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The conversion of frequency modulation to amplitude modulation (FM-to-AM) effect is harmful to the high power laser facility based on the phase modulation technique. The FM-to-AM effect of phase modulation pulse induced by the weak etalon effect in wave plates was investigated theoretically and experimentally. A bulk phase modulator with a modulation frequency of 9.2GHz was employed. The numerical simulation results show that the FM-to-AM effect with a temporal modulation depth of 2.5% and 29.7% on the top of the pulse shape was induced by the weak etalon effect in half-wave plate with thickness of 1mm and residual reflectance ratio of 0.5% for 1 pass and 12 passes respectively. On the same condition, the temporal modulation depth is 3.0% and 23.4% respectively in the experiment. The results are in good agreement with numerical simulation results. To our knowledge, it is the first time to introduce the weak etalon effect in wave plates for a complex phase modulation laser system.
©2010 Optical Society of America
1. Introduction
The high power laser facility for inertial confinement fusion(ICF) [1–3] requires broadband optical pulse to suppress buildup of Stimulated Brioullin Scattering(SBS) in large aperture laser optics and smooth the speckle pattern illuminating the target by Spectral Smoothing Dispersion (SSD) [4,5].There are many ways to impose bandwidth at the optical pulse generating system of the facility, such as chirped pulse, chirped pulse stacking [6], the Super radiation Laser Diode(SLD) based on Electric-Optic modulation technique, and phase modulation technique [7]. It is difficult to broaden the chirped pulse to a long pulse duration of several nanoseconds. For the stacked chirped pulse and the pulse based on SLD, temporal modulation would appear on top of pulse shape when the pulse transmits and is amplified in laser facility. Compared with these ways, the phase modulation technique is a widespread and practical method to impose bandwidth for the facility. Both National Ignition Facility (NIF) in America [4,8] and Laser Me’ga-Joule (LMJ) laser facility in France [9,10] have been employed phase modulattion technique in their optical pulse generating system. Ideally, imposition of bandwidth by pure phase modulation does not affect the pulse quality, but as a large number of effects, the FM converts to the AM. The FM-to-AM effect of the phase modulation pulse would seriously affect the performance of the high power laser facility in the main amplifier and frequency conversion system. Many effects may contribute to FM-to-AM modulations, such as group velocity dispersion, polarization and gain narrow in the fiber laser system. The common basis for all these effects is non-uniform spectral transmission.
So far, many contributions have been focused on the FM-to-AM effect in fiber laser system and the whole laser facility [5,11], but it was not clearly stated why and how the FM-to-AM effect happened in the complex solid-state laser system. In this letter, we theoretically and experimentally investigate weak etalon effect in wave plates for the complex solid-state laser system based on the phase modulation technique, the results indicate that the weak etalon effect in wave plates caused distortion of the phase modulation spectrum, therefore, it induced the FM-to-AM effect.
2. Theoretical analysis of weak etalon effect in wave plates
Wave plates can be divided into zero order wave plates and high order wave plates. For high order wave plates, the thickness is about several millimeters and the bandwidth of spectral transmission curve is mostly narrow. Zero order wave plates are too thin to use them independently. Generally, zero order wave plates are glued with BK7 glass, and they are called real zero order wave plates. Sometimes, the two high order wave plates whose optical axes are perpendicular are glued together, and the phase delay of the one high order wave plate is counteracted with the other. This is called the zero order wave plate. So the thickness of the wave plate applied in the complex solid-state laser system is several millimeters.
When the wave plate with certain thickness and residual reflectivity is used in the solid-state laser system, the weak etalon effect would happen. And then the spectral transmission curve can be expressed as:
for Eq. (1), F is denoted as finesse coefficient and δ is phase difference. In the Eqs. (2) and (3), R is the arithmetic product of residual reflectivity of the two wave plate surface,d is the thickness of the wave plate, λ is the center wavelength and n is the refractivity of the wave plate.When the phase modulation pulse transmits through k wave plates, each spectral transmission curve is T1,T2,……Tk, the total spectral transmission Tt can be expressed as:
if the pulse transmits through 12 same wave plates, each spectral transmission T is equal, so Tt is the twelfth power of T.The weak etalon effect in the wave plates and the transmission characteristics of phase modulation pulse transmitted through half-wave plate are numerically simulated. The thickness of the wave plate is 1mm, residual reflectivity is 0.5% and refractivity is 1.45. Figure 1 shows the phase modulation pulse shape and spectrum with a modulation frequency of 9.2GHz and those transmitted through a wave plate. Due to the weak etalon effect, there is periodical temporal modulation that could be calculated as shown in the reference [12] on top of pulse shape, and the temporal modulation depth is about 2.5% (see Fig. 1(a)). Figure 1(b) shows the spectral transmission curve of etalon effect in a wave plate, the initial spectrum of the phase modulation pulse and also the spectrum of the pulse transmitted through half-wave plate. The results show that there is slight difference between the initial spectrum and the spectrum undergone the weak etalon effect of a wave plate, It is the reason why the periodical temporal modulation on top of pulse shape occurred. But a severe spectrum distortion happened while the phase modulation pulse transmits through half-wave plate with the thickness of 1mm and residual reflectivity of 0.5% 12 passes, and the modulation depth of 29.7% is induced(shown in Fig. 2 ).
Fig. 1 The phase modulation pulse shape and spectrum before and after them transmitted through a wave plate (a) Injected pulse shape(black-line) and output pulse shape(red-line) (b) Injected pulse spectrum(black-line, the data were shifted 5 pm to compare with the output spectrum),output pulse spectrum(blue-line) and the spectral transmission curve of the weak etalon effect for 1 wave plate(red line).
Fig. 2 The phase modulation pulse shape and spectrum before and after them transmitted through a wave plate for 12 passes (a) Injected pulse shape(black-line) and output pulse shape(red-line) (b)Injected pulse spectrum(black-line, the data were shifted 5 pm to compare with the output spectrum),output pulse spectrum(blue-line) and the spectral transmission curve of the weak etalon effect in 12 wave plates(red line).
3. Experiment results and discussions
The FM-to-AM effect induced by the weak etalon effect in wave plates for phase modulation pulse are studied experimentally. The experiment scheme is shown in Fig. 3 .A seed pulse with peak power of 350W, pulse duration of 3 ns and repetition rate of 1Hz is supplied by a single-frequency fiber laser system. The output pulse goes into a bulk phase modulator that sets the bandwidth of the laser pulse. In this modulator the pulse is phase modulated at a frequency of 9.2 GHz to a total bandwidth of 90 GHz in order to suppress Stimulated Brillouin Scattering (SBS) in the large aperture laser optics.
The output phase modulation pulse shape is showed in Fig. 4 . There is no temporal modulation on top of the pulse shape. But when the pulse transmits through half-wave plate with thickness of 1mm, residual reflectivity of 0.5 and refractivity of 1.45, the periodical temporal modulation appears. The modulation period is about 108ps and modulation depth is about 3%, which are measured by a high resolution oscilloscope. The experiment results are in good agreement with the numerical simulation results.
The phase modulation pulse is injected into a multipass amplification laser system, in which a half-wave plate and faraday are used to realize the cavity. The pulse runs five passes in the cavity, and then two times passes through a wave plate out of the cavity, so the pulse passes 12 wave plates in total. The experiment schematic diagram is shown in Fig. 6 . We measured the output phase modulation pulse shape, which is shown in Fig. 7 .Because of cumulative weak etalon effect of 12 wave plates, the temporal modulation depth induced by FM-to-AM effect is about 23.4%,It has certain difference with the numerical simulation results of 29.7%.The reason is that the modualtion frequency of 9.2GHz may be very close to the temporal resolution limit of our oscilloscope.
Fig. 6 The experiment schematic diagram of the multipass amplification laser system.L1:collimating lens,M1,M2,M3,M4,M5:reflecting Mirror, FP: film polarizer, WP1, WP2:wave plate, FR:Frarday, L2, L3:lens, LDA:laser diode array
4. Conclusion and outlook
Employing the phase modulator to produce the laser pulse with certain bandwidth is a key technique in high power solid-state laser facility for ICF.The FM-to-AM effect of phase modulation pulse is introduced while it transmits in the laser system. It could induce periodic temporal modulation on top of the phase modulation pulse, which affects the output characteristics of the laser system seriously. The transmission characteristics of phase modulation pulse under the weak etalon effect in wave plates for complex solid-state optical system are investigated theoretically and experimentally. To our knowledge, it is the first time to introduce the weak etalon effect in wave plates for complex phase modulation optical system. The FM-to-AM induced by weak etalon effect is a disaster for the large laser facility, therefore, how to compensate the weak etalon effect in the complex laser system would be very important in the future.
Acknowledgments
The reported investigations were supported by the National Nature Science Foundation of China (Grant No. 60878058) and National High Technology Research and Development Program of China.
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