Introduction

Two decades after their invention, single-beam optical gradient force traps, commonly known as optical tweezers, have become indispensable tools for research (2,1). Formed by bringing an intense beam of light to a diffraction-limited focus, an optical tweezer can capture an object ranging in size from a few nanometers to several micrometers and hold it stably in three dimensions against gravity, random thermal forces, and other external influences. This article provides an overview of a generalized optical tweezer technique that uses computer-generated holograms (CGH) to create hundreds of simultaneous optical tweezers in arbitrary three-dimensional configurations, each with individually specified trapping characteristics. Introduced in 1997, holographic optical traps (3,8,4,5,6,7) have found applications in research and engineering ranging from fundamental studies of the mechanisms of phase transitions to the manufacture of wavelength-scale devices (9).

A single optical tweezer works by minimizing the electromagnetic energy stored in the fields scattered and absorbed by an illuminated object (10). Generally, this results in a small object being localized near the focus of a strongly converging laser beam. Heuristically, and semiquantitatively for sub-wavelength-scale Rayleigh objects, the attractive force may be understood as arising from a dipole moment induced in the particle by the light's fields. The induced dipole is drawn up gradients of the field toward the focus, where the light is brightest. Because the induced dipole moment typically is proportional to the field and the force on the dipole is proportional to the local field gradient, the overall trapping force is proportional to gradients in the intensity. This insight is exploited in the next section to simplify the creation of holographic trapping arrays.

Radiation pressure due to absorption and backscattering competes with the attractive gradient force and tends to blow particles downstream. Stable three-dimensional trapping in a single beam of light is possible only if the axial intensity gradients are large enough to overcome radiation pressure. This is one reason that optical tweezers generally are created with high-numerical-aperture lenses, such as microscope objectives, that are capable of bringing a beam of light to an exceptionally tight focus. Geometric aberrations degrade an optical tweezer's performance by reducing the focal spot's intensity gradients. Microscope objectives' well corrected aberrations also recommend them for this application.

A single collimated beam that fills an infinity-corrected objective's input pupil comes to a focus and forms a trap in the lens' focal plane at a position dictated by the beam's angle of incidence. Any object trapped in the tweezer therefore can be imaged conveniently with the same lens, provided that the imaging illumination can be separated from the trap-forming laser, for instance with a dichroic mirror. A diverging beam filling the lens' input pupil forms a trap downstream of the focal plane, and a converging beam forms a trap upstream. Controlling the input beam's degree of collimation and angle of incidence therefore provides a mechanism for positioning an optical tweezer in three dimensions.