There are many applications in which a laser beam with a flat-top intensity profile would be ideal, as compared to a laser
beam with a non-uniform energy distribution. Standard stable optical resonators will unfortunately not generate such a
laser beam as the oscillating mode. Single-mode oscillation would typically be Gaussian in profile, while multimode
oscillation might deliver a beam with an averaged flat-like profile in the near field, but would diverge very quickly due
to the higher order modes. In addition, if the modes are coherently coupled, then large intensity oscillations could be
expected across the beam. Techniques exist to generate flat-top beams external to the cavity, but this is usually at the
expense of energy, and almost always requires very precise input beam parameters. In this paper we present the design
of an optical resonator that produces as the stable transverse mode a flat-top laser beam, by making use of an intra-cavity
diffractive mirror. We consider the modal build-up in such a resonator and compare the mode competition between
flat-top like beams, including Flattened Gaussian beams, Fermi-Dirac beams, and super-Gaussian beams. Finally, we
remark on the use of an intra-cavity piezoelectric unimorph mirror for selecting a particular class of flat-top beam as the
fundamental mode of the resonator.
In this paper we present the design of an optical resonator that produces as the stable transverse mode a flattened
Gaussian laser beam by making use of an intra-cavity diffractive mirror. We consider the modal build-up in such a
resonator and propose the required dynamic changes to an intra-cavity piezoelectric unimorph mirror for selecting the
flattened Gaussian beam order of the stable mode. The feasibility of using a deformable diffractive mirror is
demonstrated numerically. An optimization approach is employed to determine the optimal voltage distribution required
to deform the mirror into a prescribed shape for the selection of the flattened Gaussian beam order. Good agreement
between an ideal static diffractive mirror and the proposed adaptive mirror is achieved.
This paper describes the development of a deformable mirror to be used in conjunction with diffractive optical elements
inside a laser cavity. A prototype piezoelectric unimorph adaptive mirror was developed to correct for time dependent
phase aberrations to the laser beam, such as those caused by thermal expansion of materials. The unimorph consists of a
piezoelectric disc bonded to the back surface of a copper reflective mirror. The rear electrode of the piezoelectric
ceramic disc is divided into segments so that a number of different control voltages can be applied to deform the mirror
in a desired displacement distribution. The mirror is required to be able to deform in the shape of each of the lower order
Zernike polynomials, which describe aberrations in optical systems. A numerical model of the device was used to
determine a suitable electrode configuration. Finally, the device was constructed and the deformed shapes measured
using a laser vibrometer.
An actuation system, making use of paraffin wax as a smart material, has been developed for high force, large
displacement applications. Wax actuators exploit the significant volumetric expansion (typically between 10 and 15%)
experienced during the solid to liquid phase change of paraffin wax. When contained, this expansion results in
considerable hydrostatic pressure. Traditionally, wax actuators are designed such that the wax acts directly, via a
compliant seal, on an output device such as a piston. We propose using an additional intermediate (passive) fluid to
transmit pressure to a separate remote actuator. In essence, we propose a solid-state 'pump' for hydraulic actuation, with
no moving parts and which requires no maintenance. The pump makes use of paraffin wax pellets, submerged in
hydraulic fluid. The pellets are encapsulated in silicone rubber to prevent contamination of the hydraulic fluid. Upon
melting, the volumetric expansion is used to displace the hydraulic working fluid, which is in turn used to drive a
conventional hydraulic actuator. Making use of only 65g of paraffin wax, heated from room temperature to 80ºC, the
pump generated a blocked pressure of 45MPa and displaced 15.7ml of hydraulic fluid. The pump was used to drive a
commercial actuator, and achieved a free stroke of 24.4mm and a blocked force of approximately 29kN.
Piezoelectric transducers are commonly used to excite waves in elastic waveguides such as pipes, rock bolts and rails.
While it is possible to simulate the operation of these transducers attached to the waveguide, in the time domain, using
conventional finite element methods available in commercial software, these models tend to be very large. An
alternative method is to use specially formulated waveguide finite elements (sometimes called Semi-Analytical Finite
Elements). Models using these elements require only a two-dimensional finite element mesh of the cross-section of the
waveguide. The waveguide finite element model was combined with a conventional 3-D finite element model of the
piezoelectric transducer to compute the frequency response of the waveguide. However, it is difficult to experimentally
verify such a frequency domain model. Experiments are usually conducted by exciting a transducer, attached to the
waveguide, with a short time signal such as a tone-burst and measuring the response at a position along the waveguide
before reflections from the ends of the waveguide are encountered. The measured signals are a combination of all the
modes that are excited in the waveguide and separating the individual modes of wave propagation is difficult if there are
numerous modes present. Instead of converting the measured signals to the frequency domain we transform the modeled
frequency responses to time domain signals in order to verify the models against experiment. The frequency response
was computed at many frequency points and multiplied by the frequency spectrum of the excitation signal, before an
inverse Fourier transform was used to transform from the frequency domain to the time domain. The time response of a
rail, excited by a rectangular piezoelectric ceramic patch, was computed and found to compare favorably with
measurements performed using a laser vibrometer. By using this approach it is possible to determine which modes of
propagation dominate the response and to predict the signals that would be obtained at large distances, which cannot be
measured in the lab, and would be computationally infeasible using conventional finite element modeling.
Many ultrasonic motors are based on resonators that have two modes of vibration with equal resonant frequencies. Excitation of the two modes with a 90°-phase shift is used to generate elliptical motion at the contact points between resonator and slider. An alternative motor using two modes with a resonant frequency ratio of 1:2 has been demonstrated in the literature. The contact point in this stator describes a Lissajous figure ('8') instead of an ellipse. The motor requires only a single power amplifier and piezoelectric ceramic element. The challenge of designing such a resonator is to achieve the predetermined resonant frequency ratio with corresponding modes having usable motion at the contact points. In this paper, topology optimization was applied to design a resonator that has two modes satisfying these conditions. The topology optimization problem was formulated in an unusual manner with direct minimization of the intermediate density and a constraint on the natural frequency ratio. The design domain was discretized using four-noded membrane elements with drilling degrees of freedom due to their superior efficiency. Manual shape optimization, considering 3-D effects, was performed on the design produced by the topology optimization step. A prototype resonator was constructed and tested to verify the numerical modeling.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.