THE PHYSICS BEHIND TAG OPTICS TECHNOLOGY AND THE MECHANISM OF ACTION OF APPLICATION NOTE 12-001 USING SOUND TO SHAPE LIGHT Page 1 of 6
Tutorial on How the TAG Lens Works This brief tutorial explains the science behind the TAG Lens and how to operate it. TAG Optics TAG Lens is the only device on the market that uses sound to shape light. This novel mechanism of action requires no moving parts and gives it the unique capabilities of focusing, defocusing, beam shaping, and extending depths of field in a single device. How Standard Lenses Work: The index of refraction is the property of a material that describes how much light is slowed when it passes through the material. A simple lens is made from a single material with uniform index of refraction and is shaped with a curved surface resembling a sphere or parabola. When a ray of light reaches the curved surface, it will bend according to an equation (Snell s law) which depends on the index of refraction of the lens material and the curvature of the surface. The place where all the rays of light meet is the focal point of the lens. ENABLING PRINCIPALES Figure 1: The bending of incident light rays and the wavefront curvature of light passing through a simple lens. Another way to think about this situation is to consider the wavefront of the incident light, or the locations where the incident light beam exhibits the same phase. By definition, the wavefront will always be perpendicular to the direction of light propagation. For example, in a plane wave, this would be a series of parallel lines that are perpendicular to the direction of propagation. In the case of a simple lens, the curvature of the surface causes the wavefronts to curve and the light to bend. One way to determine the location of the wavefront at a given position away from the optical axis, r, is to calculate the optical path length, λ λ(r) = n d (1) Page 2 of 6
Where n is the index of refraction of the medium and d is the distance the light travels in passing through the lens. From this equation, we can see that in the case of the simple lens, n is independent of the location in the lens and d is a function of the distance from the optical axis. But equation (1) has an important implication, if one can vary n as a function of r, one can get the same effect as a simple lens with a fixed d. This is the principle behind a gradient index of refraction (GRIN) lens. In a standard GRIN lens, the index of refraction profile is fixed during the manufacturing process. Notice in figure 2 how this case is equivalent to the standard lens in figure 1. ENABLING PRINCIPALES Figure 2: The bending of incident light rays and the wavefront curvature of light passing through a gradient index of refraction lens. Notice that it is equivalent to a standard lens even though the surfaces are flat. Page 3 of 6
Using Sound to Shape Light: The TAG Lens is a type of tunable GRIN lens that uses the action of standing sound waves to establish a constantly changing gradient index of refraction within the body of the lens. The sound waves send a vibration through the lens material causing the atoms and molecules to alternatively move closer together and further apart at specified locations. In general, when the atoms and molecules are further apart, the will exhibit a slightly lower index of refraction and when they are closer together they will increase the index of refraction. By controlling the shape and location of these sound waves, it is possible to establish an index of refraction profile that looks like a simple lens in the center of the lens. MECHANISM OF ACTION Figure 3: Solid blue line shows is a sketch of the index of refraction profile as a function of the radius in the TAG Lens. The center of this picture corresponds to the center of the TAG Lens. Dotted red line shows a parabolic index of refraction function. Solid black line represents the aperture over which the TAG lens can be considered a simple lens. One of the key advantages of this type of index profile is that the spherical aberration associated with the lens is small. Aberration refers to the fact that in a standard spherical lens, not all of the rays of light pass exactly through the same focal point resulting in a larger focal spot or a fuzziness in an image. However, it has been proven that a parabolic wavefront is much closer to an ideal wavefront than a spherical wavefront and therefore results in sharper focusing. The TAG Lens provides the user with two parameters that can be controlled, the amplitude, A, and the frequency, f. The amplitude simply changes the maximum value of the index of refraction profile and the frequency will change the distance between the peaks in it. These parameters will affect the focal length, F, which can be accurately calculated from the profile. Performing these calculations, we find that that the maximum lens power (inverse of the focal length), P in diopters is related to A and f by: P = C! A f!, (2) where C 1 is a constant that depends on the Lens design parameters which can be customized by TAG Optics to meet a user demand. Therefore, for fixed a frequency, the width of the central region remains fixed and the maximum lens power will scale linearly with the driving amplitude. Unlike a traditional optic, the TAG Lens does not have a sharp aperture within the region of focus. This is beneficial in that there are not diffraction effects. However, the implication is that the effective aperture is somewhat difficult to quantify and depends on the user tolerance for aberration. Thus TAG Page 4 of 6
Optics defines an effective aperture for the TAG Lens, d, which is independent of the driving amplitude and only depends on the driving frequency by, d =!!!, (3) where once again, C 2 is a constant that depends on the Lens design and can be customized by TAG Optics. Finally, for many applications, it is instructive to determine the numerical aperture, NA, of a lens. Traditionally, this is related to the ratio between the open aperture of the lens and the focal length. Thus for the TAG Lens, one finds NA = C! A f. (4) MECHANISM OF ACTION In general, one finds that the TAG Lens may be considered a relatively low numerical aperture device. However, by combining the TAG Lens with other optical elements such as high NA objectives or lenses it is possible to achieve high resolution in the plane while maintaining the benefits of the TAG Lens to electronically change the focus in the out- of- plane direction. Since we have a standing sound wave inside the TAG Lens, the index of refraction profile is constantly changing it time as the molecules oscillate. These oscillations are very regular and cause the index of refraction to change from a large positive curvature to an equivalent negative curvature as shown in figure 4. The period of this oscillation, T o will be related to the driving frequency by: T! =!!. (5) Figure 4: Schematic of the index of refraction profile at different times. The profile changes from the top to the bottom and returns to the top every period of oscillation. Therefore, in one T o of time, the TAG Lens will sample all focal lengths within the range of the maximum and minimum focus. Optically speaking, the TAG Lens behaves as any traditional lens meaning that it can be combined into more complicated, multi- element optical assemblies, and it can be modeled using industry standard software. In modeling the TAG Lens for optical assemblies, one can simply treat it as a GRIN lens with an appropriate index profile that can be provided by TAG Optics upon request. Page 5 of 6
Pulsed vs CW operation: Since the TAG Lens is in a continuous state of change, there are differences when using the TAG Lens with a CW source or detector as compared to using a pulse of light or a pulsed detector. MODES OF OPERATION AND APPLICATIONS When using CW light, the TAG Lens will sample all focal lengths within the range of operation as given by +/- P (the maximum and minimum lens power) from Equation 2. Although for a standard TAG Lens this value will range from positive to negative, it is possible for TAG Optics to customize a lens so that it remains entirely positive or negative depending on the user s needs. Therefore, a line focus (or defocus) will be obtained with changes in the amplitude or frequency of operation affecting its length. This line focus is fundamentally different than that of a Bessel Beam in that there are no rings around the central line. Therefore, all the optical power is concentrated within the line focus which can have particular benefits in materials processing applications. Alternatively, one can think of this as a user defined depth of field with important benefits in imaging applications. For those applications requiring a more traditional Bessel Beam, it is possible to drive the TAG Lens in an appropriate regime which can result in the desired Bessel Beam. In this case, the TAG Lens can be considered equivalent to a tunable axicon lens whereby changes in the amplitude have the same effects as changing the cone angle. When using Pulsed light, the TAG Lens will behave as a standard lens with a single focal length for each pulse. If the light source is synchronized with the TAG Lens, the result will be the same focal length for each pulse. If it is not synchronized, each pulse will exhibit a different focal length which depends on the relative phase difference between the light source and TAG Lens. Therefore, it is possible for the user to easily and quickly select any focal length by simply controlling the time delay. This effect has clear advantages in both imaging and materials processing applications where the ability to rapidly adjust the focal length can accommodate rapidly changing surfaces and opens the door to novel imaging and processing modalities. Since the TAG Lens is continuously changing in time, such changes can occur faster than the period of oscillation, down to the sub- microsecond time scale and much faster than any other adjustable focus element on the market. TAG LENS 2.0 Using Sound to Shape Light The TAG Lens is an ultra- high speed device capable of increasing the depth of field of conventional optics or providing a user- specified changeable focal length with sub- microsecond temporal resolution. Controlled from the USB output of a computer it is ideal for applications such as imaging, laser micro- processing, or metrology. No representation or warranty, either expressed or implied, is made as to the reliability, completeness or accuracy of this paper COPYRIGHT 2012 TAG OPTICS INC. Page 6 of 6