Theory of a planar free-electron maser with transverse electromagnetic flux circulation in a 2D Bragg mirror

A planar free-electron maser with a resonator consisting of a 2D entrance Bragg mirror and a 1D exit Bragg mirror is theoretically studied in the framework of a nonstationary 2D model. In such a configuration, the 2D Bragg mirror provides synchronization of the radiation emitted by a wide (compared with the wavelength) ribbon-shaped electron beam. The transverse electromagnetic energy fluxes arising in this mirror are closed through an additional coupling waveguide, which provides a single-mode single-frequency masing regime insensitive to variation of the beam parameters over wide limits.     

Spatially coherent radiation from a coaxial free-electron laser with a resonator composed of one-dimensional and two-dimensional Bragg mirrors

It is shown that the application of a resonator composed of one-dimensional and two-dimensional coaxial Bragg mirrors provides a spatially coherent radiation from a hollow electron beam with a transverse size several orders of magnitude larger than the wavelength. The two-dimensional Bragg mirror placed at the cathodic end of the resonator synchronizes the radiation across the hollow electron beam. The standard one-dimensional Bragg mirror placed at the collector end closes the feedback loop and reduces ohmic losses to as low as 5–10% of the lasing power.     

Nonlinear theory of coaxial free-electron masers with 2D distributed feedback (quasi-optical approximation)

The nonlinear dynamics of coaxial free-electron masers with 2D distributed feedback, which is realizable in 2D Bragg structures, is analyzed in terms of a quasi-optical approximation. It is shown that feedback with the spatial synchronization of radiations from tubular electron beams with a perimeter exceeding 1000 wavelengths can be provided under such conditions. The objects of investigation are the one-section design of a free-electron maser with 2D distributed feedback and a design with a combined two-mirror resonator. In the latter, an entrance 2D Bragg mirror provides the spatial synchronization of radiation and weak reflections from a conventional exit Bragg mirror are sufficient for the self-excitation of the oscillator. The advantage of the two-mirror design is a decrease in ohmic losses. The adequacy of the geometric optics approximation used earlier to describe the dynamics of such self-excited oscillators is demonstrated under various boundary conditions for transverse (azimuthal) energy fluxes at the edges of a Bragg structure.     

Frequency stabilization in free-electron masers with 2D and 1D distributed feedback

We analyze the dynamics of free-electron masers (FEMs) with two-mirror hybrid Bragg resonators using the coupling between running and quasi-critical modes in the input mirror. Such a mirror may have the form of a 2D Bragg structure with coaxial geometry or a segment of a cylindrical waveguide with axisymmetric corrugation having a period close to the wavelength. The output mirror has the traditional Bragg structure coupling two counterpropagating running waves (the corrugation period is close to half the wavelength). It is shown that a stable unimodal lasing with a radiation frequency close to the cutoff frequency of the quasicritical mode excited in the input mirror can be attained using this scheme under optimal conditions. Such a regime is insensitive to variations of the electron beam parameters. Simulation of experimentally implemented FEMs and those being developed is carried out.     

A simple linear cavity dual-wavelength fiber laser using AWG as wavelength selective mechanism

In this paper, a simple design of linear cavity dual-wavelength fiber laser (DWFL) is proposed. Operating in the C-band region stretching from 1538.3 nm to 1548.6 nm, an arrayed waveguide grating (AWG) is used to generate the dual-wavelengths output together with a broadband fiber Bragg grating as a back reflector and an optical circulator with a 10% output coupling ratio which acts as a front mirror. The measured average output power of the DWFL is about −5.66 dBm and with a side mode suppression ratio (SMSR) of 53.1 dB. The spacing between the two output wavelengths can be varied from 0.8 nm to 10.3 nm with a stable output and minimum power fluctuations.     

Effect of diffraction on the electrodynamic characteristics of two-dimensional coaxial Bragg resonators

The electrodynamic properties of coaxial two-dimensional Bragg resonators with two-dimensional distributed feedback are analyzed. These resonators are made of coaxial waveguide sections with doubly periodic corrugation, which provides coupling and mutual scattering of four partial waves. Two of them propagate along the waveguide, while the other two propagate in the transverse (azimuthal) direction. It is shown that the high azimuthal index selectivity of two-dimensional Bragg resonators may be related to a qualitative difference in topology of the dispersion characteristics of azimuth-symmetric and asymmetric normal waves propagating in infinite waveguides of such a geometry. For the finite-length systems used as two-dimensional Bragg resonators, the eigenmode spectrum is found for two types of boundary conditions that correspond to the limiting cases of perfectly matched (open) systems and, conversely, of systems closed for the extraction of transverse electromagnetic fluxes. Perimeter-to-length ratios of the resonator at which the Q factor of the fundamental azimuth-symmetric mode is greater than those of the other modes are determined. The applicability domain of the geometrical approach, which was earlier applied to two-dimensional Bragg resonators, is discussed.     

利用超格子模型对布拉格光纤的研究

为了研究布拉格光纤的模式特征和传输特性,提出了超格子模型,利用傅里叶级数表示光纤横向折射率分布,利用平面波展开法分析布拉格光纤的能带结构,基于厄米-主斯函数的局域正交函数展开法,从全矢量耦合波动方程出发,得到关于模式传播常量和电场展开系数的本征方程,从而分析布拉格光纤的模式特征。以高折射率芯布拉格光纤为例,实现了该算法,得到基模与二次模的横向电场分布、基模色散曲线和模式双折射。基模的模式双折射可用于衡量算法的精度,结果表明该算法精度较高。超格子模型不仅可以用于研究高折射率芯布拉格光纤,而且同样可以研究低折射率区域导光的布拉格光纤。     

The efficiency of parallel quantum memory for light in a cavity configuration

We present a new scheme of quantum memory for optical images (spatially multimode light fields) that allows mapping the quantum state of the signal onto the long-lived coherence of the ground state of an ensemble of stationary atoms or impurity centers. The memory medium is embedded in an optical cavity with degenerate transverse modes, which increases the effective optical thickness of the medium and allows one, in principle, to store information in optically thin atomic layers. Since, in reality, storage and retrieval of limited-duration signals, including signals shorter than the lifetime of the field in the cavity, is of interest, we do not use the low-Q cavity approximation. The influence of losses due to partial reflection of the nonstationary signal field incident on a coupling mirror on the storage efficiency is considered. We used the method of approximate impedance matching, wherein losses due to reflection can be minimized by controlling the coupling parameter of the light field with memory medium in time, thus creating conditions for destructive interference of the signal and local fields on the coupling mirror. The influence of diffraction on the transverse resolution of memory at the writing and readout stages is investigated, and the number of effectively stored transverse spatial modes of the signal is estimated.     

Peculiarities of mode spectrum in two-dimensional Bragg structures

The fundamental difference in the eigenmode spectrum for traditional one-dimensional (1D) periodical Bragg structures and novel two-dimensional (2D) periodical Bragg structures of planar and coaxial geometry is discussed. In the case of 1D Bragg structures, the eigenmode frequencies are located outside the Bragg reflection zone while for 2D Bragg structures the highest Q-factor modes are located just near to the frequency of Bragg resonance and the mechanism for the formation of these modes is related to the coupling of the longitudinal and transverse propagating wave fluxes. The main eigenmode possesses a Q-factor which substantially exceeds the Q-factor of the other modes even in the case when the system transverse size is much greater than the wavelength that encourage the use of 2D Bragg structures for mode selection in powerful oscillators with oversized microwave systems.     

Transverse mode competition in defect states of a waveguide with corrugated walls

We investigate the defect states arising in the Bragg and non-Bragg gaps by inserting a straight duct into a waveguide with periodically corrugated walls. In periodic waveguides, the Bragg gap is created by the interference of the same transverse modes whereas the different mode coupling leads to the non-Bragg one. Due to the involved high-order modes, there are two defect states observed in the non-Bragg gap while only one in the Bragg gap, indicating that transverse modes play a significant role in the creation of defect states. Furthermore, the frequency of each defect state highly relies on the defect geometries and their band widths can be optimized by the number of waveguide segments. The proposed transverse mode competition analysis reveals the mechanism of frequency shifting and provides an opportunity for guided wave control engineering, which would definitely benefit their applications in various functional devices, such as filters, sensors, and amplifiers.     

Astigmatism in tapered slot antennas

A series of scale model measurements of transverse electromagnetic mode tapered slot antennas are presented. They show that the beam launched by this type of antenna is astigmatic. It is shown how an off-axis spherical mirror can be used to correct this astigmatism to allow efficient coupling to quasi-optical systems. A millimetre wave antenna and mirror combination is described and, with the aid of solid state noise diodes, the coupling of the launched beam to a quasi-optical spectrometer is shown to be in good agreement with that predicted by the scale model measurements.     

Tunable dual-wavelength fiber laser based on a polarization-maintaining fiber Bragg grating and a Hi-Bi fiber optical loop mirror

We demonstrate experimentally the operation of a linear cavity dual-wavelength fiber laser using a polarization maintaining fiber Bragg grating (PM-FBG) as an end mirror that defines two closely spaced laser emission lines. The PM-FBG is also used to tune the laser wavelengths. The total tuning range is ∼8 nm. The laser operates in a stable dual-wavelength mode for an appropriate adjustment of the cavity losses for the generated wavelengths. The high birefringence (Hi-Bi) fiber optical loop mirror (FOLM) is used as a tunable spectral filter to adjust the losses. The FOLM adjustment was performed by the temperature control of the Hi-Bi fiber.     

Fabrication and characterization of 1.55 μm single transverse mode large diameter electrically pumped VECSEL

We report on the design, fabrication, and characterization of InP-based 1.55 μm wavelength large diameter (50 μm) electrically pumped vertical external cavity surface emitting lasers (EP-VECSELs). The hybrid device consists of a half vertical cavity surface emitting laser (1/2-VCSEL) structure assembled with a concave dielectric external mirror. The 1/2-VCSEL is monolithically grown on InP substrate and includes a semiconductor Bragg mirror and a tunnel junction for electrical injection. Buried (BTJ) and ion implanted (ITJ) tunnel junction electrical confinement schemes are compared in terms of their thermal and electrical characteristics. Lower thermal resistance values are measured for BJT, but reduced current crowding effects and uniform current injection are evidenced for ITJ. Using the ITJ technique, we demonstrate Room-Temperature (RT) continuous-wave (CW) single transverse mode laser operation from 50-μm diameter EP-VECSEL devices. We show that the experimental laser optical output versus injected current (L–I) curves are well-reproduced by a simple analytical thermal model, consistent with the thermal resistance measurements performed on the 1/2-VCSEL structure. Our results indicate that thermal heating is the main mechanism limiting the maximum CW output power of 50-μm diameter VECSELs, rather than current injection inhomogeneity.     

Frequency stabilization and output power undulations of diode lasers with feedback by volume holographic gratings

The mode-hop behavior and the power characteristics of a laser diode with wavelength-selective optical feedback are experimentally investigated. The feedback is provided by external volume holographic gratings, also called ‘Bragg mirrors’, at normal incidence. We demonstrate that a Bragg mirror forces a laser diode to operate only within a narrow wavelength range, and that the emission wavelength of the laser diode is stabilized against variations of the injection current. Moreover, we present periodic undulations of the power characteristics of the laser, depending on the driving current. They can be qualitatively explained with a simple model which takes into account that the threshold gain in the laser system strongly depends on the wavelength.     

Generation of Spatially Coherent Radiation in Free-Electron Lasers with Two-Dimensional Distributed Feedback

We study the possibility of using two-dimensional distributed feedback (DF) to generate spatially coherent radiation of ribbon and hollow relativistic electron beams whose transverse dimensions exceed the wavelength by several orders of magnitude. Such a feedback can be realized in planar and coaxial two-dimensional Bragg resonators with a two-period corrugation of their side walls. This corrugation gives rise to additional transverse (with respect to the reciprocal motion of the electrons) fluxes of electromagnetic energy which synchronize emission from different parts of the electron beam. Simulations of the onset of autooscillations in free-electron lasers (FELs) with a two-dimensional DF show the possibility of obtaining single-mode monochromatic coherent generation by beams with transverse dimensions up to 10²-10³ wavelengths. We also analyze the use of hybrid resonators composed of two-dimensional input and one-dimensional output Bragg mirrors. In such a scheme, the two-dimensional mirror ensures synchronization of the emission perpendicular to the electron beam, while reflection from the output one-dimensional mirror is sufficient for the self-excitation of the generator. In the case of a system closed in the transverse direction, such a scheme permits one to reduce significantly the ohmic losses resulting from the electromagnetic fluxes locked in the transverse direction. It is shown that the two-dimensional DF can also be used to synchronize radiation in a multibeam generator consisting of planar FEL modules fed by a ribbon electron beam and coupled via the transverse electromagnetic-energy fluxes which are formed by two-dimensional Bragg structures. The experimental studies aimed at realization of ultrahigh-power FELs with a two-dimensional DF are discussed.     

Strong coupling of localized and surface plasmons to microcavity modes

We strongly couple surface plasmon modes on a thin metal layer via localized plasmons of nanowires to photonic microcavity modes. In particular, we place an array of nanowires close to a mirror and position a second mirror at Bragg distance. The coupling becomes evident from an anticrossing of the resonances in the dispersion diagram. We experimentally determine the dispersion by applying external pressure to the microcavity and find excellent agreement with simulations.     

Doppler optomechanics of a photonic crystal

A laser beam directed at a mirror attached onto a flexible mount adds friction to its mechanical motion by the Doppler effect. For a normal mirror the efficiency of this radiative Doppler friction is very weak and practically masked by laser shot noise. We find that it can become very efficient using a photonic crystal mirror near its photonic band gaps. As an example, a Bragg mirror used at the long wavelength edge of its band stop can be efficiently optically cooled using the Doppler friction. The opposite effect opens new routes for optical pumping of mechanical systems: a laser pointing at a Bragg mirror and tuned at its short wavelength edge induces amplification of the vibrational excitation of the mirror leading eventually to its self-oscillation. These new effects rely on the strong dependency of a photonic crystal reflectivity on the wavelength.     

Feedback coupling loss in single mode fiber lasers

Based on the expansion of the fundamental mode LP₀₁ in single mode fiber in terms of Laguerre-Gaussian free space modes, the feedback coupling losses for two different types of cavity mirror, i.e., a curvature mirror and a combing mirror of a lens and a plane mirror, are numerically calculated for the first time. The results show that, for the curvature mirror, the lowest coupling loss is obtained when its curvature radius matches the wavefront curvature. In particular, if a plane mirror is used as the cavity mirror, it has to be placed close to the fiber end to obtain the low coupling loss. For the combing mirror, the lowest coupling loss can be obtained when the plane mirror is placed at the back focal plane of the lens, and the variation of the coupling loss is insensitive to the mirror positions for the lens with longer focal length. Finally, the plane mirror and the combing mirror of a lens and a plane mirror are suggested to be the cavity mirror in the practical construction of the high power fiber lasers.     

Short-wave sectioned free-electron masers with Bragg resonators based on the traveling and quasi-critical wave coupling

We consider the possibility of implementation of a free-electron maser with a two-mirror resonator composed of modified and conventional Bragg mirrors, operated in the short-wave part of the millimeter-wave range. The use of a modified Bragg mirror based on the traveling and quasicritical wave coupling at the input of the interaction space permits the transverse-index selection of modes. Amplification of the synchronous co-propagating wave by an electron beam is reached mainly in the regular part of the resonator. Even slight reflections from the conventional output Bragg cavity, which directly couples the co- and counter-propagating traveling waves, turn out to be sufficient for generation of self-excited oscillations. It is shown that the new scheme of a free electron maser ensures the oscillation frequency stabilization with respect to the electron-energy variation. With the optimal choice of the parameters, the oscillation frequency is close to the cutoff frequency of a quasi-critical wave excited in the modified Bragg structure.     

Optical modeling of laterally-corrugated ridge-waveguide gratings

The paper presents some model improvements for the optical simulation of laterally-corrugated ridge-waveguide distributed feedback lasers. Simulation results are discussed and design principles for achieving single-longitudinal-mode operation are outlined. The effects of the laterally-corrugated ridge geometry both on the coupling coefficient and on the Bragg wavelength of different transverse modes are presented. The improved modeling has been used to design 980 nm distributed feedback lasers with laterally-corrugated ridge-waveguide third-order gratings. The lasers fabricated using nanoimprint lithography exhibited single-mode operation with 50 dB side-mode suppression ratio.