode lasing in stadium-shaped cavities which are rigorously known to be fully chaotic is investigated both theoretically and experimentally. By a nonlinear dynamical model, it is shown that there exist multi- attractors of limit cycles and chaos corresponding to the final lasing states for large microst.adiums. We also show that the envelopes of the far field patterns of the actual microstadium laser diodes are excellently approximated by fully chaotic ray-dynamics.

We fabricated and tested mufti-electrode quasi-stadium laser diodes having GaAs/AlGaAs GRIN-SCH-SQW structures. Axis and ring mode switching was achieved under CW operation for output powers up to 15 mW by selecting the electrode used. (C) 2007 Optical Society of America

We report a demonstration of lasing in a two-dimensional (2D) microcavity which is a semiconductor diode structure with a stadium shape finely formed by reactive-ion-etching technique and pumped by electric current injection. The laser exhibits output over a wide angle, although the fundamental lasing modes have highly complex wave structures which do not correspond to any simple set of rays inside the cavity. The applications of 2D microcavity lasers are also discussed.

We found alternate oscillations in AlGaAs/GaAs single-quantum-well (SQW) quasi-stadium laser diodes (QSLD). The alternate oscillations in QSLD can be well explained by the interactions of two different cavity modes due to the geometrical symmetry of QSLD. We also showed the alternate oscillation frequencies are inversely proportional to the amplitudes of two different cavity modes.

We found alternate oscillations in AlGaAs/GaAs single-quantum-well (SQW) quasi-stadium laser diodes (QSLD). The alternate oscillations in QSLD can be well explained by the interactions of two different cavity modes due to the geometrical symmetry of QSLD. Unlike the alternate oscillations in semiconductor ring lasers that need the waveguides to extract the light signals, the alternate oscillation signals in QSLD are obtained from the emitting lights spreading over the space. We also showed the alternate oscillation frequencies are inversely proportional to the amplitudes of two different cavity modes. This result is consistent with the theory of locking of two modes explaining the locking phenomenon between two nearly degenerated modes due to the nonlinear interactions in an active medium.

In order to demonstrate controlling directional emissions corresponding to the ring trajectory modes by using external optical injection, we fabricate the AlGaAs/GaAs single-quantum-well tandem quasi-stadium laser diodes consist of the front slave and the rear master laser diodes. The geometry of the laser cavities have been defined by using a lithography system and a reactive-ion-etching technique. The optical injection is performed from the master laser to the slave laser. The ring mode control with the optical injection is evaluated by far-field patterns for the output from the curved end mirror.

We fabricated quasi-stadium laser diode which has a 'window' on the top of cavity by ion-etching technique to epitaxial wafer and demonstrated to observe direct lasing mode observation. In the carrier poor region, bright line can recognize. On the other hands, in the rich carrier region, lasing pattern was recognized as dark line. Both lines well fit extended Fox-Li simulation. From these results, it can understand that the lasing pattern condition depend the carrier density.

We study the far-field characteristics of oval-resonator laser diodes made of an GaAs/AlxGa1-xAs quantum well. The resonator shapes are various oval geometries, thereby probing chaotic and mixed classical dynamics. The far-field pattern shows a pronounced fine structure that strongly depends on the cavity shape. Comparing the experimental data with ray-model simulations for a Fresnel billiard yields convincing agreement for all geometries and reveals the importance of the underlying classical phase space for the lasing characteristics.

The Sagnac effect in two-dimensional resonant microcavities is studied theoretically and numerically. The frequency shift due to the Sagnac effect occurs as a threshold phenomenon for the angular velocity in a rotating microcavity. Above the threshold, the eigenfunctions of a rotating microcavity become rotating waves while they are standing waves below the threshold.

We fabricated the AlGaAs/GaAs three quantum well quasistadium laser diodes with two electrodes and succeeded in controlling directional laser emission by applying different currents to each electrode. We showed the ratio of laser emission with two different directions is proportional to the ratio of currents injected into two electrodes. These devices are applicable for beam switching and splitting. (c) 2006 American Institute of Physics.

We show that the solution of fully nonlinear lasing equations for stadium cavities exhibits a highly directional emission pattern. This directionality can be well explained by a ray-dynamical model, where the dominant ray-escape dynamics is governed by the unstable manifolds of the unstable short periodic orbits for the stadium cavity. Investigating the cold-cavity modes relevant for the lasing, we found that all of the high- Q modes have the emission directionality corresponding to that of the ray-dynamical model. © 2006 The American Physical Society.

Unidirectional beam emission was obtained from strained InGaAsP multiple-quantum-well quasi-stadium laser diodes. The unidirectional beam emission can be explained by the phase locking of two resonator modes with different symmetry classes. © 2005 Optical Society of America.

We propose a novel ring laser gyroscope that gives the Sagnac beat frequency as the oscillation frequency of the amplitude of the only unidirectional propagating mode instead of the coupled counter-propagating laser lights in the conventional ring laser gyroscope. © 2006 Optical Society of America.

A semiconductor fiber-optic ring laser gyroscope, which consist of a semiconductor optical amplifier as a gain medium and polarization-maintaining fiber to form a ring resonator, generate Sagnac beat signals demonstrating good agreement with theoretical calculations. (35 words) © 2006 OSA/OFS 2006.

In two-dimensional microcavity lasers, as a way to extract highly directional emission, it has been proposed to deform the cavity shape smoothly from perfect circularity [1]. As a result, rays start to exhibit a variety of dynamics from integrable to strongly chaotic, which is tunable by the deformation. The ray picture has been providing a simple and intuitive method to explain experimental observations of emission directionality. For example, emission directionality has been associated with the existence of a periodic ray orbit with a particular geometry [2], drastic shape dependence of emission directionality has been successfully explained by the difference of phase space structure [3], and the far-field intensity patterns have been closely reproduced by ray-tracing simulations [4]. Among various cavity shapes the stadium is a simple geometry for which ray dynamics has been proven to become strongly chaotic [5]. That is, for almost all initial conditions, a ray trajectory explores the entire phase space uniformly. Even for such a strongly chaotic cavity, a ray model can generate highly directional emission patterns as a consequence of the openness of the cavity. Namely, strongly chaotic dynamics and highly directional emission are compatible, as was demonstrated by Schwefel, et al. [3] In this presentation, we report evidence for the ability of a ray model to describe the lasing states of the stadium-cavity lasers. Earlier work has focused on establishing a relationship between the ray model and a few quasi-bound state solutions of the linear wave equation without pumping or gain. In this case, however, there remains an intrinsic arbitrariness about which modes to choose, although plausibility argument can be made based on their Q values. Here we show that the solution of the full nonlinear lasing equations [6] for a stadium cavity, uniquely determined by the pumping conditions, exhibits highly directional emission pattern in good agreement with the ray model. Moreover, we reveal the property of cold-cavity modes that allows the robust appearance of the emission directionality in the lasing states.

We report the Sagnac effect in resonant microcavities. The Sagnac effect is the phase and frequency difference between two counter propagating laser beams in a rotating ring resonator, and has been studied for a long time [1, 2]. It forrns the basis for the optical gyroscopes, such as ring laser gyroscope or fiber optic gyroscopes [1-3]. Conventional theoretical approach for the Sagnac effect has been derived from the assumption that the light propagates one-dimensionally and the wavelength of the light is typically much smaller than the cavity length. However, nowadays, micro-fabrication techniques are developed enough that the cavity size can approach the size of the wavelength of the light [4-6]. The conventional formalism for the Sagnac effect, therefore, breaks down and needs to be replaced.
We derive the Sagnac effect in resonant microcavities theoretically and numerically without the conventional assumption and show that the frequency shift due to the Sagnac effect occurs as a threshold phenomenon for rotation velocity in a rotating microcavity by employing perturbation theory typically used in quantum mechanics. The threshold exists even in the absence of the backscattering, which causes the lock-in phenomenon [2, 3], and depends on the geometric shape and the symmetry of resonant cavities.
It is also shown that the eigenfanctions of a rotating microcavity become rotating waves above the threshold while they are standing waves below the threshold.
Our theoretical approach can be applied to the resonant cavities of arbitrary shapes and can make it possible to design compact optical gyroscopes that have a low threshold.

We demonstrate mode switching in tandem quasi-stadium laser diodes. Switching is achieved by optical injection between lasing in the cavity axis and the closed ring trajectory of a quasi-stadium laser resonator. © 2006 Optical Society of America.

The relation between unstable periodic orbits and resonator modes in a fully chaotic open-sided two-dimensional laser resonator is theoretically investigated in the short wavelength limit. We derive a periodic-orbit-sum formula for eigenvalues of the resonator modes by applying the semiclassical approximation to the extended Fox-Li mode calculation method. With this formula, we show that the complicated wavelength dependence of the power-coupling coefficients of the fully chaotic quasi-stadium laser resonator can be explained by a few kinds of unstable periodic orbits. © 2006 The American Physical Society.

We investigate the lasing characteristics of oval-resonator laser diodes made of AlGaAs/GaAs quantum wells both experimentally and theoretically. The resonator shapes are various oval geometries, thereby probing chaotic and mixed classical dynamics. The far field pattern shows a pronounced fine structure that strongly depends on the cavity shape.

We fabricated the AlGaAs/GaAs 3QW quasi-stadium laser diodes with two-electrodes and succeeded in controlling directional laser emission by applying different currents to each electrode. We showed the ratio of laser emission with two different directions is proportional to the ratio of currents injected into two electrodes. These devices are applicable for beam switching and splitting.

We succeeded in selectively lasing only the lowest order ring mode of a confocal quasi-stadium laser diode by optimizing the electrode contact area shape. The lasing mode had excellent agreement with the numerically calculated mode.

We investigate the lasing characteristics of oval-billiard microcavity laser diodes made of AlGaAs/GaAs single-quantum well both experimentally and theoretically. Experiments with various oval-billiard microcavity laser diodes enable us to observe chaotic and mixed classical dynamics.

Mode switching operation of multi-electrode strained InGaAsP multiple-quantum-well quasi-stadium laser diodes is reported. Far-field patterns exhibit highly directional emission along the laser cavity axis for current injection at the axis electrode and highly directional emission at angles +/- 19 degrees from the cavity axis for current injection at the ring electrode.

We present locking of two modes in GaA/AlGaAs single-quantum-well quasi-stadium laser diodes and unidirectional emission from InGaAsP multiple-quantum-well quasi-stadium laser diodes.

We describe the mode switching operation of multielectrode strained InGaAsP multiple-quantum-well quasistadium laser diodes. Far-field patterns exhibit highly directional emission along the laser cavity axis for current injection at the axis electrode and highly directional emission at angles ±19° from the cavity axis for current injection at the ring electrode. These directions correspond to the axis mode and the ring trajectory mode of the laser cavity. We also succeeded in obtaining single peak output beams using narrow curved end mirrors of 40 μm width. © 2005 American Institute of Physics.

The boundary element method is one of the reliable numerical schemes to solve the eigenvalue problem of the Helmholtz equation, which is justified by the Fredholm theory for domains with a smooth boundary. When a domain has corners, however, the corresponding integral equation is singular, so that the boundary element method lacks its well-established base. Employing a cutoff technique, we here formulate a well-grounded version of the boundary element method, and also give a certain justification to the standard boundary element method even for domains with corners. © 2005 IOP Publishing Ltd.

We present theoretical models of two-dimensional (2D) microcavity lasers. The relation between stationary lasing modes and resonances or metastable states is elucidated for arbitrary shapes of 2D resonant microcavities.

We have studied transport properties in the low-temperature magnetoresistance through the ballistic narrow path restricted by a short width metallic gate on the 2 dimentional electron gas (2DEG) system. An alternate and systematic variation between a Lorentzian line fitting and a cusp-like line fitting in the zero-field peaks has been observed, as sweeping the gate voltage. It indicates a possibility of existence of chaotic and regular paths on the short gated ballistic/tunneling transport. We will discuss on the quantum chaos behavior on the systematic variation between the Lorentzian and the cusp-like peakshape based on the disordered path system under the short gate. © 2005 American Institute of Physics.

We present unidirectional emission from strained InGaAsP multiple-quantum-well quasistadium laser diodes, whose resonators consist of two confocal end mirrors and two long, straight, sidewall mirrors. Far-field patterns exhibit highly directional emission at a 20° angle from the cavity axis. This angle corresponds to a unidirectional ring trajectory inside the resonator. We also report that the unidirectional emission can be explained by the phase locking of two resonator modes with different symmetry classes based on the extended Fox-Li mode calculation method. © 2005 American Institute of Physics.

Multimode lasing in a fully chaotic cavity is investigated numerically by using a nonlinear dynamics model. We report a transition process from single-mode lasing to multimode lasing and reveal interactions among the lasing modes. In particular, both mode-pulling and mode-pushing interactions are shown to decrease the number of effective lasing modes. In addition, coexistence of different types of attractors of the final lasing states is numerically confirmed. © 2005 The American Physical Society.

A famous inverse problem posed by M Kac 'Can one hear the shape of a drum?' is concerned with isospectrality of drums or planer billiards, and the first counter example was constructed by Gordon, Webb and Wolpert (1992 Invent. Math. 110 1). Here we present pieces of numerical evidence showing that 'One can distinguish isospectral drums by measuring the scattering poles of exterior Neumann problems'. This is based on the observation that the Fredholm determinant appearing in the boundary element method admits a factorization into interior and exterior parts. © 2005 IOP Publishing Ltd.

The lasing dynamics of a stadium-cavity laser is studied by using a mode expansion model which is a reduction of the Schrodinger-Bloch model. We study the properties of stationary lasing states when two cavity modes are selectively excited, while examining the validity of the mode expansion model by comparing its results with those of the Schrodinger-Bloch model. Some analytical results are obtained for single-mode and two-mode stationary lasing states for the mode expansion model.

We present theoretical and experimental studies on two-dimensional microcavity laser diodes with stadium and quasi-stadium shapes. We report a demonstration of lasing for the first time in a fully chaotic microcavity - a stadium-shaped cavity which is rigorously known to be fully chaotic. We also present systematic studies on quasi-stadium laser diodes for three types of resonator conditions: stable, marginally stable, and unstable. Morphological dependence of lasing characteristics of quasi-stadium laser diodes is elucidated. We also show examples of the application of quasi-stadium laser diodes to beam switching operation and optical signal distribution by using patterned electrodes and the phase locking phenomenon between two resonator modes.

Fractal behavior in magnetoconductance fluctuations in coupled quantum dots has been studied by means of exact and statistical self-similarity. The fractal dimensions from the different features are not coincident exactly but show the similar gate voltage dependences, where the values increase with increasing negative gate voltage. Moreover, results of statistical fractal dimensions obtained from two types of dot-array samples show the same dependence on the gate voltage variation. It seems a common feature of coupled-dot systems that the fractal dimension increases by decreasing the inter-dot coupling. © 2003 Elsevier B.V. All rights reserved.

We study theoretically the effect of deformed microelliptical cavities on lasing characteristics. We show that the transition of stationary lasing states from unidirectional rotational waves to a mixture of clockwise and anticlockwise rotational waves occurs when the shape of a disk is deformed to that of an ellipse. (C) 2004 Optical Society of America.

The relation between resonator modes and unstable periodic orbits in a fully chaotic quasi-stadium laser resonator is investigated. The complicated wavelength dependence of the power-coupling coefficient is explained by a simple coupling model, which considers some unstable periodic orbits. ©2003 Optical Society of America.

Three types of quasi-stadium laser diodes, which have confocal, concentric, and geometrically unstable end mirrors, were fabricated by a reactive-ion-etching technique. It is shown that the experimental results on the lasing characteristics of these lasers excellently correspond to the theoretical results by the extended Fox-Li mode calculation method. The morphological effects on lasing modes are discussed from the viewpoint of raywave correspondence. © 2004 Optical Society of America.

Locking of two resonance modes of different symmetry classes and different frequencies in 2D resonant microcavity lasers is investigated by using a nonlinear dynamical model. The patterns of stationary lasing states and far fields are asymmetric in spite of the symmetric shape of the resonant microcavity. The corresponding phenomenon is actually observed in the experiment of a 2D semiconductor microcavity laser diode.

We have observed lasing in a complicated eigenmode of a quasi-stadium laser diode with an unstable resonator consisting of two curved end mirrors obeying an unstable resonator condition and two straight side-wall mirrors. The laser was fabricated by application of a reactive-ion-etching technique to a molecular beam epitaxy - grown graded-index separate-confinement heterostructure single-quantum-well GaAs/AlGaAs structure. The far-field pattern shows that the lasing mode corresponds to the complicated lowest-loss mode obtained numerically by an extended Fox - Li method. © 2003 Optical Society of America.

A fully nonlinear dynamical treatment of lasing in a fully chaotic cavity was shown to give single-mode oscillation of a spatially chaotic wave function. For the cavity shape, Bunimovich's stadium was chosen, and for the laser model, the Schrödinger-Bloch model was employed. Furthermore, it was illustrated that the spatially chaotic wave function of the stationary lasing oscillation excellently corresponds to the quasistationary state of the resonance obtained by an extended boundary element method.

The lasing on scar modes in fully chaotic microcavities was discussed. The scar wave functions in a fully chaotic cavity was found to be obtained numerically by an extended Fox-Li method. The laser on scar modes was found to be observed in a semiconductor microcavity with a selective excitation of different scars controlled by corresponding shape of electrodes for current injection.

The quantum billiard problem, that is the Dirichlet problem for the Helmholtz equation, can be rewritten as a Fredholm integral equation of the second kind and the eigenenergies can be characterized as the zeros of the Fredholm determinant on the positive real axis. However the Fredholm determinant also has complex zeros corresponding to the resonances when the billiard table is regarded as a scatterer against the exterior wave function. That naturally leads us to a new question "Can one determine the shape of billiard table through the interior eigenenergies and exterior resonances, i.e., all zeros of the Fredholm determinant?" instead of the famous Kac's question "Can one hear the shape of a drum?", which was solved negatively.

Lasing modes in a two-dimensional quasi-stadium resonator with confocal curved end-mirrors were investigated. Asymmetric output beam emission was obtained by the locking of two modes of different symmetry classes corresponding to a closed ring-trajectory. © 2000 Optical Society of America.

Scar wave functions in a fully chaotic cavity are obtained numerically by an extended Fox-Li method. Lasing on the scar modes are observed in a semiconductor microcavity with a selective excitation of different scars controlled by corresponding shape of electrodes for current injection.

We propose a flower-shaped billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles in the shape of a flower, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form using different schemes, all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance in reproducing the precise parameter dependence of the diffusion coefficent. © 2002 The American Physical Society.

We fabricated quasi-stadium laser diodes whose resonators consist of two concentric curved end mirrors and two straight sidewall mirrors. We observed two lasing modes that correspond to different beam propagations along the cavity axis and along a ring trajectory, and different far-field patterns with wide angular separation. The modes can be selected by control of an electrode pattern. We also show that the far-field patterns numerically obtained by the extended Fox-Li mode calculation method are in good agreement with the experimental results. © 2002 Optical Society of America.

The quantum level statistics affected by bifurcations in classical dynamics is studied by using a one-parameter family of lemon billiard systems. The classical phase space of our system consists of regular and irregular regions. We determine an analytic solution of the phase volume for these regions as a function of the system parameter and show that the function reveals a cusp singularity at the bifurcation point. The function is compared with its quantum mechanical counterpart, the Berry-Robnik parameter. By estimating the semiclassical regime from the effective Planck constant that validates the quantum-classical correspondence of the Berry-Robnik parameter, we determine a region of the system parameter where the cusp can be reproduced by the statistical properties of the eigenenergy levels. © 2001 The American Physical Society.

We report on a class of spatially extended mechanical systems sustaining a transport process of diffusive type. These systems consist of a point particle subject to a constant vertical acceleration and bouncing on a one-dimensional periodically corrugated floor. We show that the deterministic dynamics of these systems is chaotic with small elliptic islands for many parameter values. The motion of particles perturbed by a small noise has a horizontal diffusion that is normal. In such a case, we show that the diffusion coefficient oscillates periodically as the energy of particles increases. In the absence of noise, there still exists an effective numerical value for the diffusion coefficient and this value has an irregular dependence on energy. © 2001 The American Physical Society.

We studied the energy level statistics for one parameter family of quantum oval billiards. The classical phase space of this system consists of a mixture of both regular and irregular regions. We analyzed localization phenomenon of the wavefunction on the phase space structures and verified numerically the validity of the Berry-Robnik formula which is based on the Berry-Robnik's surmise.

The lasing of the whispering gallery modes of the microdisc are investigated theoretically by solving the Maxwell equation with the nonlinear effect of the light field on the polarization due to the lasing medium as well as the circular boundary condition. The light of the lasing modes are trapped inside the microdisc even in the case that the angle of incidence of the light to the disc boundary is smaller than the critical angle.

We derive a functional equation for the Fredholm determinant of the boundary element method. By assuming that the functional equation holds for the semiclassical Fredholm determinant for strongly chaotic billiards, we obtain a real function whose zeros are the semiclassical eigenenergies. We also show by the numerical experiment of concave triangle billiards that the semiclassical eigenenergies are very close to the exact eigenenergies.

We investigate the "semiclassical Fredholm determinant" for strongly chaotic billiards derived from the semiclassical limit of the Fredholm determinant of the boundary element method. We show that it is the same as a cycle-expanded Gutzwiller-Voros zeta function when the bounce number of the periodic orbit with the billiard boundary corresponds to the length of the symbolic sequence of its symbolic dynamical expression. A numerical experiment on a "concave triangle billiard" shows that the series defining the semiclassical Fredholm determinant does not converge absolutely in spite of the absolute convergence of the series defining the Fredholm determinant. However, the series behaves like an asymptotic series, and the finite sum obtained by optimal truncation of the series defining the semiclassical Fredholm determinant gives the semiclassical eigenenergies precisely enough such that the error of the semiclassical approximation is much smaller than the mean spacing of the exact eigenenergies.

The stationary lasing of the modes in a microdisk is formulated as a nonlinear eigenvalue problem for a nonlinear Maxwell equation. It is shown that whispering gallery modes can be obtained as stationary lasing solutions with finite pumping thresholds. Further, it is discovered that whispering gallery lasing modes can exist even though the angle of incidence to the disk boundary is smaller than the critical angle for total internal reflection. © 1999 The American Physical Society.

We studied the energy level statistics for one parameter family of oval billiards whose classical phase space consists of some regular and some irregular components. As the parameter is varied, a transition from an integrable system to a strongly chaotic one occurs with successive bifurcations. We applied the Berry-Robnik formula to the level-spacing distributions for a variety of shapes of quantum oval billiards and found some striking effects of bifurcations in the classical mechanical systems on the level-spacing distributions. The validity of the Berry-Robnik formula is also checked for those shapes of the oval billiard for which there exist two separated chaotic components in the phase space. © 1999 The American Physical Society.

We propose a novel reflector, called a chaos mirror, designed by use of the principles of chaotic reflection. A feature of the reflector is that it converts a one-dimensional spread of incident rays into a two-dimensional spread of reflected rays. This can be useful for making free-space optical beam links by sweeping a transmission beam in only one dimension. © 1998 Optical Society of America.

A Selberg type zeta function is derived from the semiclassical limit of the boundary element method. It implies that the boundary element method with replacing the Hankel function by its asymptotic form can be interpreted as a type of resummation of the periodic orbit sum. © 1992.

Periodic orbits in a dispersing billiard system consisting of three circular arcs are studied numerically by using a partial coding rule together with an efficient method for enumerating periodic orbits on the real billiard plane. By examining several statistical measures, it is shown that the length spectrum and the stability exponents are highly uncorrelated. The validity of the semiclassical trace formula is also tested, and a remarkable agreement of the semiclassical and quantum density of states is obtained at least for about the lower 15 levels.