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Abstract
For active beam manipulation devices, such as those based on liquid crystals, phase-change materials, or electro-optic materials, measuring accumulated phase of the light passing through a layer of the material is imperative to understand the functionality of the overall device. In this work we discuss a way of measuring the phase accumulation through a switched layer of Ge2Sb2Te5, which is seeing rapid use as means to high speed dynamic reconfiguration of free space light. Utilizing an interferometer in the switching setup and modulating the phase of one arm, the intensity of a probe beam can be captured and phase data pulled from it. Simulations were used to discover the connection between the intensity modulations and the phase information. The technique was tested experimentally and it was found that within error, the measurement was robust and repeatable.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Manipulating light in modern device applications requires the ability to control both its amplitude and phase [1,2], whether these devices are used in optical communications, lasers, microscopy, astronomy, or others. To achieve full functionality of many of those devices, it is desirable for any such control to be dynamic, which would enable both applications that require high-speed manipulation of light, as well as static ones where the benefit is in low-cost reconfiguration of optical functions. One current technology used for these purposes is the spatial light modulator (SLM) [3–5] in both Amplitude-only and Phase-only implementations. Modern SLMs are expensive and limited in their speed to around 2kHz [6,7] and most off the shelf SLMs will cap out at 180Hz (one of the fastest currently available from ThorLabs, for example, the EXULUS-HD1 has a frame rate of 180Hz). While this is fast enough for some uses such as display holography, other more technical uses for light manipulation constantly require us to push the limits of speed capabilities [8]. One limiting factor to achieving faster and less expensive SLMs is the active medium used. Liquid crystals (LCs) are a common active medium used in these devices. If the LCs were replaced with something less expensive, easier to manufacture, and faster, the cost of SLMs could drop and the utility could climb. Recent proposals and demonstrations have shown the potential in using PCMs [9], and in particular GST [10,11], which makes a good candidate for an SLM in the near infrared telecommunications wavelength of 1550 nm. The benefits of GST are the high index contrast between the amorphous and crystalline state of nearly 2 at 1550 nm wavelength [12,13] and the fact that it has been shown to have even sub nanosecond switching [14,15] times. This would facilitate at least a 2 orders of magnitude increase in the speed of any future free-space light modulation device. Crucially, GST is a relatively inexpensive material and is already used in manufacturing for things such as rewritable DVDs and PCRAM [16] and has shown the potential for nanosecond switching speeds [17] and beyond.
Since phase manipulation is at the heart of these needed devices a straightforward way to analyze the phase accumulation of a device is necessary. This work proposes a phase measurement technique that utilizes an interferometry setup with a steady known phase modulation in one of the arms (the carrier) to capture the phase accumulation in a single phase change cycle. The interference of the waves then imprints the phase shift of the sample arm into the carrier signal and can be read as a shift in the phase of the combined amplitude wave for a modulation depth of 2$\pi$ or a change in the relative amplitude of the combined waves for a modulation depth of $\pi$. We note that the technique developed is a single-shot technique that can directly characterize "static" phase and amplitude patterns [18,19] as well as those aimed at rapid reconfiguration [20].
2. Theory and simulations
In order to create a useful SLM [21], the phase of light propagating through the device needs to be controlled fully from 0 to 2$\pi$ [22], thus the amount of phase accumulation that occurs with the switching of the material needs to be fully understood. To accomplish this, the phase accumulation must be measured for light passing through the device. We have devised a way of measuring the phase making use of an interferometer [23] within our optical switching setup for PCMs (Fig. 1, details about the switching setup is in Ref. [20] with the phase measurement detailed in the experimental section). The two arms of the interferometer [24] come from the pick-off before the microscope and the output of the microscope after being reflected off the sample (after filtering out pump beam). By modulating the phase of the pre-microscope arm in a sinusoidal pattern and then recombining the beams we can look at the interference pattern in the amplitude of the intensity of light and glean important phase information from the data.
Fig. 1. Optical System for Phase and Amplitude Modulation. The relevant component here is the pre/post microscope arms (w/o phase modulator) that lead to the Phase measurement part of the setup.
Figure 2 shows an example Python simulation of what we expect to see from the setup. This was accomplished by simply adding two waves and taking their amplitude. If their starting amplitudes are equal, it is a pretty straightforward process to find the combined amplitude of the waves. We start with the equations for two waves, $\Psi _1$ and $\Psi _2$, ignoring the propagation term $kz$ since the waves are coupled and will not deviate, therefore this term won’t play an important role in the derivation,
From here we add them together and use the relation,
to get,We can now use the Trig identities,
to transform (6) into,Fig. 2. Simulations showing the effect of a phase shift of $\dfrac {\pi }{6}$ for different starting phases. On the right hand side, we add an 81.5% drop in amplitude shown in order to match the drop in reflectivity with the switching of the material that we experimentally observe.
Another way that the phase can be pulled from the 0 to $\pi$ modulated data is from the peak positions. The peak positions can be pulled by looking for the extra peak growing from the top or bottom and taking the position of the closest peak or trough. The difference between the peak position and the center of the extra peak is then recorded as the shift in the data. If the extra peak is growing from the bottom (stalagmite) a shift of half the period should be added. The number should then be subtracted from the position of the center peak, divided by the period, and the remainder kept. The final phase can then be looked up on a chart. Remember that there will always be two different but equally spaced possibilities for the phase on either side of $\dfrac {\pi }{2}$ if the base phase is between 0 and $\pi$ (stalactites) and $\dfrac {3\pi }{2}$ if the base phase is between $\pi$ and $2\pi$ (stalagmites). Figure 4(a) gives an example of where to pull the peak position from and Fig. 4(b) gives a look up graph for finding the phase.
These measurements become slightly easier if the modulator is allowed to run from 0 to $2\pi$, however we can’t get around the uncertainty with the two possible phases for each measurement. Figure 5(a) shows a model of the data and Fig. 5(b) show look up graph for the case of 2$\pi$ modulation. In this case, we again look for the extra peak. It is easier to identify since it will be the smaller of the two peaks that don’t make it fully to the top or bottom of the modulated range. We first find the difference in positions between this extra peak and the nearest maximum or minimum (adding half the wavelength if the extra peak is coming from the bottom), divide by the period, and finally keep the remainder. If there is not a smaller peak readily visible the phase is very close to 0 or $\pi$. If this is the case, we look for the peak that is the flatter of the two. If it is on top, the phase is 0, if it is on bottom, the phase is $\pi$. Once the difference is found, we divide by half the modulation period and use the look up graph. The fit to the data was accomplished with a 3$^{\textrm{rd}}$ order polynomial.
In order to get as much contrast as possible in the measurement it is important that both arms of the interferometer stay at equal amplitudes. This is difficult since the index of refraction of the material changes so drastically with the change in phase. We need the high contrast in the index in order to get the phase accumulation we are looking for, however it hurts us since the two distinct material phases will have very different reflectivities. To minimize this we attempted to find a thin film stack that would have as near a 2$\pi$ phase accumulation as possible, while keeping the change in reflectivity as constant as possible throughout the range of 0-100% crystallization. It was decided to use Silicon Dioxide (SiO$_2$) as the lower index material in our stack and limit the total device stack to 4 layers including an initial layer of tungsten as a reflective layer. The limit was put in place by the fact that we only want one active GST layer. Python was used to write a code that would cycle through a given array of thickness possibilities for the materials and find a good candidate for the stack.
A final stack was decided on to be 100 nm of tungsten, 130 nm of SiO$_2$, 205 nm of GST, and finally 285 nm of SiO$_2$. The phase accumulation and reflectivity as a function of crystallization percentage is shown in Fig. 6. This sample should have a phase accumulation of 2.96 radians and a highest change in reflectivity of 20.6%. While the measurement system is not limited to the phase it can measure (modulo $2\pi$), we chose a system that yields a phase close to $\pi$ for ease of fabrication and switching, in addition to its importance in binary phase modulators. Even as small of a change as 5 nm in any of the layers can have an effect as big as 5% in the reflectivity and 0.19 radians. Beyond the $\pm$5 nm point these numbers get drastically higher. This is a very tight range to hit with our nanofabrication capabilities here. The final stack that was fabricated was 96 nm of tungsten, 117 nm of SiO$_2$, 219 nm of GST, and 285 nm of SiO$_2$. A SEM image of the stack is shown in Fig. 7 along with the simulated data for those thicknesses. The simulations show that the stack should give us a phase accumulation of 2.32 radians and have a reflectivity drop of 19.6%. However, experimental results on the amplitude shift of the reflectivity tell a different story. Looking at a single pulse with peak power of 1.8 W, we can see a much more drastic reflectivity drop than what we expected. Figure 8 shows that with that single pulse there is a drop of $\sim$81%, which, while is not what we intended to fabricate, is well suited to demonstrate the power of the measurement technique. Moreover, due to the variety of proposed phase and amplitude modulators based on PCMs, it is crucial for a measurement to simultaneously detect phase and amplitude modulation while handling experimental imperfections that could lead to unexpected results.
Fig. 7. Reflectivity (a) and phase accumulation (b) as a function of crystallization percentage. c) SEM of fabricated stack.
In order to verify the simulation data the results from the code were compared to the results from OpenFilters [26], which is an open-source thin film solver. The results matched very well. That means that the indices that are being used in the simulation must not completely match the indices of the materials we grew. The remedy for this would be to grow blanket films of each of the materials we are using and characterize them separately. On the other hand, the positive side to this imperfection is that simulations show that with a higher change in reflectivity also comes a larger change in phase accumulation that validates the measurement for large phase shifts.
3. Measurement setup
The measurement setup relies on an interferometer with it’s arms coming from the probe signal before and after it reflects off the sample. By modulating the phase in the arm before the sample and recombining the two beams we can glean phase data from the sample. We use the same basic setup as seen in previous papers [20,27]. However, since this measurement requires a phase modulator and polarization control, the final portion of the setup gets relatively complex. A diagram of the setup can be seen in Fig. 9. From the split off before the sample, the light is coupled back into a fiber and passes through a polarization controller. This controller matches the polarization of the light to the phase modulator in order to achieve the highest signal possible. The light then passes through the phase modulator which modulates the phase from 0 to $\pi$ using a signal from a sinusoidal wave generator that is set to 100 MHz for this data and amplified by a high speed amplifier and combined with a DC voltage in order to get a 0 to 7V (V$_{\pi }$=7V for the modulator for 1590 nm light) sine wave sent to the modulator. The modulated signal is then sent into a 50-50 coupler where it combines with the arm from the sample which has passed through its own polarization controller in order to match the polarization for the largest amplitude modulation.
4. Experiment and results
For the experiment several different single pulse powers were used to switch the material and take the data. Here we will look at the 2.55W peak power pulse results. For this power three sets of data were analyzed. All three of them were analyzed using the amplitude method and one was able to be analyzed using the peak method. First a measure of the reflectivity change was needed so that the amplitude shift could be taken into account. The graph used to capture this data is shown in Fig. 8. It can be seen that the lower part of the graph is approximately 19% of the upper portion. This was used to scale the max possible amplitude of the data after the switch. The peak amplitudes were then scaled by a factor taken from the part of the graph that dips below the zero point in Fig. 8. In this instance that point was approximately -0.56 a.u. That number was divided by the average of the upper part of the graph before the change to obtain the scaling factor. Each peak was scaled by adding itself multiplied by the scaling factor. The average of all the peaks was then taken and multiplied by the 81% to find the max amplitude for the part of the data after the switch. The average of all the valleys was then subtracted from the average peak value giving the amplitude of data before the switch. The amplitude was divided by the max value to obtain a percentage that was then used to look up the two possible phase values from the look up graph in Fig. 3. Each of these data sets had "stalactites" in the pre-switch data, meaning the phase would be between 0 and $\pi$. An example of the difference between "stalactites" and "stalagmites" in the data can be seen in Fig. 10(a) and Fig. 10(b).
After the pre-switch data was analyzed the post-switch data was looked at. Again, several valley and peak amplitudes were taken. They were averaged together and subtracted from each other to get the amplitude for the post-switch data. This data did not need to be scaled since there isn’t danger of it falling below the zero point. The max amplitude for this section was found by multiplying the max amplitude from the pre-switch data by the 29% scaling factor. Since that data had "stalactites" it can be considered to be at the top of the possible amplitude range. The calculated amplitude of the post-switch data was then divided by this max amplitude for a percentage that could be looked up in the look up graph. This time the phase would be between $\pi$ and 2$\pi$ since there were "stalagmites" in the data.
The time position of peaks was then taken from before and after the switch and divided by the period, in this case $10^{-8}$ seconds. The remainders were compared from before and after the switch and for all the data sets they were equal. Looking at Table 3b it can be seen that since our data is flipped and "=", the phases must come from the same side of their respective positions. This means that if the first phase was from the 0 to $\dfrac {\pi }{2}$ range, the second phase must be from the $\pi$ to $\dfrac {3\pi }{2}$ range. If the first phase is from the $\dfrac {\pi }{2}$ to $\pi$ range, the second phase must be in the $\dfrac {3\pi }{2}$ to 2$\pi$ range. This gives us a limit on the possibilities of different phases available. The three sets of phases can be seen in Table 1. The phases came out relatively close considering that there is a noise level of approximately 6% of the max amplitude.
Table 1. Phases from amplitude method.
Finally, the peak method was attempted on the third set of data. A peak with a clear split was found on both the pre and post switch sides of the data. The time position for one of the sides of the peak was obtained and the difference was found to the center of the split peak as shown in Fig. 4b section 2. The difference was then divided by the period and the remainder was kept. The post-switch side had 0.5 added to it to account for the flip in the data. The lookup graph was then used to find the two possible phases for each side and the difference between them was found. The results are shown in the final rows of Table 1. They are not as close as the others, but still within reason for the noise and errors.
5. Discussion of application space
Our measurement was based on a multilayer stack of PCMs and dielectrics and metals, with the goal of demonstrating the phase measurement technique rather than a full device implementation. In particular, the film under study does present certain challenges [28] that make thermal/electrical switching prohibitive especially during re-amorphization. However, recently [20,29], we have shown that reversible optical switching of such thicknesses is possible under opto-thermal excitation and where the volume of the switched region and the excitation source wavelength are carefully considered.
Ultimately, however, as the technique is agnostic to the film/device under study apart from the desired operating wavelength (1550 nm) and response time ( ns speeds or slower) other systems for phase control could be readily studied. In fact, recently, several works have shown that even in a thin film that is on the order of less than 100 nm, it is entirely possible to achieve large phase shifts [30,31] by exploiting resonances in low-loss metasurface geometries. Additionally, in 2021, it was shown that a thin conductive transparent oxide (ITO) could be used as means toward independent phase and amplitude control of reflected light. Future experiments in a similar vein could greatly benefit from our measurement technique by enabling the measurement of the phase and amplitude response at the pixel level without necessitating a full device implementation.
6. Conclusion
In conclusion several different methods for measuring the phase accumulation during a switch of a phase change material were proposed. A setup was built and the experiment was done showing that these are viable measurement techniques. The setup was limited to a phase modulation of 0 to $\pi$ so only those measurement techniques could be verified, however, the others were shown to work using models for the full $0-2\pi$ measurement range. Moreover, the setup has shown the versatility needed to measure the phase in more complex scenarios in which the amplitude upon phase change is not constant, which bodes well for the system as means for single-shot high-speed phase measurement independent of the mechanism of phase accumulation. There are definitely ways to improve the measurement such as increasing the sampling rate, growing samples with flatter amplitude response, and increasing the modulation depth of the lithium niobate modulator to 2$\pi$. We believe that the measurement can be used not only to characterize PCM-based devices, but others based on alternative technologies that aim at high speed phase and amplitude modulation of light.
Funding
Ford Foundation Fellowship Program; Air Force Office of Scientific Research (FA9550-20RYCOR059); Defense Associated Graduate Student Innovators (DAGSI) (RY18-22); National Science Foundation (ECCS-236 1710273).
Acknowledgements
J.R.H. acknowledges support from the Air Force Office of Scientific Research (Program Manager Dr. Gernot Pomrenke) under Award No. FA9550-20RYCOR059. J.A.B. gratefully acknowledges financial support from the National Academies under the Ford Foundation Fellowship Program.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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