Study of performance of a He-Ne laser having an annular gain zone

A He-Ne laser with an annular gain zone is studied theoretically. It is demonstrated that the He-Ne medium in the annular discharge zone possesses enough gain to maintain laser oscillation. A multipass ring resonator, which is composed of two annular spherical mirrors, is described, and it is shown that the resonator is suitable for extracting optical energy from the He-Ne medium in the annular gain zone. Considering the availability of population inversion in the traveling-wave cavity and the influence of the crossover of the folded light beam in the resonator on the output power, a calculation formula for the output power of the laser with the multipass ring resonator is given. Calculating results prove that a 1 W output of the He-Ne laser can be obtained by a 1 m length annular discharge zone.     

Vector modes of lasers with radially birefringent elements

A general theory of steady-state diffractive vector modes for lasers with polarizing optical elements is reviewed. The problems inherent in including radially birefringent media such as solid-state rods are emphasized. A trade-off between ease of implementation, ease of interpretation, and cost of computation arises from the choices of representations of the field. In the scalar theory for axisymmetric resonators, the polar representation with expansion of the field in azimuthal Fourier series yields separation into an integral equation for each azimuthal index. A theoretical investigation of this approach for the vector case is presented. For a simple resonator composed of two mirrors and a bifocal lens, separation into coupled pairs of integral equations is obtained. Numerical solutions that use fast Hankel transforms from scalar theory are straightforward. Complications arise when other optical elements are introduced into the resonator. Methods for handling the general case are discussed.     

Iterative method for the design of a dual-phase-conjugation-mirror resonator with multiple apertures

Apertures have been used to select the low-order transverse modes in resonators. The additional diffraction losses result in a change in the transverse-mode structure, and the presence of apertures inside a resonator generally distorts the mode shape. The optimization of a multiple-aperture resonator demands an approach that differs from the conventional method in which the mode theory is used. We demonstrate an iterative design method to find optimal phase profiles for the reflector surfaces to build a resonator with multiple apertures to produce a lowest-order mode with much smaller diffraction loss and to satisfy the phase-conjugation conditions at the mirrors. The results are compared with conventional stable resonators, and we show that substantial improvement in round-trip loss and beam quality can also be obtained.     

Dark field imaging of semicrystalline polymers by scanning transmission electron microscopy

Scanning transmission electron microscopy (STEM) has been suggested to have advantages over conventional transmission electron microscopy (CTEM) for the observation of diffraction contrast features and diffraction patterns from radiation sensitive crystalline polymers. Because of image intensification, control of illumination location and magnification independent focus, STEM operation for focusing, area selection and set up of optics permits a high yield of systematic data. Dark field (DF) imaging is most useful when employed in conjunction with scanning microarea diffraction. For convergent beam microdiffraction and efficient DF imaging of thin crystals the beam divergence should be less than 5×10^–3 radians. For single beam DF, the reflection of interest is selected by the intermediate lens aperture. Use of a STEM annular detector to collect more than one reflection results in increased DF image intensity and resolution. Use of the entire azimuthal range of a single powder pattern reflection permits examination of crystal texture — in particular, images produced by chain axis reflections show the detailed arrangements of lamellae.     

Axicon-based Bessel resonator: analytical description and experiment

We present a new scheme for an optical resonator for production of Bessel and Bessel-Gauss light beams. The resonator with Bessel modes is composed of two plane mirrors with an axicon placed close to one of them. If this mirror is concave, the modes are Bessel-Gauss light beams. Analytical expressions relating parameters of the resonator and characteristics of its modes are obtained and analyzed. The results are verified with the Fox-Li algorithm. The resonator scheme was implemented in an experiment to confirm the possibility of the generation of zero-order Bessel beams. It was found that multipass modes can also oscillate in the resonator if its apertures are large enough.     

Novel unstable resonator configuration with a self-filtering aperture: experimental characterization of the Nd:YAG loaded cavity

A novel cavity design based on a confocal negative branch unstable resonator configuration is presented. A proper choice for the size of the field limiting aperture, set at the common focal plane of the mirrors, results in removal of the hot spot inside the cavity and in the smoothing of the spatial profile of the oscillating mode. Application of this scheme to a pulsed Nd:YAG oscillator is thoroughly characterized in a variety of operational modes (fixed-Q, Q-switching, mode-locking). The main results are a high efficiency of energy extraction and excellent phase and amplitude profiles of the output beam, which shows real transform-limited performances.     

Observation of stable cylindrical modes in electrically pumped circular grating-coupled surface-emitting lasers

We present the results of a comprehensive experimental study of the modal behavior of electrically pumped circular grating-coupled surface-emitting lasers with resonant second-order gratings. Our results show stable cylindrical mode operation with azimuthal orders m = 1 and m = 52. We have found that, when a passive, unpumped 0.7-mum-deep indentation is included at the center of the circular resonator contact, the modal behavior becomes more stable with respect to increasing current. This result manifests itself in the lasing of two orthogonal m = 1 modes along with one higher-order mode from threshold to 2.2 times threshold or more. The spatial coherence of the cylindrical modes over the area of the resonator leads to better beam quality. Lasers without passive central indentations exhibit mode hopping between quasi-linear modes and higher-order cylindrical modes as the current is increased.     

Phase locking of CO(2) lasers by the use of diffraction effects

A technique to phase lock CO(2) lasers with spatially separated active media was investigated. Only reflective optics (except for the output coupler) were used, in view of applications of this method in the field of high-power lasers. Phase locking was established when the beams of two resonator branches were made to propagate very close to each other along the so-called coupling path. As a result of diffraction effects both resonators were exchanging energy, establishing a phase-locked operation mode when several locking conditions were fulfilled. A maximum coupling coefficient (the ratio between the diffracted intensity in the second cavity and the intercavity intensity in the first resonator) of 2.6% could be achieved. Because phase locking was highly dependent on the difference between the two resonator lengths, a length control that uses a piezoelectric translator connected to one of the resonator mirrors was used. To detect phase locking, the intensity maximum of the interference pattern of the two laser beams was monitored with a fast detector. By application of a ramp signal to the piezoelectric translator and detection of the peak intensity, the locking range could be measured. Up to a mismatch of the resonator lengths of λ/130, locking could be maintained. The measurements were compared with results of a computer simulation with Huygens-Fresnel integrals to describe diffraction and the one-dimensional Maxwellian equations to calculate supermodes and to analyze their stability. The numerical results showed an excellent agreement with the measured values.     

Unstable resonator with reduced output coupling

The properties of a laser beam coupled out of a standard unstable laser resonator are heavily dependent on the chosen resonator magnification. A higher magnification results in a higher output coupling and a better beam quality. But in some configurations, an unstable resonator with a low output coupling in combination with a good beam quality is desirable. In order to reduce the output coupling for a particular resonator, magnification fractions of the outcoupled radiation are reflected back into the cavity. In the confocal case, the output mirror consists of a spherical inner section with a high reflectivity and a flat outer section with a partial reflectivity coating. With the application of the unstable resonator with reduced output coupling (URROC), magnification and output coupling can be adjusted independently from each other and it is possible to get a good beam quality and a high power extraction for lasers with a large low gain medium. The feasibility of this resonator design is examined numerically and experimentally with the help of a chemical oxygen iodine laser.     

Annular resonator with a Cassegrain configuration

An advanced annular resonator is studied both theoretically and experimentally. This resonator has a Cassegrain mirror configuration and is designed to extract circular and high-quality beams from annular gain media. We carried out beam propagation in this resonator, calculating the intensity distributions of the laser beam. We also proved the performance experimentally by applying the resonator to a CO2 laser. The operation of the new resonator is demonstrated successfully. The quality of the output beam is in good agreement with theoretical calculations of laser output power of 20 W.     

Effects of Output-coupling Apertures in a Resonator on Spatial Coherence of CO2 Laser

The degree of spatial coherence S n₁₂ (0) S has been measured for a CO₂ laser beam of radiation emerging from a central output-coupling hole, or four output-coupling holes in the centre-symmetric annular region, in a plane mirror of the Fabry-Perot resonator. The effects of these two kinds of output-coupling apertures on the spatial coherence are studied in association with mode structure in the resonator. The value of S n₁₂ (0) S is always above 0·9 for two points in any location in the beams of radiation emerging from the four output-coupling holes, while it varies with the time in the range 0·5 to 1·0 in a beam of radiation emerging from the central output-coupling hole. Some analytical considerations are given, according to which the value of S n₁₂ (0) S should be approximately unity over the cross-sectional area of a beam of radiation emerging from an output-coupling hole of 6 mm in diameter. This is partly in agreement with the results of the measurements. For the central coupling hole, the fact that S n₁₂ (0) S varies with time is explained qualitatively to be due to the intensity fluctuation in every operating mode, competing with each other in the active resonator. For the four coupling holes a particular mode may be made to survive due to relatively strong mode competition arising from the mode selective effects of the off-centred four coupling holes. On this account a high value of S n₁₂ (0) S may be obtained at two points in the beam separated by 25 mm.     

One-Step 360 degrees Rainbow Holography with Two Spherical Mirrors

A new optical configuration producing one-step 360 degrees rainbow holograms is presented. The method makes use of two concave mirrors in confocal position, with an annular aperture between the two. An experimental demonstration is given.     

Propagation of elliptical Gaussian beams modulated by an elliptical annular aperture

An analytical propagation expression for a generalized astigmatic elliptical Gaussian beam (EGB) modulated by an elliptical annular aperture and passing through an axially nonsymmetrical optical system is obtained by the use of vector integration. The derived analytical results provide more convenience for studying the propagation and transformation of EGBs than the usual method of using the diffraction integral directly, and the efficiency of the numerical calculation is significantly improved. Some numerical simulations are illustrated for the propagation properties of EGBs passing through a free space with an elliptical annular aperture, an elliptical screen, or an elliptical aperture. Further extensions are also pointed out.     

Modulation of a General Periodic Object with Triangular Transmission Profile by an Annular Aperture Using Incident Incoherent Light

Expressions for the intensity distribution in the diffraction images of a general triangular wave-object have been obtained. The diffracting aperture considered is an aberration-free annular aperture. The circular aperture system appears as a particular case when the obstruction ratio is zero. Use of incoherent light has been assumed throughout. General triangular wave response of such systems to spatial frequencies in the object has been plotted and the object function, which gives a wave response nearly similar to that of the sine wave, has been pointed out.     

Near- and far-field properties of annular CO(2) waveguide lasers

The theoretical and experimental investigation of field properties of annular waveguide lasers with a Fabry-Perot resonator is presented. Oscillation with high azimuthal mode order leads to an annular intensity distribution in the far field with almost linear dependence of the annular diameter on the mode order. Low-order fields form a distinct focal spot in the far field. A laser device with a discharge area of 6-cm diameter and 53-cm length yields an output power of 600 W.     

Interferometer for optical coupling and mode selection in a multichannel laser array

A theoretical consideration is presented of the optical coupling and selection of laser array modes by the use of a developed Lummer-Gehrcke interferometer as a resonator reflector. Control of the mirror reflection of the proposed interferometer permits laser power to be redistributed through channels on the outlet resonator mirror; in particular, it makes it possible to lead power out of the resonator by a single beam. In this way it is possible to diminish the sidelobes in the far-field radiation profile of multichannel lasers and to raise the efficiency of the optical coupling of the laser array with waveguides and fibers. This method may be used for the redistribution of laser power on the outlet mirror in striped lasers as well.     

Analysis of lasing in gas-flow lasers with stable resonators

A model is developed that describes the power extraction in chemical oxygen-iodine lasers (COIL's) and CO(2) gasdynamic lasers with stable resonators when a large number of transverse Hermite-Gaussian eigenmodes oscillate. The extraction efficiency, mode intensities, and intensity distribution along the flow depend only on two parameters. The first is the ratio gamma(0) of the residence time of the gas in the resonator to the O(2)((1)D) or N(2)(v) energy extraction time and the second is the ratio of the threshold to the small-signal gain. The efficiency is maximum for gamma(0) ? infinity and decreases rapidly as gamma(0) decreases. It is found that for a range of parameters corresponding to the highest efficiencies the intensity distribution along the flow is nonuniform and has two peaks near the upstream and downstream sections of the resonator. In this case only the highest-order modes that totally fill the resonator cross section oscillate (the so-called, experimentally observed sugar scooping bimodal intensity distribution). For the range of parameters corresponding to smaller efficiencies the intensity is uniform. In this case all the modes participate in lasing; however, the intensities of the high-order modes are larger than those of the low order. The current model is compared with the plane-mirror Fabry-Perot resonator model and with the constant intraresonator intensity and rooftop models of COIL's with stable resonators. The extraction efficiency calculated with the last two models is close to that estimated from our model. However, the intensity distribution cannot be calculated correctly using the Fabry-Perot, the constant intraresonator intensity, or the rooftop model.     

Phase Locking of CO(2) Lasers

A method of phase locking two CO(2) lasers by radiation exchange is presented. This phase-locking was achieved by use of a copper prism as a beam folding device in the resonators and extraction of the output radiation by a common output coupler. Energy exchange led to a phase-locked state if several locking conditions were fulfilled. The amount of radiation injected from one resonator to the second cavity could be adjusted by movement of the prism. The influence of the strength of coupling on the locking range was studied. The beat signal between the two unlocked lasers could be measured, whereas in the case of phase-locked operation twice the intensity was detected. Despite the inclusion of several assumptions, a simplified mathematical model delivered good agreement between calculated and experimental results.     

Equivalent circuit for the microstrip ring resonator suitable for broadband materials characterisation

A simple equivalent circuit of the edge coupled microstrip ring resonator is developed based on both circuit and electromagnetic theory. The new model extends the work done by previous authors by including the effects of radiation loss, the coupling gap and the feed network as well as extending the frequency range by including higher-order modes. The model accurately predicts the resonant frequencies of the ring including the effects of dispersion and thick conductors. The equivalent circuit allows measurement of the resonance frequencies and the Q factors to be made independently of the coupling gap dimensions, which traditionally have been difficult to accurately model. A method of determining radiation loss is also presented, which has often been incorrectly neglected in the past. Experimental results support the accuracy of the equations and measurements on alumina rings that demonstrate a frequency accuracy of better than 1% over 12 resonant modes in the frequency range 3-33 GHz.