Rapidly reconfigurable optically induced photonic crystals in hot rubidium vapor

Through periodic index modulation, we create two different types of photonic structures in a heated rubidium vapor for controlled reflection, transmission and diffraction of light. The modulation is achieved through the use of the AC Stark effect resulting from a standing-wave control field. The periodic intensity structures create translationally invariant index profiles analogous to photonic crystals in spectral regions of steep dispersion. Experimental results are consistent with modeling.Comment: 6 pages, 6 figure

Precision frequency measurements with interferometric weak values

We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 kHz per root Hz with only 2 mW of continuous wave, single mode input power. We describe the measurement of a weak value and show how even higher frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as precision relative frequency measurements and laser locking without the use of atomic lines.Comment: 4 pages, 3 figures, published in PR

Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification

We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 560 femtoradians and the linear travel of a piezo actuator down to 20 femtometers

Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values

The amplification obtained using weak values is quantified through a detailed investigation of the signal to noise ratio for an optical beam deflection measurement. We show that for a given deflection, input power and beam radius, the use of interferometric weak values allows one to obtain the optimum signal to noise ratio using a coherent beam. This method has the advantage of reduced technical noise and allows for the use of detectors with a low saturation intensity. We report on an experiment which improves the signal to noise ratio for a beam deflection measurement by a factor of 54 when compared to a measurement using the same beam size and a quantum limited detector

Continuous phase amplification with a Sagnac interferometer

We describe a weak value inspired phase amplification technique in a Sagnac interferometer. We monitor the relative phase between two paths of a slightly misaligned interferometer by measuring the average position of a split-Gaussian mode in the dark port. Although we monitor only the dark port, we show that the signal varies linearly with phase and that we can obtain similar sensitivity to balanced homodyne detection. We derive the source of the amplification both with classical wave optics and as an inverse weak value.Comment: 5 pages, 4 figures, previously submitted for publicatio

Trajectory Design Leveraging Low-Thrust, Multi-Body Equilibria and Their Manifolds

A key challenge in low-thrust trajectory design is generating preliminary solutions that simultaneously specify the spacecraft position and velocity vectors, as well as the thrust history. To mitigate this difficulty, dynamical structures within a combined low-thrust circular restricted 3-body problem (CR3BP) are investigated as candidate solutions to seed initial low-thrust trajectory designs. The addition of low-thrust to the CR3BP modifies the locations and stability of the equilibria, offering novel geometries for mission applications. Transfers between these novel equilibria are constructed by leveraging the associated stable and unstable manifolds and insights from the low-thrust CR3BP

Access to Mars from Earth-Moon Libration Point Orbits:

This investigation is focused specifically on transfers from Earth-Moon L(sub 1)/L(sub 2) libration point orbits to Mars. Initially, the analysis is based in the circular restricted three-body problem to utilize the framework of the invariant manifolds. Various departure scenarios are compared, including arcs that leverage manifolds associated with the Sun-Earth L(sub 2) orbits as well as non-manifold trajectories. For the manifold options, ballistic transfers from Earth-Moon L(sub 2) libration point orbits to Sun-Earth L(sub 1)/L(sub 2) halo orbits are first computed. This autonomous procedure applies to both departure and arrival between the Earth-Moon and Sun-Earth systems. Departure times in the lunar cycle, amplitudes and types of libration point orbits, manifold selection, and the orientation/location of the surface of section all contribute to produce a variety of options. As the destination planet, the ephemeris position for Mars is employed throughout the analysis. The complete transfer is transitioned to the ephemeris model after the initial design phase. Results for multiple departure/arrival scenarios are compared

Incorporation of trajectory behaviors in the vicinities of different planetary moons using Finite-Time Lyapunov Exponent Maps

There is an increasing interest in future space missions devoted to the exploration of key moons in the Solar system. These many different missions may involve libration point orbits as well as trajectories that satisfy different endgames in the vicinities of the moons. To this end, an efficient design strategy to produce low-energy transfers between the vicinities of adjacent moons of a planetary system is introduced that leverages the dynamics in these multi-body systems. Such a design strategy is denoted as the moon-to-moon analytical transfer (MMAT) method. It consists of a general methodology for transfer design between the vicinities of the moons in any given system within the context of the circular restricted three-body problem, useful regardless of the orbital planes in which the moons reside. A simplified model enables analytical constraints to efficiently determine the feasibility of a transfer between two different moons moving in the vicinity of a common planet. Additionally, Finite-Time Lyapunov Exponent (FTLE) maps within the context of the MMAT scheme are incorporated to enable direct transfers between moons that offer a wide variety of trajectory patterns and endgames, such as temporary captures, transits, takeoffs and landings. The resulting technique is demonstrated to be applicable to several mission scenarios

Interferometric weak value deflections: quantum and classical treatments

We derive the weak value deflection given in a paper by Dixon et al. (Phys. Rev. Lett. 102, 173601 (2009)) both quantum mechanically and classically. This paper is meant to cover some of the mathematical details omitted in that paper owing to space constraints

All Optical Waveguiding in a Coherent Atomic Rubidium Vapor

We demonstrate an all optical waveguide imprinted by a low power Laguerre Gaussian control laser beam using a coherent Raman process in warm atomic rubidium vapor. We show that the signal beam propagates with a small spot size over several diffraction lengths. We also show that the coupling efficiency of the signal beam into the waveguide varies linearly with the signal power