Thorlabs’ Lab Facts are dedicated to providing additional information and useful tips for using select products or products lines that are generated by our Applications and Design Engineers through rigorous laboratory testing and analysis. This Electro-Optic (EO) Modulator Lab Fact explains how to extend the functional wavelength range of Thorlabs’ HVA200 High Voltage Amplifier when used with our free-space EO Amplitude Modulator. For the free-space EO Modulator product page, please click here.

Click to Enlarge
Figure 1: The Half-Wave Voltage (V_pi) Dependency on Wavelength

Click to Enlarge
Figure 2: Electro-Optic Phase Modulator

Click to Enlarge
Figure 3: Electro-Optic Amplitude Modulator

Thorlabs' free-space electro-optic (EO) amplitude and phase lithium niobate modulators use MgO-doped lithium niobate for high power operation. We offer both broadband DC-coupled and high Q resonant models, as well as a high voltage amplifier that is compatible with all our models. Electro-Optic Modulators (EOMs) are able to provide control over the phase or intensity of propagating radiation and have found many applications for engineering and science purposes, including Q-switching, mode locking of lasers, generation of optical pulses, and side-band generation, just to name a few. They do so by utilizing the Pockels effect, a linear electro-optic phenomenon that produces a change in the index of refraction within a crystal proportional to an applied electric field. Thus by applying a modulating signal, V(t), one can influence the phase or amplitude of a laser beam (or other propagating optical radiation).

Free-space EO modulators are high voltage devices, typically requiring 100’s of volts for normal operation. The HVA200 has been designed to function with Thorlabs’ EOMs. It features a ±200 V output, a continuous current output of 100 mA, a 1 MHz bandwidth, and low noise. Additionally, an adjustable voltage bias allows for precise DC offset control. However, the half-wave voltage (V_pi) needed for proper modulation scales with wavelength (see Figure 1). Due to this dependency, the effective wavelength range for any high voltage amplifier, such as the HVA200, can quickly become limited at higher wavelengths.

In this Lab Fact, we will demonstrate how to extend the functional wavelength range of the HVA200 for amplitude modulation by using a quarter-wave plate before the modulator input. We present laboratory measurements for maximizing the operating voltage range for driving Thorlabs’ Free-Space Electro-Optic (EO) Amplitude Modulators. The figure at the top shows the experimental setup used for this investigation with the major components called out and listed in the table below the image. For this system, the modulating signal is applied normal to the propagation of the beam, in the transverse geometry. For the context of this Lab Fact, this will be along the Z-axis (see Figures 2 & 3), and we will call this crystal orientation the Z-cut crystal axis. This orientation prevents the electrodes from occluding the clear aperture of the crystal. Additionally, in this geometry, the overall retardation induced in the beam is proportional to the product of the applied field and crystal length (thus longer crystals will produce larger retardations).

Click to Enlarge
Figure 4: Phase Modulator Output as a Function of Applied Voltage (Listed in Terms of V_pi), X's Correspond to the Phase Shifts Listed in the Table Above the Graph

Click to Enlarge
Figure 5: Amplitude Modulator with DC Offset Output as a Function of V_pi, X's Correspond to the Resultant Polarizations Listed in the Table Above the Graph

Phase Modulation
A phase modulator induces a phase shift to the transmitted laser beam without changing the output polarization. In this configuration, the applied voltage creates a change in the optical path through the crystal. It’s this change which creates the phase shift in the output. For phase modulation, the input polarization of the beam is aligned parallel with the Z-axis of the crystal (parallel to the applied voltage). Figure 4 shows the phase shift as a function of the applied voltage, which is a linear response. The applied voltage is listed in terms of V_pi (the X's correspond to the values listed in the table above the graph). V_pi is called the half-wave voltage and is defined as the voltage required to shift the output phase by π radians.

Phase modulators are particularly useful for the generation of frequency side bands on a laser source. Applying an AC voltage, typically a sine wave, to the phase modulator produces a time-dependent phase shift. This creates frequency side bands about the center frequency of the laser given by, f = f_L ± n × f_M; the side band frequency is given by f, f_L is the frequency of the laser, f_M is the modulation frequency, and n = 1, 2, 3…. Unlike Acousto-Optic Modulators (AOMs), EOMs do not produce spatial deflections of the frequency modulated components, making them very useful in applications requiring multiple frequency components within the laser spectrum, such as Raman side-band cooling or quantum optics. Additionally, they can be used in laser stabilization techniques such as the Pound-Drever-Hall lock. 

Amplitude Modulation
An amplitude modulator induces a change in the output polarization of the laser beam; when coupled with an output polarizer, the result is a modulation in the intensity of the output beam. For amplitude modulation the input polarization is set to be 45° to the Z-axis. For ease of use, all of Thorlabs’ EO Modulators have an internal crystal orientation that utilizes vertically polarized light (with respect to the mounting base). Figure 5 shows the output polarization and the output amplitude after the polarizer, demonstrating the sinusoidal modulation of the light. The applied voltage is listed in terms of V_pi (the X's correspond to the values listed in the table above the graph). This is shown over a peak-to-peak modulation range of 2V_pi; however, for proper modulation, a peak-to-peak voltage of V_pi is required, along with a bias voltage of V_pi/2 in order to ensure distortion-free, full-depth modulation. 

Amplitude modulators provide a method to very quickly control the output intensity of a laser source without having to modulate the source directly. In this way, an amplitude modulator can be used for intensity stabilization of a source or even simulating an optical chopper. Applying an AC voltage, typically a sine or triangle wave modulation, to the amplitude modulator, a time-dependent intensity output is produced. This form of modulation can be particularly useful in Q-switching in lasers or for intensity-dependent applications such as stimulated Raman scattering.

Figure 7: An EO Amplitude Modulator Mounted on a PY005 Five-Axis Platform

Click to Enlarge
Figure 6: Electro-Optic Amplitude Modulator with Quarter-Wave Plate at Input

Our experiments focused on obtaining the largest operating voltage range (thus the largest operating wavelength range) for our EO modulators using the HVA200 High Voltage Amplifier. To do so we used either the previous-generation HRS015 Stabilized HeNe Laser (633 nm, replaced by the HRS015B) or LP980-SF15 Pigtailed (980 nm) Laser as the light source. A linear polarizer (LPNIR100 or previous-generation LPVISB100) was used to set the polarization axis normal to the table surface. A second linear polarizer at the output of the modulator was aligned parallel to the first. We used a function generator to create a 100 kHz triangle wave, amplified by the HVA200; the amplified signal was used as the modulating signal. An EO Amplitude Modulator (EO-AM-NR-C1) was chosen to examine the effects of the modulating signal. Experiments were run with and without a quarter-wave plate (WPMQ05M-633 or WPMQ05M-980) in order to demonstrate the use of the full voltage range of the HVA200 (see Figures 6 and 3, respectively).

An EO amplitude modulator is driven by either a sine or triangle waveform in order to produce a sinusoidal modulation of the output intensity (it should be noted that resonant EO modulators require sine wave modulation). The output intensity is given in the equation below.

Here, I_o is the output intensity, I_i is the input intensity, V is the applied voltage, and V_pi is the half-wave voltage. We can see from this equation that an applied modulation voltage will produce a nearly sinusoidal modulation of the output intensity.

For an amplitude modulator like the one shown in Figure 3, the amplitude of this modulation needs to be 0 V to V_pi (or -V_pi to 0 V) for full modulation. Typically the modulation signal will require a bias voltage of V_pi/2 to ensure distortion-free, full-depth modulation. Figure 5 explains why; in order to capture both a maximum and minimum, the modulator must pass through 0 V and either +V_pi or -V_pi. Thus, for proper modulation, an accurate measure of V_pi is essential. The most common method of measuring V_pi is to overmodulate the device (apply a peak-to-peak voltage greater than V_pi) and measure the optical modulation and applied voltage on an oscilloscope. V_pi will then be defined as the voltage between the maximum and minimum optical modulation. For the EO-AM-NR-C1 modulator, we measured V_pi to be 220 V at 633 nm and 368.8 V at 980 nm (V_pi increases linearly with wavelength).

Results at 633 nm
Using the HVA200, it is not possible to fully modulate the output signal at this wavelength using the typical recommended alignment, since its absolute maximum output is 200 V (V_pi = 220 V at this wavelength). Attempting to fully modulate a laser beam in such a system will result in either distortions to the modulated optical signal caused by saturation of the drive voltage (from trying to drive the HVA200 past its output limits) or incomplete modulation (not fully attenuating or transmitting) from underdriving the EOM. Figure 8 shows the results of just such an attempt and clearly demonstrates distortions in the output signal caused by the saturation of the HVA200.

One solution to this limitation is to put a quarter-wave plate in front of the modulator to input circularly polarized light into the EOM (as shown in Figure 6). Doing so creates a form of optical bias, shifting the output polarization of the device and thus bringing the location of the maximum and minimum transmission to within the operational range of the amplifier. Figure 9 shows the output polarization along with the amplitude after the polarizer for a quarter-wave plate-balanced amplitude modulator. Here we see that to capture both maxima and minima, a drive voltage range of -1/2 V_pi to 1/2 V_pi is needed. For our setup, that corresponds to -110 V to 110 V, well within the range of the HVA200.

Using the quarter-wave plate (QWP) technique, we repeated the experiment above. This time, we found that we could properly modulate the laser’s intensity as shown in figure 8.

Click to Enlarge
Figure 8: Modulation Response with DC Offset at 633 nm

Click to Enlarge
Figure 9: Amplitude Modulator with Quarter-Wave Plate Output as a Function of V_pi

Click to Enlarge
Figure 10: Modulation Response with Quarter-Wave Plate at 633 nm

Results at 980 nm
To test the upper limit of the functional wavelength range for the HVA200 using the QWP technique, we repeated the above tests using a 980 nm laser source. Figure 11 shows the result of the overmodulation test used to determine V_pi at 980 nm; from this, we measured V_pi to be 368.8 V. This should fall within the capabilities of the HVA200 using the QWP technique. Figure 12 demonstrates just this, having used the HVA200 to produce smooth, sinusoidal modulation of the 980 nm laser.

Click to Enlarge
Figure 11: Measuring V_pi by overmodulating the output signal and recording the HVA200 voltages for the minimum and maximum optical signals.

Click to Enlarge
Figure 12: Modulation Response with Quarter-Wave Plate at 980 nm

We have demonstrated full modulation depth at 633 nm and 980 nm using Thorlabs’ EO-AM-NR-C1 and HVA200. The quarter-wave plate technique functionally doubles the operating range of the amplifier. With this technique, the HVA200, which could not modulate properly at 633 nm using the standard alignment, can be used to drive the EO-AM-NR-C1 across its entire operating range and drive the EO-AM-NR-C2 up to 1000 nm. This is particularly advantageous for financial reasons, as the price of amplifiers rises dramatically with the maximum voltage output. For details on the experimental setup employed and the results obtained, please click here.

From the measurements of V_pi at 633 nm and 980 nm, it was determined that we could, theoretically, obtain full depth of modulation out to 1064 nm (noting that the half-wave voltage scales linearly with wavelength). However, as we approach the limit of the HVA200 voltage range, it becomes increasingly difficult to resolve overmodulation and obtain an accurate measure of V_pi. 

There are additional techniques that could be used to lower V_pi for a modulator. While beyond the scope of this Lab Fact, the alignment of a beam through a modulator can influence the half-wave voltage. For instance, the standard alignment procedures for these EO Modulators include aligning the beam to have normal incidence upon the crystal. This ensures that an appropriately sized beam passes through the input and output apertures without clipping. However, deviation of tip/tilt from normal incidence can increase the optical path length through the crystal, effectively reducing V_pi.

Finally, this Lab Fact focused on using the HVA200 with our free-space modulators; in doing so we experimentally verified operation up to 980 nm. Additionally, our fiber-coupled modulators are designed with significantly lower half-wave voltages (as low as several volts) and typically operate from 1525 nm to 1605 nm.

Click to Enlarge
Figure 14: Quarter-Wave Plate Method for Producing Sinusoidal Amplitude Modulation

Click to Enlarge
Figure 13: DC Bias Method for Producing Sinusoidal Amplitude Modulation