Spatial Light Modulator

A spatial light modulator is a device used to impose a spatially varying modulation on the beam of incident light [22, 23]. The modulation can be in various forms: amplitude, phase, and polarization. In this subsection, we will review three devices - the liquid crystal cell array, digital micromirror device, and deformable mirror - that are widely used in the field of wavefront shaping.

Liquid crystal phase is characterized by a state between conventional liquid and solid crystal. The molecules in liquid crystal may be aligned and/or oriented like a solid crystal, but have a much greater freedom to move like a liquid. Liquid crystal can be divided into three classes: thermotropic, lyotropic, and metallotropic liquid crystals. These are classified by the condition required for the phase transition. Ther- motropic and lyotropic liquid crystals, which are composed of organic molecules, occur in a certain temperature range. While the thermotropic phase is induced merely by

temperature, the lyotropic phase requires a amphiphilic solvent (both hydrophilic and liphphilic) and exhibits a phase-transition controlled by the concentration of the liquid crystal molecule and solvent. In contrast, a metallotropic liquid crystal is composed of both organic and inorganic components and the phase transition depends on the organic-inorganic composition ratio, in addition to temperature and concentration.

In most practical applications, rod-shaped liquid crystal molecules (a sub-category of the thermotropic phase) are used. In the liquid crystal phase, the long axis of the molecules are oriented in a certain direction (director’s direction). Typically, several subphases and alignments of liquid crystals are observable by modifying the temperature. For example, in the smectic phase (which can be typically found at relatively lower temperatures), the molecules are arranged in planes such as in a conventional crystal. In contrast, in the nematic phase, the molecules are randomly positioned like a liquid. The nematic phase is most widely used in electrooptical applications as the director’s direction can be easily controlled with an electric field. The operation mode of a liquid crystal-based spatial light modulator depends on the director’s direction in the response of the external electric field. Depending on the direction of the permanent or induced dipole moments, the long axis of the liquid crystal molecule can either be aligned along or perpendicular to the direction of the applied electric field. Here, we introduce two types of liquid crystal alignment that can be used to control the phase and amplitude of the light, respectively.

1. Parallel aligned nematic liquid crystal. In the PAN phase, the LC molecules are initially aligned parallel to the two alignment layers where the electrodes are aligned as well. When the electric field is applied, the LC molecules are aligned to the direction of electric field (rotation angle depends on the strength of the electric field). Based on the birefringence of the LC molecule, the phase of the light beam that passes through the LC cell can be modulated.

2. Twisted nematic liquid crystal. This type of LC molecules is aligned in a helical twist. Thus, the first molecule and the last molecule between the alignment layers are perpendicular to each other at the beginning. Therefore, the polarization of the beam is gradually rotated. When the electric field is applied, the polarization angle of

the light beam is no longer rotated by the LC cell as the LC molecules are aligned to the direction of the electric field. By placing the polarizers on the input and output sides of the LC cell, the amplitude modulation can be achieved. This is the working principle of the conventional LCD screen. In the wavefront shaping experiment, it should be taken into account that the phase of the light is also modulated by the bifringence.

A deformable mirror is a reflective surface that can be deformed into a desired shape. Historically, deformable mirrors have been widely used in astronomical tele- scopes to adaptively compensate the wavefront distortion from the atmosphere, re- sulting in an improvement on the resolution and brightness of the image [24, 25]. The first successful design was implemented with a thin aluminized glass facesheet bonded to a slab of piezoelectric material. Voltages applied to the electrodes (which are placed underneath the piezoelectric material) imprint the desired local defor- mation. Alternatively, the continuous facesheet can be supported and deformed by discrete actuators (up to a few thousand). Either piezoelectricity or electrostatic force can be used as an actuator module. The concept of the deformable mirror can also be implemented with segmented mirrors which consist of an array of discrete mirrors. Typically, each mirror is controlled by three actuators for three degrees of freedom in movement: piston and tip/tilt. In contrast to the continuous facesheet design, each of the mirror elements are free of crosstalk. However, the drawback lies in the fact that the gaps between mirror segments generate undesired scattered light.

A digital micromirror device (DMD) is an optical semiconductor composed of 105 to 106 _{microscopic mirrors arranged on a CMOS integrated circuit. Each micromirror}

is attached to the torsional hinge aligned along the diagonal of the mirror. Two electrodes, which are controlled by the CMOS circuit, are used to apply electrostatic force to the mirror elements and hold the micromirrors in the two operational positions (typically,−10◦_{and +10}◦_{). A DMD is used to modulate the amplitude of the incident} light beam by guiding the light component reflected in either of the angles (referred to as the ON state) into an optical system of interest. In display applications, grayscales are produced by controlling the ratio of ON and OFF time within one frame time of

the human eye.

When choosing a spatial light modulator for a wavefront shaping experiment, a number of parameters, such as the number of degrees of freedom and the response time, should be taken into an account. The number of degrees of freedom determines the complexity of wavefront that the SLM can reproduce and the response time determines the range of applications depending on the dynamic characteristics of the specimen. A typical liquid crystal-based spatial modulator has 106_–107 _elements,

refreshing at∼60 Hz. A digital micromirror device has a similar number of elements, but can operate at a frequency of up to ∼30 000 Hz. Thus, it is the most suitable for fast applications. A deformable mirror typically has a 10–1000 elements, operating at∼1000 Hz.