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Athermal Holographic Filters
Hung-Te Hsieh, Demetri Psaltis, Yu-Chong Tai

Figure 1: Recording a holographic grating inside a LiNbO3 crystal at lrec= 488 nm in the transmission geometry and then operating it as a WDM filter in the reflection geometry.

Abstract. Holographic filters are used as optical sensors and in wavelength division multiplexing (WDM) filtering applications. Temperature dependence is a critical concern for telecommunications. We realize the design of an athermal holographic filter employing a thermally actuated MEMS mirror to compensate for the drift of Bragg wavelength due to changes of temperature. The center wavelength of our holographic filter is shown to remain constant from 21°C to 60°C.

Summary. A grating holographically imprinted inside a recording material can be operated as a WDM filter in the reflection geometry, as shown in Fig. 1. The wavelength satisfying the grating equation (1) will be strongly reflected, whereas the other wavelengths pass through the filter unaffected.

Figure 2: The athermal design of holographic filter utilizing an Al-Si composite beam microactuator whose tip deflects as the temperature changes.

where n(T0) is the refractive index of the material at lB at temperature T0 and L(T0) is the period of the index grating at T0. By inspecting (1), we notice that we can Bragg match the grating to a shorter wavelength if we tilt the incident beam away from the normal.

Temperature changes affect holographic filters mainly through two mechanisms: (Other possible effects will be neglected here, e.g. the thermal dependence of the piezoelectric tensor will manifest itself when stress is being applied.)

1. Thermal expansion or contraction of the bulk material (in our experiments, LiNbO₃:Fe).
2. Thermal dependence of the dielectric constant of the bulk material.

Assume the Bragg wavelength of the filter is corresponding to an incident angle ( is the angle measured inside the crystal, whereas ’ is measured outside the crystal) at temperature T₀. When the temperature changes to T₀+, the Bragg wavelength of the filter will have a corresponding shift and move to +. If we adjust the incident angle by such that the Bragg wavelength shifts back to , we will have

Based on (3), we propose an athermal design to maintain the Bragg wavelengths of WDM filters as invariant as possible with respect to temperature fluctuations. The principle of operation is illustrated in Fig. 2. We use a bimetallic composite beam to control the direction of the incident beam. The device makes use of the TEC discrepancy between two properly chosen materials (in our case, aluminum and silicon) and deflects as the temperature changes.

In our experiments, holographic filters are recorded in an iron-doped lithium niobate (LiNbO ₃:Fe, 0.05 wt. % Fe₂O₃) crystal by interfering two coherent continuous wave (cw) laser beams inside the crystal, as shown in Fig. 1.

To specify the MEMS mirror parameters, we first figure out the Bragg wave-lengths for a series of incident angles at three different temperatures (21.79°C, 45.68°C, 58.46°C). Temperature monitoring is made possible by reading the resistance off a thermistor in close contact with the LiNbO3 crystal when the whole system is in thermal equilibrium. A thermoelectric (TE) cooler is used to control the temperature of the system. The results are shown in Fig. 3.

Our data suggest that for operation around an incident angle
=5°, an angular correction of 1.18 degrees will be required for a temperature change of 100°C. The aluminum-silicon composite beam was designed to deflect about 0.59 degrees for a temperature change of 100°C.

We mount the holographic filter and the MEMS mirror on two separate TE coolers. Two identical thermistors are used to monitor the temperatures of the filter and the mirror. The output from a tunable laser is reflected off the mirror toward the filter at an (outside) incident angle of 5 degrees. At this point both the filter and the mirror are at room temperature. The filter response is measured and the Bragg wavelength is determined. Then the TE coolers are turned on and raise the temperatures of both. The readings of the two thermistors are kept the same throughout the measurements of filter response. The filter shapes at =5° for three different temperatures are plotted in Fig. 4. Compared with Fig. 3, the drift of the Bragg wavelength is indeed compensated for by the deflection of the mirror.

We have shown that the temperature dependence of the Bragg wavelength of a holographic filter can be compensated by incorporating a passive, thermally actuated MEMS mirror into the system. To improve the performance of the athermal filter design, it’s vital to gain a deeper understanding of the evolution of filter shapes away from normal incidence. Other topics such as beam walk-off, polarization dependent loss (PDL) and the elimination of mirror hysteresis are also important considerations in practical applications.

Figure 4: Filter response measured in the through channel at qB’=5∞ for three different temperatures with the compensating MEMS mirror.

MEMS mirror into the system. To improve the performance of the athermal filter design, it’s vital to gain a deeper understanding of the evolution of filter shapes away from normal incidence. Other topics such as beam walk-off, polarization dependent loss (PDL) and the elimination of mirror hysteresis are also important considerations in practical applications.

References
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