Angular Drift of CrystalTech 38 197 (164nm, 8MHz) AOMs due to Thermal Transients Alex Piggott July 5, 21 1
.1 General Overview of Findings The AOM was found to exhibit significant thermal drift effects, resulting in beam angle drifts on the order of.1.1mrad depending on the RF power. The thermal drift effects were found to be very repeatable, but they were partially obscured by noise due to pointing instability of the laser, air currents, and possibly the vibrations of optical components. The noise in the beam angle measurement could be drastically increased simply by blowing air in the path of the laser beam. Thus, all graphs (with the exception of graph 6.1, which shows the noise inherent in the beam angle) show the average of 4 samples. The general findings were as follows: 1) For on/off switching transients: Horizontal: exponential decay to steady state position, time constant of 2 3s,.5mrad angular drift at maximum RF power. Vertical: quickly points downwards, reaching minimum in 1 2s,.3mrad angular drift at maximum RF power. It then drifts upwards in an exponential decay, time constant of ~1s,.12mrad drift at maximum RF power. Note that the above applies to 1 st order diffracted beams only. The th order undiffracted beam also displays very similar behavior of the same scale. 2) Ramp transients (1s 2s ramps): Produces a time lagged ramp in angular displacement, nearly reaching the steady state angular drift for the 1s and 2s ramps. 3) Steady State Angle vs RF Power: The steady state RF power was proportional to the steady state angular position of the beam (with respect to the initial position), for both the 1 st order and th order beams. 4) Long Term Drift: Little long term drift was observed; the drift was orders of magnitude smaller than the initial transients..2 Sign Conventions for Angles The sign conventions for the horizontal (X) and vertical (Y) angles are as follows: X (Horizontal) Y (Vertical) + away from undiffracted ( th order) beam towards undiffracted ( th order) beam + down up Note that the angles are only relative measurements, rather than absolute measurements, due to the difficulty of determining the absolute angle. In addition, we were only interested in angular drift due to thermal affects; thus, only relative angles were important..3 Table of Contents Section Content Page 1 Experimental Setup and Method 3 2 Switching Transients (figures only) 7 3 Ramp Transients (figures only) 1 4 Steady state Angle vs. RF power (figures only) 11 5 Long term Drift 12 6 Errors and Noise 13 7 Effects on Fiber Coupling Efficiency 16 2
1. Experimental Setup The following optical setup was used to measure the pointing stability of the AOM: LEGEND Beam Dump SETUP Crystalaser (164nm) Cleanup polarization and reduce power Collimating Lenses (F=1. cm lenses, 22.5cm distance) Lens focuses beam onto photodiode (F = 6. cm) Quadrant Photodiode Photodiode for intensity feedback NOTE: The setup above is for measuring the 1 st order diffracted beam. When measuring the th order beam, the beamdump position and the angling of the mirrors after the AOM was slightly different in order to direct the th order beam into the quadrant photodiode instead. Important Parameters: Beam Diameter at AOM (1/e 2 ): 165 ± 4 μm AOM Efficiency at Max RF Power: 88.6% efficiency Beam Diameter at Quadrant Photodiode (1/e 2 ): 697 ± 82 μm (vertical), 579 ± 76 μm (horizontal) Path length to Quadrant Photodiode: 49.5cm (1 st order beam), 397.5cm ( th order beam) 3
The following electronics setup was used to power the AOM and measure the beam angle and RF power: HP 3325A Function Generator Synchronization Output/ Trigger or AOM Laser Power Stabilization (ALPS) Servo ~.1 Hz Photodiode for feedback Quadrant Photodiode 18AF AIFO 2. 8 MHz AOM Driver Coupler 8 MHz ADS8362 RF to DC Converter PDS522S OWON Oscilloscope AOM The AOM was powered by an 8MHz AOM driver; the RF power was monitored using a 3dB coupler and a logarithmic RF amplitude detector (AD8362). The RF power was modulated by the output of the ALPS servo, which used feedback via the photodiode to precisely control the laser intensity. The function generator coordinated the entire experiment, commanding the laser intensity and triggering the oscilloscope. All measurements were taken by the oscilloscope. Due to a lack of channels, not all instruments could be connected at the same time. 1.1 Beam Position Calculations The quadrant photodiode consists of a large silicon sensor subdivided into 4 quadrants: Figure 1.1: Quadrant photodiode subdivisions (from PDQ8A datasheet) The quadrant photodiode has 3 outputs: the X difference signal ( ), Y difference signal ( ), and the sum signal ( ), which are given by: 4
To calculate the position of the beam using these quadrant photodiode signal, several assumptions were made: 1) It was assumed that the beam had an elliptical Gaussian intensity profile, i.e: Where:, = Intensity = x position = y position = horizontal radius = vertical radius, Justification: When the diffracted beam s profile was measured using the razor blade technique, it was found to match this profile very well. 2) The quadrant photodiode signals were directly proportional to the incident power. Justification: when a photodiode is used in the photoconductive mode (such as in the PDQ8A quadrant photodiode), the photocurrent is linearly proportional to the incident power. 3) The quadrant photodiode was infinite large (no beam walkoff from sensor), i.e: Where: = some constant = sum signal from quadrant photodiode, Justification: The quadrant photodiode diameter (7.8mm) was slightly larger than the 1/e 2 diameter of the beam (~6 7mm). In addition, the laser beams were always centered as well as possible on the quadrant photodiode when taking measurements. 4) The gaps between the quadrants of the quadrant photodiode sensor were infinitely narrow, i.e:, Where: = horizontal displacement = X difference signal from quadrant photodiode,,, Where: = vertical displacement = Y difference signal from quadrant photodiode Justification: The gaps between the quadrants of the photodiode sensor (.1mm) were much smaller than the 1/e 2 diameter of the beam (~6 7mm). 5
Given these assumptions, the following results for the horizontal and vertical displacement of the beam can be derived: 6
2. AOM Switching Transients.6.5.4 1.27 W.79 W.45 W.24 W.1 W.3.2.1.1 1 2 3 4 5 Figure 2.1: Horizontal angle of 1 st order diffracted beam after AOM is switched on @ T = 5s, for several RF powers..4.2.2.4 1.27 W.79 W.45 W.24 W.1 W.6.8 1 2 3 4 5 Figure 2.2: Vertical angle of 1 st order diffracted beam after AOM is switched on @ T = 5s, for several RF powers. 7
.3.25.2.15.1.5. 1.27 W.69 W.41 W.17 W.5.1.15 1 2 3 4 5 Figure 2.3: Horizontal angle of th order undiffracted beam after AOM is switched on @ T = 5s for several RF powers..6.4.2.2.4.6 1.27 W.69 W.41 W.17 W.8.1.12 1 2 3 4 5 Figure 2.4: Vertical angle of th order undiffracted beam after AOM is switched on @ T = 5s for several RF powers. 8
.45.4.35.3.25.2.15.1 1.27 W.69 W.41 W.17 W.5.5 1 2 3 4 5 Figure 2.5: Horizontal angle of th order undiffracted beam after AOM is switched off @ T = 5s for several RF powers..2.2.4.6.8 1.27 W.41 W.69 W.17 W.1.12.14 1 2 3 4 5 Figure 2.5: Vertical angle of th order undiffracted beam after AOM is switched off @ T = 5s for several RF powers. 9
3. Ramp Transients 35 3 25 2 s 1 s 5 s 1 s.5.4.3 Laser Intensity (mv) 2 15 1.2.1.1 5.2 5 1 15 2 25 3 35 Figure 3.1: Horizontal angle of 1 st order diffracted beam for 1s, 5s, 1s, and 2s ramps. NOTE: Black lines are for laser intensity; coloured lines are beam angles..3 35 3 2 s 1 s 5 s 1 s.5.4 25.3 Laser Intensity (mv) 2 15 1.2.1.1 5.2.3 5 1 15 2 25 3 35 Figure 3.2: Vertical angle of 1 st order diffracted beam for 1s, 5s, 1s, and 2s ramps. 1
4. Steady state Angle vs. RF power.6.4.2.2.4 Horizontal Vertical.6.8.2.4.6.8 1 1.2 1.4 RF Power (W) Figure 4.1: The steady state angular deflection of the 1 st order diffracted beam with respect to RF power. Both the horizontal and vertical angular deflections are shown (note that the beam angles are all relative). The angular deflection of the beam appears to be very linear with respect to power. Note that zero degrees corresponds to the initial beam angle..4.2.2.4.6 Horizontal Vertical.8.1.12.2.4.6.8 1 1.2 1.4 RF Power (W) Figure 4.2: The steady state angular deflection of the th order undiffracted beam with respect to RF power. Both the horizontal and vertical angular deflections are shown (note that the beam angles are all relative). The angular deflection of the beam appears to be very linear with respect to power. It is interesting to note that the change in beam angle for different RF powers is on the same order of magnitude for both the 1 st order and th order beams. 11
5. Long Term Drift After the AOM stabilized in the first few seconds, little long term angular drift was observed:.6.4.2.2.4 Vertical Horizontal.6.8 5 1 15 2 25 3 35 4 45 5 Figure 5.1: Horizontal and vertical beam angle of 1 st order diffracted beam after the AOM is switched on at T = s. The long term angular drift of the AOM appears to be small compared with the initial thermal drift. 12
6. Errors and Noise Three major concerns will be addressed in the following sections: 1) Were the observed changes in beam position at the photodiode due to a change in beam angle or beam displacement at the AOM? 2) Did the on/off switching speed of the AOM affect our beam position calculations? 3) Significant beam position noise was observed. 1) Angle vs Displacement The change in beam position observed at the quadrant photodiode was originally assumed to be a change in beam angle; however, it was also possible that the beam was experiencing a displacement instead. To isolate these effects, the same switching transient was measured using the quadrant photodiode at 2 distances from the AOM output aperture..6 3.5 25.4.3.2.1 2 15 1 5 Beam Displacement (μm).1.2 Angle Displacement 1 2 3 4 5 Figure 6.1: Horizontal beam angle and displacement of 1 st order diffracted beam after AOM is switched on @ T = 5s, with 1.27W of RF power. The quadrant photodiode was placed at two locations to calculate the beam angle and displacement: 49.5cm and 122cm away from the AOM output aperture. 5 1.4 2.2 1.2.4.6 1 2 3 Beam Displacement (μm) Figure 6.2: Vertical beam angle and displacement of 1 st order diffracted beam after AOM is switched on @ T = 5s, with 1.27W of RF power. The quadrant photodiode was placed at two locations to calculate the beam angle and displacement: 49.5cm and 122cm away from the AOM output aperture 13.8.1 Angle Displacement 1 2 3 4 5 4 5
From figures 6.1 and 6.2, the beam displacement appears to be relatively small compared with the beam angle changes, especially at extended ranges from the AOM (> 1m). It is important to note that the beam displacement calculations are not very precise, since they depend on the precise subtraction of beam positions measured at two different locations. Any small error in the beam position measured at the quadrant photodiodes, for example due to inaccurate beam size measurements, would result in a significant under or over estimation of the beam displacement. 2) On/off switching speed Due to a lack of oscilloscope channels, only the X and Y signals from the quadrant photodiode were recorded during the switching transient measurements, and it was assumed the SUM signal was constant. Since the power of the diffracted beam reaches steady state extremely quickly in <6μs (see next figure), it appears to have been a valid assumption. 4 35 35 3 3 Sum Output (mv) 25 2 15 1 5 5 Sum Output Photodiode Output 2 4 6 8 1 12 14 16 18 2 Time (μs) 25 2 15 1 5 Photodiode Output (mv) Figure 6.3: 1 st order diffracted beam power as measured by the quadrant photodiode (Sum output) and the feedback photodiode (photodiode output) after the AOM is switched on @ T = 3μs. It can be clearly seen that the laser intensity stabilizes extremely quickly and does not influence our beam angle calculations. 14
3) Noise Significant noise was observed in the position of the beam. The following is a plot of two raw samples of the angular position of the beam, for.98w and.26w. The RF power was switched on 2s before taking measurements, to eliminate transient thermal effects:.12.1.8 Horizontal.98W Horizontal.26W Vertical.98W Vertical.26W.6.4.2.2.4.6 Figure 6.4: Long term position noise of the beam angle for the diffracted beam. The noise appears to be more or less independent of axis (the vertical and horizontal noise is fairly similar) and RF power (the.98w and.26w measurements recorded roughly the same position noise). No high frequency noise was observed the fastest noise was on the scale of.5s. Thus, significant external electronic interference was unlikely. The quadrant photodiode itself was not the source of this noise. When an LED, a diffuse light source, was used as a light source instead, it was not possible to measure any noise in the X, Y and SUM outputs of the quadrant photodiode, even using the Tektronix TDS12 oscilloscope on the 2mV/DIV setting. Laser intensity variations could not have been responsible for this noise either, due to the ALPS servo which controlled the intensity of the diffracted beam. The intensity of the diffracted beam, when measured using the quadrant photodiode SUM output and the feedback photodiode output, was found to be highly stable. Thus, this noise must have been due to position changes in the beam at the quadrant photodiode. The noise also appeared to be independent of AOM RF power, as seen in figure 6.4, and was thus probably independent of the AOM. Air currents are a likely cause for this position noise. It was found that slightly disturbing the setup, such as by blowing air in the path of the laser beam, or even walking near the setup, significantly increased the noise. Turning off the HEPA fan was also found to significantly reduce noise. Another likely source of noise is the pointing instability of the laser itself. The CrystaLaser has a pointing stability of only.5mrad according to its specifications. I independently verified the angular stability of the Crystalaser using the quadrant photodiode, and measured.43mrad angular noise over a period of 2s, which matches the specifications well. However, several lenses are between the CrystaLaser and the AOM, somewhat reducing the pointing instability noise from the Crystalaser. Thus, the noise in the measurements were probably largely due to air currents and the pointing instability of the laser. To isolate the thermal drift data from this noise, 4 samples were averaged for each measurement. 15.8.1 5 1 15 2 25 3 35 4 45 5
7. Effects on Fiber Coupling Efficiency Coupling a laser from free space into a single mode fiber optic cable is highly dependent on the angle and location of the beam. If the diffracted beam from an AOM is coupled into a fiber, changes in beam angle and position due to thermal drift effects in the AOM may result in drastically reduced efficiency. 7.1 Calculating Fiber Coupling Efficiency The following typical setup was analyzed (same symbols as diagram on page 3): Incident beam th order beam Single mode 164nm PM Fiber NA =.11.15 1 st order beam Aspheric Lens Thorlabs C26TM C (F = 15.29mm,.16NA) To calculate the fiber coupling efficiency, the following assumptions were made: 1) The beam from the AOM is collimated, and has the same beam width as a beam coupled out of the fiber (i.e. it has the optimal beamwidth). 2) The change in beam angle at the aspheric lens is insignificant only the displacement of the beam is considered. 3) The efficiency of coupling is proportional to the convolution of a beam coupled out of the fiber, and the beam from the AOM, at the surface of the aspheric lens, i.e:,, Where: = horizontal axis parallel to surface of aspheric lens = vertical axis parallel to surface of aspheric lens, = intensity of beam from AOM, at surface of aspheric lens, = intensity of beam coupled out of fiber, at surface of aspheric lens 7.1 Fiber Coupling Efficiency Results The efficiency of fiber coupling for a given AOM RF power was calculated by assuming that the beam was perfectly aligned with the fiber when the AOM was first turned on. The steady state AOM diffraction angle of the beam for the given RF power was then used to calculate the drop in coupling efficiency. Typical 164nm single mode polarization maintaining fibers from Thorlabs have a NA of.11.15. The effects of beam misalignment are greater for fibers with a smaller numerical aperture. To give an idea of the range of possible fiber coupling efficiency losses due to the AOM, fiber coupling efficiencies were computed for fibers with an NA of.11 and.15 for a range of RF powers. The graphs are shown on the following page. 16
1.5 1. Fiber Coupling Efficiency.95.9.85.8 1.27W.79W.45W.24W.1W 2 4 6 8 1 Distance from AOM (m) Figure 7.1: Relative coupling efficiencies at different RF powers, for a NA =.11 single mode fiber and a 15.29mm aspheric lens. Note that the AOM thermal drift effects result in a very small change in coupling efficiency for lower RF powers, and for distances <2m from the AOM. 1.5 1. Fiber Coupling Efficiency.95.9.85.8 1.27W.79W.45W.24W.1W 2 4 6 8 1 Distance from AOM (m) Figure 7.2: Relative coupling efficiencies at different RF powers, for a NA =.15 single mode fiber and a 15.29mm aspheric lens. Note that the AOM thermal drift effects result in a very small change in coupling efficiency for lower RF powers, and for distances <2m from the AOM. 17