Resonant Cavity Electro-optic Modulators and Active Compression

It has come to our attention that the ever increasing demands and requirements on lasers used in RF photoinjectors has exceeded much of the currently available technology. Ongoing research of beam dynamics in high gradient accelerators, including studies on ultra-high brightness beam transport and emittance evolution, compensation, and maintenance, have led to strict requirements on optical pulse characteristics. Amplitude stability, peak energy, timing jitter, and pulse length tailoring are just some of the parameters of interest. Presently, there are many sources of short optical pulses available commercially. Unfortunately, most of these sources do not provide low timing jitter or much flexibility in their output pulse width due to cost or technological limitations.

How It Works

In order to overcome the pulse width deficiency, many groups have relied on passive pulse compression using self-phase modulation in optical fibers. In general, compression is obtained by first creating a frequency sweep (linear chirp or quadratic phase modulation) across the optical pulse and then using a linear dispersive delay of the proper sign to compress the pulse (remove the chirp). In active compression, an electro-optic modulator (EOM) is used to create the frequency sweep instead of a fiber. The EOM works on the Pockels effect, which produces a change in the index of refraction that is linear in an applied external field. Therefore, if a sinusoidal field is applied along the material, there will be regions of no index change (nodes) and regions of maximum index change (cusps). It is the cusp regions that are of greatest interest, for if we apply a Taylor series expansion we find that the electric field variation near the maxima is quadratic. This leads to a quadratic change in the index. Thus, if the electric field is propagating within the material, as with a traveling RF field, then any optical pulse which is copropagating within a cusp will experience a quadratic phase change or linear frequency chirp. The amount of phase modulation is dependent on many factors including: strength of electric field (RF power), strength of electro-optic coefficient, and the total interaction length. Another important factor is the phase matching between the optical group velocity and the RF phase velocity. If these are not exactly matched then the optical pulse will exhibit "walkoff". In other words, the pulse will slip away from the RF cusp as they propagate through the media causing higher order phase modulation in the pulse.

Almost all commercial modulators are of a traveling wave design. Unfortunately, for our purposes, these do not offer a very efficient use of the microwave power. This can be avoided by using a microwave resonant structure, thus increasing the electric field strength for a given microwave input power. Although simple in principle, the design is a challenge due to the many constraints required for use as an optical phase modulator. In order to demonstrate a practical active pulse compressor we designed and fabricated a time lens based on a microwave resonant structure which would compress the pulses originating from our modelocked Nd:YAG laser (80 MHz rep. rate). A schematic diagram of the active compression system is shown in Figure 1. The basis of the initial RF resonator design was from the early work of Kaminow and is cast in the form of a partially loaded dielectric ridge waveguide. We chose lithium niobate, as the electro-optic crystal for several reasons. It has a large electro-optic coefficient, high optical transmission, low RF loss, good thermal conductivity, large RF and optical power limits, and it is readily available in reasonable sizes at reasonable costs. The RF drive frequency we used was 1.76 GHz. Many factors come into consideration when making this choice. First, it is a harmonic (22nd) of the laser's repetition rate. Second, the RF period is > 6 Tp where Tp is the laser pulse width, 85 ps (FWHM). This insured the phase modulation would be quadratic. Finally, the drive frequency in combination with the resonator and crystal geometry, determined how well the RF phase velocity was matched to the optical group velocity and was important in minimizing single pass walkoff.

Figure 1. Schematic diagram of the the basic active compression scheme showing the origin of the RF drive power and variability of the pulse width.

A diagram of the resonant phase modulator is shown in Figure 2. It is closed in on each end except for small apertures which give optical access to the crystal. The resonator supports a TE101 mode at the design frequency of 1.76 GHz and the crystal is 40 mm in length. The resonator design was fine tuned using Hewlett-Packard's High Frequency Structure Simulator (HFSS) program which uses finite element analysis to model electromagnetic fields in arbitrary geometries. This was necessary in order to account for the changes in resonant frequency due to the insertion of the coupling probe and tuning dielectric.

Figure 2. Partially loaded ridge waveguide resonator used as a electro-optic modulator. The resonant frequency is 1.76 GHz and the guided propagation constant (beta) is 78.539 /m. Note: the ends of the resonator are capped except for a hole in front of the crystal for optical access.

Single Knob Adjustable Pulse Compressor

If we have the capability of obtaining a large peak modulation index ( > 25), then it is possible to use active compression as a source of variable width picosecond pulses. Because the modulation index is dependent on the RF drive power, we can adjust the pulse width via a single knob, the RF power. A schematic diagram of how this might be done is shown in Fig. 1. A common reference frequency is necessary to phaselock the RF drive power and the pulses coming from the laser. The delay line is used to shift the phase of the RF so that the optical pulses enter the modulator under a cusp of the electric field.

Figure 3 demonstrates how the pulse characteristics will vary with changing RF power when a configuration similar to the one shown in Fig. 1 is used. In this instance, the dispersion has been optimized for the minimum pulse width at the maximum RF power, which produces a modulation index of 25 radians. The RF drive frequency is 1.76 GHz and the input pulse width is 85 ps. With no RF power, the pulse is broadened by the dispersion to 87 ps (although this is not visible in the plot). As the power is increased to 100% the pulse compresses to a minimum of 8.5 ps. This yields a compression ratio of ~10:1.

The pulses coming from the compressor will be chirped if the RF drive power is reduced from the optimum (highest compression). For many uses, such as RF photocathode illumination and photoconductive switches, residual chirp is not a concern. If the application requires transform limited pulses, then the dispersion must be adjusted for each setting of RF drive power.

Figure 3. Theoretical example showing how a variation in RF drive power effects the output pulse of an active compression system. For this case the modulation frequency is 1.76 GHz, Tp is 85 ps, and the modulation index is 25 radians at 100% RF power

Another way of viewing how the active pulse compressor operates as a variable pulse width source is shown in Fig. 4. The performance of the compressor can be optimized for a given value of modulation index by adjusting the dispersion to cancel the imparted chirp. The maximum compression ratio is shown by curve (e). Curves a-d are plots of the compression ratio for varying peak phase deviation (proportional to sqrt[RF Power]) and a fixed value of dispersion. Notice that the compression ratio in curves a-d increases steadily from modulation index=0 to the peak, but begins to decrease if you exceed the optimum compression point for a curve (i.e., increase modulation index beyond the optimum value of fixed dispersion). Also, the chirp of the pulse will change sign once the modulation index exceeds the optimum value.

Figure 4. Theoretical plot of pulse compression ratio showing the dependence on peak modulation index. Curves (a-d) represent the compression ratio as function of modulation index and fixed values of dispersion. Curve (e) is the optimum compression ratio for peak modulation index. The drive frequency is 1.76 GHz, and the input pulse width is 85 ps.

Future Investigation

The next logical step in pulse compression systems would be the design and implementation of a compound time lens system. This would allow very large compression ratios while keeping the demands on a single lens reasonable. For example, a compression system with a final compression ratio of 120:1 could be realized using a two stage compression scheme. The first stage giving a compression ratio of 12:1 and the second stage giving a compression ratio of 10:1. The peak phase deviation for each time lens is below 30 rad. To do this in a single stage at 1.76 GHz would require the lens to have 300 rad of peak phase deviation!

One of the drawbacks to a compound system is the possibly low throughput efficiency. The system discussed in this page had a system efficiency of 32%. If we assume about the same efficiency for both stages of a compound system, we obtain a total system efficiency of 10% and a 12:1 increase in peak power. Therefore, in the future it will be important to develop time lenses which operate at higher frequencies for use in the second stage and also improve the system efficiencies of each lens.

For additional information on active pulse compression, electro-optic time lenses, or temporal imaging in general, see the publications section or contact Ryan Scott