This paper presents an optical apparatus for characterizing frequency multiplexing of color in leaky mode, anisotropic waveguide modulators. This type of characterization is particularly useful for informing the design of full color holographic video displays. The primary function of the apparatus is to map the frequency response and angular overlap of red, green, and blue outputs. The apparatus also allows measurements of other parameters such as scan center frequency, optical and RF bandwidth, and scan linearity.

Typically, color images are achieved in modern displays by multiplexing red, green, and blue light in time using a color filter wheel or by multiplexing in space by having dedicated red, green, and blue pixels. In a previous paper, author Smalley et al. proposed frequency multiplexing, or frequency division, of color as an alternative to spatial and temporal multiplexing of red, green, and blue light in displays.1 Frequency multiplexing of color allows each pixel element to display red, green, or blue light or any weighted combination of these primaries as a function of the frequency content of the drive signal sent to the display element. In addition to creating color imaged frequency, multiplexing of color can also be used as a solution for low cost, high bandwidth holographic video displays.

One platform for achieving frequency multiplexed color is in waveguide systems with guided to leaky mode interactions. Figure 1 shows that with this type of device red, green, and blue light can be coupled into an integrated optical waveguide. A surface acoustic wave (SAW) can then be induced on the surface of the waveguide such that light can be coupled into a mode that is no longer guided in the waveguide. The wave that is no longer guided it is called a leaky mode. With the proper design, it is possible to independently couple one color into a leaky wave without coupling out the other colors. Frequency multiplexing of color is attained if the guided to leaky wave coupling for each color occurs at different frequencies but each leaky waves couples out of the substrate at the same angle.

FIG. 1.

Frequency multiplexing of color consists of coupling red, green, and blue light into waveguide and then coupling the colors out using surface acoustic waves with different frequencies.

FIG. 1.

Frequency multiplexing of color consists of coupling red, green, and blue light into waveguide and then coupling the colors out using surface acoustic waves with different frequencies.

Close modal

Any guided mode can potentially couple to any leaky mode so the total number of guided to leaky mode transitions can become large for multimode waveguides. Multimode waveguides are advantageous for frequency division coupling, because they have high order guided modes with larger evanescent fields. Modes with larger evanescent fields have improved coupling efficiencies. This is because, in proton exchanged waveguides, the optical properties are degraded within the waveguide itself so the most efficient interaction happens outside the waveguide in the region where the mode is evanescent.2 

In order to choose the transitions appropriate for frequency division of color, it is necessary to gather a large amount of carefully collected and correlated frequency input and angular output data for each color of interest. Figure 2 shows that a simple frequency response graph is insufficient to determine whether the design meets the requirements of frequency multiplexing of color. Figure 3 shows that individual guided-to-leaky mode transitions can be distinguished by collecting data for both frequency and output angle.

FIG. 2.

Simple frequency response graph, which consists of more than eight guided-to-leaky mode coupling transitions.

FIG. 2.

Simple frequency response graph, which consists of more than eight guided-to-leaky mode coupling transitions.

Close modal
FIG. 3.

Individual guided-to-leaky mode transitions can be distinguished by collecting data for both frequency and output angle.

FIG. 3.

Individual guided-to-leaky mode transitions can be distinguished by collecting data for both frequency and output angle.

Close modal

However, no existing instrument provides the ability to collect these data. These data will need to be gathered in order for designers to use this technology in the development of next generation holographic displays.

We present a semi-automatic apparatus for mapping the angle and frequency response of guided to leaky mode coupling for multiple colors. The apparatus is a prism coupler on a rotation stage with a photodetector on a linear stage scanning the device output. Data collected by the apparatus form a data map of the outputs of guided to leaky-mode transitions. By creating these data maps for red, green, and blue illumination, we can choose interactions that provide separation of colors in frequency and overlap of colors in angle. In addition, the test samples can be chosen to maximize a number of criteria including efficiency, bandwidth, low or high frequency operation, low or high angle operation, compactness of frequency response, high frequency separation, scan linearity, and scan resolution.

Scanned aperture holographic video3,4 operates by optically scanning to produce one or more lines in the final holographic display output. The larger the number of channels in the modulator, the greater the total available pixel bandwidth available to the display system to be used for increased resolution, frame rate, output angle, or other parameters.5 Anisotropic leaky mode modulators can be fabricated inexpensively and possess channels that are ten times more densely packed than existing holographic displays.6 Additionally, these devices exhibit larger angular deflections, polarization rotation of signal light, and frequency division multiplexing of color. These characteristics make leaky mode couplers promising devices for scanned aperture holographic video displays and motivate the desire to carefully characterize their limitations and useful properties (affordances).

Anisotropic leaky mode couplers are composed of waveguides indiffused into an anisotropic, crystalline, piezoelectric substrate like lithium niobate. An interdigital transducer on the surface of the substrate is driven by an electrical input which excites SAWs, which are launched collinear with light trapped in waveguide.

The guided mode light interacts with the acoustic wave and may be coupled to other modes including leaky modes of orthogonal polarization if the phase matching condition is satisfied as given by

(1)

where βguided is the guided mode propagation constant, βleaky is the propagation constant for the leaky mode, and Kgrating is the momentum vector for the grating formed by the surface acoustic wave.6,7 The leaky mode output can be scanned and encoded with holographic information and the leaky mode interaction, in general, occurs at different surface acoustic wave spatial frequencies for different illumination wavelengths. The spatial frequency of the surface acoustic wave is directly related to the input RF frequency as given by

(2)

where Λ is the SAW period, fRF is the applied RF frequency, and v is the velocity of the surface acoustic wave. The dispersive nature of leaky mode couplers makes frequency division of color possible if the correct leaky mode transitions are chosen for red, green, and blue.

Frequency division color allows for the independent control of multiple superimposed colors propagating in a single waveguide channel. Typically, red light is outcoupled by a band of lower frequencies. Green and blue light tend to outcouple at mid and high frequencies, respectively. For certain guided to leaky mode transitions, all three colors will exit the device at similar angles. Red, green, and blue light may be made to scan a range of angles that overlap. Generally for frequency multiplexed color in displays, we seek separation in frequency and overlap in output angle. Additionally, we may want to maximize bandwidth and minimize wasted bandwidth (the amount space between color RF frequency passbands). We may also wish to know about the linearity and relative efficiency of particular guided to leaky mode transitions.

Figure 4 provides an illustration of the characterization apparatus. In order to characterize the guide to leaky mode outputs available in a sample, we employ a prism coupler equipped with a moving detector placed at the output of the sample. The function of the apparatus proceeds as follows.

FIG. 4.

Diagram of characterization apparatus. Light from one of the lasers is sent through a variable attenuator (adjusted to prevent optical damage of sensitive samples), a half wave plate to adjust polarization and a focusing lens to reduce the laser beam waist to a size small enough to efficiently prism couple into the device. If input beam waist is large, many guided modes may be excited in the device. This may be advantageous as it allows the simultaneous characterization of more guided to leaky mode transitions than would be possible by coupling into one guided mode at a time. The RF frequency is swept which results in a corresponding sweep of SAW spatial frequencies on the surface of the sample under test. Spatial frequencies, which result in guided to leaky mode transitions, produce light at the output. The output is recorded as the power meter, which is fitted with a slit and a polarizer (oriented in accept output light), scans the output of the sample.

FIG. 4.

Diagram of characterization apparatus. Light from one of the lasers is sent through a variable attenuator (adjusted to prevent optical damage of sensitive samples), a half wave plate to adjust polarization and a focusing lens to reduce the laser beam waist to a size small enough to efficiently prism couple into the device. If input beam waist is large, many guided modes may be excited in the device. This may be advantageous as it allows the simultaneous characterization of more guided to leaky mode transitions than would be possible by coupling into one guided mode at a time. The RF frequency is swept which results in a corresponding sweep of SAW spatial frequencies on the surface of the sample under test. Spatial frequencies, which result in guided to leaky mode transitions, produce light at the output. The output is recorded as the power meter, which is fitted with a slit and a polarizer (oriented in accept output light), scans the output of the sample.

Close modal

The guided wave modulator (GWM) to be analyzed is coupled with either red, green, or blue laser light (color inputs are tested one at a time). A RF signal used to control the deflection of the GWM is swept over a range of frequencies of interest (e.g., 100–800 MHz for proton exchanged lithium niobate samples). A slit-masked optical power meter mounted on a precision linear actuator is swept orthogonally across the deflected light’s linear sweep range. The measured optical power, linear actuator position, and input RF frequency are recorded at each sample. These data are used to build a three dimensional intensity graph in order to map input RF frequency to angular deflection of the output light.

The frequency resolution of the apparatus is governed by the signal generator, and the spatial resolution is limited by the size of the slit in front of the detector. Details for each component are given in Table I.

TABLE I.

The specific equipment used in our experiment was the following.

Instrument Model
RF signal generator  Agilent 8648D 
RF power amplifier  MiniCircuits Hela-10B in SMA package 15542 
Linear actuator  Newport MFN25PP 25 mm range, 74 nm resolution 
Linear actuator driver  Newport ESP7000 
Optical power meter sensor  Thorlabs S130C Photodiode 400 nm-1100 nm 
Optical power meter controller  Thorlabs PM100D 
Control program/environment  LabVIEW 2011 SP1/Microsoft Windows 7 
Instrument Model
RF signal generator  Agilent 8648D 
RF power amplifier  MiniCircuits Hela-10B in SMA package 15542 
Linear actuator  Newport MFN25PP 25 mm range, 74 nm resolution 
Linear actuator driver  Newport ESP7000 
Optical power meter sensor  Thorlabs S130C Photodiode 400 nm-1100 nm 
Optical power meter controller  Thorlabs PM100D 
Control program/environment  LabVIEW 2011 SP1/Microsoft Windows 7 

Typical operation of the characterization is as follows.

  1. The GWM of interest is placed in an alignment device, connected to a RF amplifier and signal generator, and is coupled with a monochromatic laser beam. Input RF power to the GWM is typically set to 30 dBm (this first step is done manually).

  2. A computer controlling the RF signal generator, linear actuator, and power meter is programmed to sweep the RF frequency and detector position.

  3. The linear actuator is set to a position step by the computer.

  4. The RF signal generator output is enabled.

  5. The RF frequency is set to a frequency step by the computer.

  6. The measurement of the optical power meter, the RF frequency, and the position of the optical power meter/linear actuator are recorded simultaneously and appended to the dataset of the test.

  7. Steps (5) and (6) are repeated until data spanning the entire frequency range of interest is recorded.

  8. The RF signal generator output is disabled, and step (8) is repeated to record background noise.

  9. Steps (5) through (10) are repeated until data spanning the entire position range of interest is recorded.

  10. A new dataset is created by subtracting the optical power background noise of each position step from the optical power measurements made at that location.

  11. The new dataset is parsed to plot output power as a func tion of input RF frequency and optical power meter linear position.

  12. The plot is analyzed, and the experiment is repeated with changes to parameters of interest.

Note: For Nos. (4) and (8) above, our RF signal generator uses a mechanical element to normally enable/disable the RF output, so we chose to vary the power level and frequency instead, to reduce possible wear and decrease testing time. While in the “disabled” mode, the output power was set to 0 dBm, and the frequency output was set to the minimum frequency of the signal generator (9 kHz). While in the “enabled” mode, the output power was set to 20 dBm and the frequency output was set to the frequency of interest. It was verified that this alternative technique had an impact equal to the mechanical control.

Currently, the primary use for the data maps generated by the apparatus is to identify favorable guided to leaky mode transitions for RGB display. Favorable transitions have color signals separated in frequency but overlapping in angle. Data maps are generated for the same sample in three colors. Data maps are compared to find transitions that meet the criteria for good frequency separation and good angular overlap. In Figure 5, data for these transitions are isolated on the data map and projected against the frequency and angle axis. The resulting graphs give input frequency response and the output angular response for the transitions of interest. These isolated transitions can be combined from red, green, and blue illumination to give the plots in Figure 6. Notice that the frequency response of each signal is separated, but the outputs are overlapping in angle as shown in Figure 7.

FIG. 5.

We can separate the guided to leaky mode transition of interest and use its projections to give frequency and angle information.

FIG. 5.

We can separate the guided to leaky mode transition of interest and use its projections to give frequency and angle information.

Close modal
FIG. 6.

For frequency division, color control is desirable for the frequency response of red, green, and blue light to be separated in frequency (this is the RF frequency labeled, f, in Figure 1). The vertical axis is optical output power, normalized for each color. Above, we see that red light is outcoupled and scanned for applied RF frequencies just above 400 MHz while green just below 600 MHz, and blue exits below 800 MHz. The bandwidth of each of these signals is proportional to the angular sweep of the optical output.

FIG. 6.

For frequency division, color control is desirable for the frequency response of red, green, and blue light to be separated in frequency (this is the RF frequency labeled, f, in Figure 1). The vertical axis is optical output power, normalized for each color. Above, we see that red light is outcoupled and scanned for applied RF frequencies just above 400 MHz while green just below 600 MHz, and blue exits below 800 MHz. The bandwidth of each of these signals is proportional to the angular sweep of the optical output.

Close modal
FIG. 7.

Ideally, the optical output of red, green, and blue light will be separated in frequency but overlapping in output angle. The vertical axis is optical output power, normalized for each color. Here, we see the optical output angles for red, green, and blue for the signals shown in Figure 6 above. For this sample, the red, green, and blue outputs show good separation in frequency and good overlap in angle. This is not always that case for every guided to leaky mode transition which provides our motivation for an apparatus to identify and characterize favorable transitions.

FIG. 7.

Ideally, the optical output of red, green, and blue light will be separated in frequency but overlapping in output angle. The vertical axis is optical output power, normalized for each color. Here, we see the optical output angles for red, green, and blue for the signals shown in Figure 6 above. For this sample, the red, green, and blue outputs show good separation in frequency and good overlap in angle. This is not always that case for every guided to leaky mode transition which provides our motivation for an apparatus to identify and characterize favorable transitions.

Close modal

Information in data maps can be used to determine the fitness of other device criteria. Figure 8 shows the relative linearity of the output of several guided to leaky mode transitions. Figure 9 shows the characterization apparatus has enough resolution to identify standing wave patterns from undamped surface acoustic waves bouncing off of sample boundaries. A cross section of the data map at a constant frequency will give a measure of the angular point spread function as shown in Figure 10. This shows how finely the device under test can address angle. This parameter has ramifications for achievable depth in holographic video displays.

FIG. 8.

This figure shows two modes, one which diverges significantly from linearity.

FIG. 8.

This figure shows two modes, one which diverges significantly from linearity.

Close modal
FIG. 9.

The apparatus’ resolution is sufficiently high distinguish periodic effects caused by standing wave SAWs. Usually, this occurs when SAWs bounce off of sample boundaries and reenter the optically active region.

FIG. 9.

The apparatus’ resolution is sufficiently high distinguish periodic effects caused by standing wave SAWs. Usually, this occurs when SAWs bounce off of sample boundaries and reenter the optically active region.

Close modal
FIG. 10.

The angular point spread can be found from the vertical cross section. This parameter will help determine the number of angles the device can address.

FIG. 10.

The angular point spread can be found from the vertical cross section. This parameter will help determine the number of angles the device can address.

Close modal

We have demonstrated an analysis system for characterizing anisotropic leaky-mode couplers. This semi-automatic apparatus allows us to quickly gather enough information to map the location of guided to leaky mode transitions in frequency and angle space. These data maps enable us to identify favorable transitions for frequency division color displays. Furthermore, these maps make it possible to quantify the center frequency, bandwidth, diffraction efficiency, linearity, and point spread of guide to leaky mode coupling.

The authors would like to thank Dr. Stephen Schultz for his suggestions and for use of his laboratory equipment. This research was supported by the Air Force Research Laboratory Contract No. FA8650-14-C-6571.

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