Lab 5 - Electro-Optic Modulation Goal To measure the characteristics of waveplates and electro-optic modulators Prelab Background Saleh and Tiech Section 1st edition 18.1-18.3 or 20.1-20.3 in second edition. The use of Jones matrices is assumed. This material is in Section 6.1 in both editions. Problems 1. Using Jones matrices for a λ/4 waveplate, a polarizer, and a mirror show that if the incident linear polarization to the λ/4 waveplate is oriented so that the output polarization is circular, then after reflection from the mirror and passing back through the λ/4 waveplate, the polarization state is again linear, but orthogonal to the incident polarization. 2. In designing an EO crystal to act as a half-wave plate, how thick should it be for λ = 0.632 µm, n 0 n e = 10 3? 3. A KD*P crystal has n 0 = 1.502 and γ 63 = 24.1 10 12 m/v (in the book γ = r). a) What is the axial ratio of the polarization ellipse resulting from 2500V being applied (longitudinally) across a 1mm thick crystal (see Fig.3 of notes)? Assume input polarization is linear and at 45 with respect to x, and λ = 0.5145 µm. b) What voltage would have to be applied across a second crystal in series with the first one to achieve counterclockwise circular polarization? 4. Optimal biasing of EO modulator. a) Illustrate and explain two configurations for achieving an approximately linear response between applied voltage and output light intensity using an E-O crystal. b) At the optimal point for linear operation, determine the total harmonic distortion for the harmonic input V in (t) = A cos(2πt) where A = πv /2V π. The total harmonic distortion is the fraction of the output lightwave power signal that is not contained in the fundamental. This output signal is I out (t) = cos 2 [A cos(2πt) π/4] 1 2 1
where the factor of 1/2 removes the DC bias. The distortion may be determined by numerically evaluating the first Fourier series coefficient of the output waveform and determining the fraction of the optical power contained in this component relative to the total power. The difference is the total harmonic distortion which is the fraction of the output power that is not in the fundamental. Plot the harmonic distortion as a function of A = πv /2V π over the range of 0.01 < A < 0.5. Lab Fiber-coupled Electro-optic modulator The setup for lab is shown in the figure below Laser Polarization controller EO Modulator Modulated Lightwave signal Optical Detector Scope/ function generator Bias voltage Figure 1: Set-up for EO Modulator For this experiment, we will start with a fiber-coupled lightwave source. The EO modulator requires a specific polarization state to produce the maximum extinction ratio between the minimum lightwave power P min and the maximum lightwave power P max. The polarization state is adjusted using a polarization rotator. One input to the EO modulator is the lightwave signal. The second input is an electrical signal that comes from a function generator that is integrated with the scope. The output of the EO modulator is then detected and displayed on the scope. The electrical signal in vs. lightwave power out is given by ( P out (V ) = P max sin 2 π V ) + φ. 2V π where φ is the intrinsic birefringence of the modulator with no applied voltage and P max is the peak power. Quick Measurement of V π 1. Set the voltage on the function generator to 2.5 V peak-to-peak and set the frequency to 15 MHz. Display the input signal on the scope. The laser should be set to 3 dbm. 2. The polarization rotator may not be aligned. Turn the rotator until you see an output signal on the scope. Now there should be two signals. 3. Change the bias voltage until you see an approximately double frequency signal. Record the voltage. Increase the voltage until you see it again. This difference is roughly V π 2
Optimization of the Polarization Rotator 1. Set the bias voltage half-way between the maximum value of the output and the minimum value of the output. This is the approximate value that produces linear modulation. 2. Adjust the polarization rotator to maximize the peak-to-peak signal at this point. 3. Now press down on the fiber that connects the laser to the EO modulator. What happens? Why? 4. Now starting at 0 V, increase the voltage in 0.5 V step up to 9V and record the peak-to-peak voltage. Accurate measurement of V π using doubled frequency 1. Set the aquisition mode to average and use a value of 128. Change the bias voltage until you see the frequency of the output sine wave to about double the frequency of the input sine. Now turn the FFT measurement feature of the scope. (Under the Math/operator menu.) Set it to the output channel and use a center frequency of 50 MHz and a span of 100 MHz and the time base to 50 ns/div. 2. You should see multiple harmonics in increments of 15 MHz. Adjust the bias voltage until the power in the 15 MHz frequency component is at a minimum. At the minimum the power in the fundamental should be at least 30 db less than the power in the second harmonic. You should see that this is extremely sensitive to the voltage. 3. Repeat for the other value of the bias voltage that produces a double frquency component. Determine V π and compare the value determined in this technique with the value determined using the set of voltage values. Harmonic Distortion 1. Reduce the voltage to 100 mv on the function generator. 2. Using the FFT feature determine the bias voltage that produces the minimum power in the other frequency components excluding the fundamental. Use the cursor functions to do this. 3. Now increase the voltage on the function generator in the following steps: 200 mv, 400 mv, 1 V, 2 V, 5 V. For each of these values, measure the total power in every frequency component other than the fundamental with respect to the fundamental. This is the total harmonic distortion. Note that you should not change the bias point. 3
Output Distorted output Bias point Ideal undistorted output Input Audio modulation 1. Connect the audio player s output to the oscilloscope and check the audio signal 2. Directly apply the signal to the EO modulator. 3. Observe modulation of laser beam on the oscilloscope. 4. Connect speaker to Analog output of the power meter to hear the signal carried by the laser beam. 5. Adjust the bias point to produce a frequency-doubled output. How does the sound compare to that when the bias point is at the optimal? Post Lab 1. Complete the Plot I out /I in vs. V and fit the data to ( I out = sin 2 π V ). I in 2V π Calculate the Contrast Ratio (the ratio of maximum to minimum output intensity). 2. For the measured value of V π, and using the results of the Prelab, determine the maximum voltage V max of an input sinusoidal function that will limit the harmonic distortion to 1%. 3. Assume that the input is a square-wave that has significant overshoot as shown in the figure below where the dashed lines represent a voltage swing of V π about the optimal bias point. 4
Qualitatively draw the output waveform for this input and discuss what happens. 5