Polarization-selectable cavity locking method for generation of laser Compton scattered γ-rays

Nowadays, generation of energy-tunable, monochromatic γ-rays is needed to establish a nondestructive assay method of nuclear fuel materials. The γ-rays are generated by collision of laser photons stored in a cavity and relativistic electrons. We propose a configuration of an enhancement cavity capable of performing polarization control fabricated by a combination of a four-mirror ring cavity with a small spot inside a cavity and a three-mirror of reflective optics as an image inverter for polarization-selectable γ-rays. The image inverter introduces a phase shift of specific polarization which can be used to generate an error signal to lock an optical cavity at a resonance condition. ©2014 Optical Society of America OCIS codes: (140.4780) Optical resonators; (260.5430) Polarization; (060.2320) Fiber optics amplifiers and oscillators; (320.7160) Ultrafast technology. References and links 1. C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436(7048), 234–237 (2005). 2. R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94(19), 193201 (2005). 3. I. Pupeza, T. Eidam, J. Rauschenberger, B. Bernhardt, A. Ozawa, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, A. Tünnermann, T. W. Hänsch, and F. Krausz, “Power scaling of a high-repetitionrate enhancement cavity,” Opt. Lett. 35(12), 2052–2054 (2010). 4. I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, Th. Udem, A. Tünnermann, T. W. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact highrepetition-rate source of coherent 100 eV radiation,” Nat. Photonics 7(8), 608–612 (2013). 5. A. Ozawa, J. Rauschenberger, Ch. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Hänsch, and Th. Udem, “High harmonic frequency combs for high resolution spectroscopy,” Phys. Rev. Lett. 100(25), 253901 (2008). 6. A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012). 7. R. Hajima, T. Hayakawa, N. Kikuzawa, and E. Minehara, “Proposal of Nondestructive Radionuclide Assay Using a High-Flux Gamma-Ray Source and Nuclear Resonance Fluorescence,” J. Nucl. Sci. Technol. 45(5), 441–451 (2008). 8. T. Hayakawa, N. Kikuzawa, R. Hajima, T. Shizuma, N. Nishimori, M. Fujiwara, and M. Seya, “Nondestructive assay of plutonium and minor actinide in spent fuel using nuclear resonance fluorescence with laser Compton scattering γ-rays,” Nucl. Instr. Meth. A 621(1-3), 695–700 (2010). 9. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munely, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983). 10. D. A. Shaddock, M. B. Gray, and D. E. McClelland, “Frequency locking a laser to an optical cavity by use of spatial mode interference,” Opt. Lett. 24(21), 1499–1501 (1999). 11. T. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35(3), 441–444 (1980). 12. Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009). 13. R. H. Dixon, “Use of a three-mirror image rotator in a laser-produced plasma experiment,” Appl. Opt. 18(23), 3883–3884 (1979). 14. S. Saraf, R. L. Byer, and P. J. King, “High-extinction-ratio resonant cavity polarizer for quantum-optics measurements,” Appl. Opt. 46(18), 3850–3855 (2007). #203494 $15.00 USD Received 26 Dec 2013; revised 26 Feb 2014; accepted 2 Mar 2014; published 14 Mar 2014 (C) 2014 OSA 24 March 2014 | Vol. 22, No. 6 | DOI:10.1364/OE.22.006613 | OPTICS EXPRESS 6613 15. R. C. Jonse, “New calculus for the treatment of optical systems: electromagnetic theory,” J. Opt. Soc. Am. 46(2), 126–131 (1956).


Introduction
A resonantly enhanced optical pulse inside the cavity, namely enhancement cavity, has recently received broad attention because of high harmonic generation (HHG) inside a cavity with a multimegahertz repetition rate [1][2][3][4].Owing to its outstanding optical properties, such as a short wavelength region and a high repetition rate, the HHG from an enhancement cavity is expected to be used for high-resolution spectroscopy [5,6].Nowadays, in the field of accelerator physics, the generation of hard X-ray or even γ-ray via inverse Compton scattering of laser photons stored in a cavity by a relativistic electron beam, which is produced by Energy Recovery Linac (ERL), is expected in many scientific and industrial applications.In particular, it has been proposed that the ERL γ-ray source is applied for the nondestructive measurement of isotope for the purpose of nuclear security and safeguards.We aim for the realization of a new nondestructive assay method for uranium 235, plutonium 239, and minor actinides in spent nuclear fuel assembly in a water pool [7].Nuclear fuel materials are detected using nuclear resonance fluorescence with laser Compton scattering (LCS) γ-rays [8].The angular distribution of nuclear resonance fluorescence γ-ray via multipole transitions is dependent on the polarization of LCS γ-ray.From the principle of Compton scattering, the polarization of the LCS γ-rays is identical with that of the laser.In the nondestructive assay for nuclear materials, this polarization control enables us to distinguish between the signal from the nuclear resonance fluorescence and background γ-rays.In this paper, we propose the enhancement of optical pulses inside the cavity performing polarization control fabricated by a combination of a four-mirror ring cavity with a small spot inside a cavity and a three-mirror of reflective optics as an image inverter for polarization-selectable LCS γ-rays.

Scheme of the cavity locking technique
We employ a four-mirror ring cavity with two concave mirrors to produce a small spot inside a cavity.If this cavity is employed for a LCS γ-ray source, in which γ-rays are generated by collision of laser photons and relativistic electrons, a small spot at a point inside the cavity is required because of the collision spot size of the ERL electron beam is about 10 μm.
To enhance an optical pulse inside a cavity, the repetition frequency of the enhancement cavity must be locked actively to maintain the resonance condition between the cavity and the seeding laser.A feedback loop to lock the cavity requires an "error signal" which becomes zero when the value of the controlled parameter and the target value are equal.Various schemes have been developed to obtain an error signal to lock the cavity, such as the Pound-Drever-Hall method which uses the phase modulation sidebands of the frequency as an error signal [9], the method based on the spatial mode (Tilt-locking method) which utilizes the spatial modes interference between the carrier field (TEM 00 ) and a directly reflected [10], and the Hänsch-Couillaud (HC) method which utilizes polarization by monitoring changes in the polarization of the light field reflected from the cavity [11].The HC method comprises an internal element such as a Brewster plate, a polarizer or a birefringent crystal.This method is very versatile owing to its simple setup, but this transmission element may limit the intracavity power due to optical damage.Recently, in contrast to the original HC scheme, some variations of HC method have been reported without an additional transmission element inside the cavity [3,12].
In this study, a three-mirror image inverter which consists of two 45° HR mirrors and one 0° HR mirror [13] is used for cavity locking on the basis of HC method.Since only the horizontal image is inverted through the three-mirror image inverter, it corresponds to the phase shift of π with respect to the vertical phase.In the field of interferometric gravitational wave detection, this method is used as not only a cavity locking but also a spatial, spectral and polarization filter [14].Furthermore, the linearly polarization inside the locking cavity is able to select vertical and horizontal direction by controlling the incident polarization.
In order to demonstrate our cavity locking stabilization method, we set up an enhancement cavity as shown in Fig. 1, which is a four-mirror ring cavity, a three-mirror image inverter and a cavity locking configuration.The incident light pulses from an Yb-doped fiber laser are assumed to be linearly polarized and polarization is adjusted to be at an arbitrary angle of θ with respect to horizontal plane by using a half-wave plate (HWP).
The electric field of injected light wave can be decomposed into horizontal and vertical components, i.e.E i // and E i ⊥ , which can be expressed in the plane wave approximation // cos , sin where E i is the amplitude of the injection light wave.The incident light with controlled polarization is injected to the enhancement cavity through an input coupler.The reflected light from the input coupler is used for a reference signal of the HC locking scheme.Here, the reflected light contains both direct reflection of the incident light and transmission of the light stored in the cavity.The complex amplitude of the reflection light wave, E r // and E r ⊥ , can be written as follows where R 1 and T 1 are the reflectivity and transmissivity of the input coupler.We ignore the internal loss of the input coupler, i.e.R 1 + T 1 = 1.R // and R ⊥ are the amplitude reduction factor of the horizontal and vertical optical component inside the cavity, respectively.δ is the roundtrip phase shift due to free space propagation in the cavity, determined by the cavity length L.
Here, the first minus sign in the right-hand side of Eq. ( 2) originates from the phase shift π for the reflected light.When the phase shift satisfies the condition δ = 2mπ (m = any integer), only the vertical polarization light can be enhanced inside the cavity.Conversely, when the phase shift satisfies the condition δ = (2m + 1)π (m = any integer), only the horizontal polarization light can be enhanced inside the cavity.When the cavity is on-resonance, both reflection coefficients, i.e.E r // and E r ⊥ , are real so that their superposition is linearly polarized.When the cavity is off-resonance, however, owing to the appearance of the imaginary parts of E r // and E r ⊥ , the reflected light acquires an elliptical polarization.The magnitude of the ellipticity depends on the deviation of phase shift from the resonance.
The reflection light from the input coupler is guided to the cavity locking loop [Fig.1(a)] consisting of a quarter-wave plate (QWP), a polarizing beam splitter (PBS) and two photodiodes (PDs).Elliptically polarized light can be divided into left-hand and right-hand circularly polarized components with different amplitude.The QWP generates linearly polarized light from these two components with orthogonal components that are detected by the two PDs.Namely, an error signal is proportional to the difference of the intensities measured with PD1 and PD2.
E 1 and E 2 are the electric fields after passing through the QWP and PBS.And the light intensity I 1 and I 2 are proportional to the squared electric field |E 1 | 2 and |E 2 | 2 .The electric field of E 1 and E 2 can be derived by using the Jones matrices [15] as follows where the first Jones matrix describes a PBS and the second one a QWP with the fast axis horizontal.Hence, the difference signal of the light intensity is readily calculated The light intensity I 1 and I 2 at the two outputs are monitored by two PDs (PD1 and PD2) connected to a differential amplifier.Equations ( 1), ( 2) and ( 4) show that the differential signal of the light intensities (I 1 -I 2 ) is related to the cavity locking as follows We calculate the light intensity monitored by PDs, I 1 , I 2 and (I 1 -I 2 ), and the intracavity power as a function of the round-trip phase shift δ to apply the HC method for the cavity locking.Figure 2 shows calculated results, where we use the parameters in our experiment: R 1 = 0.95, T 1 = 0.05, R // = 0.94 and R ⊥ = 0.97.The error signal of (I 1 -I 2 ) shows a steep zerocrossing at a resonance phase shift so that we can employ the signal for the cavity locking.By using a servo loop system, it is possible to lock the cavity to a resonance point.The horizontally and vertically polarized light are selectively enhanced in the cavity for phase shift of δ = 2mπ and δ = (2m + 1)π, respectively.Thus, when injected light containing both polarizations is incident on an enhancement cavity, only one polarized light can be enhanced at a certain cavity length.

Experiments
We have performed the cavity locking experiment using the four-mirror ring cavity with the three-mirror image inverter which is based on the HC scheme.The seed pulses are generated by a home-built mode-locked Yb-doped fiber oscillator with 75 MHz repetition rate.The pulses sent to a two-stage Yb-doped fiber based narrow bandwidth chirp pulse amplifier with two bandpass filters and a spatial mask.After the amplification, the FWHM bandwidth of 1.8 nm centered around 1030 nm are obtained.Subsequently, the pulses are compressed to 1.2 ps with two fused silica transmission gratings.After the compression, the average power is 600 mW.Our enhancement locking cavity is composed of a ring resonator whose round-trip time is adjusted to inverse of the seeding laser repetition rate.Instead of the 0° HR mirror of the three-mirror image inverter, a 1% transmittance mirror is placed in order to measure the light property of inside the cavity, such as light polarization, power stability and beam profile under locking condition.The input coupler has a reflectivity of 95% which is almost equal to all reflectivity of the cavity except the input coupler.The error signal is observed as a function of the cavity length, which is varied with a piezo electric transducer (PZT), attached to the one of the cavity mirror.The reflection light from the input coupler is guided to the cavity looking loop system and it can be used successfully to lock the cavity to resonance by means of a digital-based cavity lock system (TEM Messtechnik GmbH).
Figures 3(a) and 3(b) show the measured resonances for linear scan of the cavity length and the typical error signal observed when the injected light has linear polarization that is rotated in θ = −45° relative to the horizontal plane, respectively.The PZT in the cavity is driven periodically with a voltage which is proportional to the red signal and the black signal indicates the measured intracavity power, measured with a PD through one of the cavity mirror.The polarization of the two adjacent peaks of the resonance condition (δ = 0 and δ = π in Fig. 3   with the calculated error signal in Fig. 2. Then, Fig. 4 shows a polar plot of the normalized intensity which is detected by PD versus the angle of the rotatable linear polarizer oriented along an axis described by polar angle relative to the horizontal plane.The solid lines are fitted with a sine function to the experimental data.The injected light is adjusted to be at an angle of Fig. 4 With the lock-point properly adjusted by the servo loop system, the long-term cavity locking stability of the enhancement cavity recorded over a period of 30 min., which is 0.8% standard deviation as demonstrated in Fig. 5  mm), we measured the beam quality M 2 factor of the enhanced beam.The measurement resulted in a near diffraction-limited beam with a measured M 2 below 1.1.The locking power stability and spatial profile are monitored by observing the leakage light from the cavity mirror with a power meter (OPHIR) and a CCD camera (The Imaging Source Europe GmbH).

Conclusion
In conclusion, we have demonstrated the enhancement of optical pulses inside the cavity with a linear polarization at a resonance condition with a high spatial beam quality.Our proposed enhancement cavity consists of a four-mirror ring cavity with a small spot inside a cavity and a three-mirror image inverter to obtain an error signal and this cavity locking method is a variation of the HC method.By adopting this technique, we obtained 20 of enhancement factor and controlling the angle of the incident polarization enabled us to select the polarization inside the cavity.This cavity locking technique and further increase of enhancement factor are expected to generate the linearly and polarization selectable LCS γrays for the purpose of nondestructive detection of isotopes in the spent nuclear fuel by using nuclear resonance fluorescence.

Fig. 1 .
Fig. 1.(a) Schematic diagrams of the enhancement locking cavity which consists of a fourmirror ring cavity and a three-mirror image inverter, and a cavity locking loop configuration.(b) Three-mirror image inverter system.A typical image is traced through the system for illustration.
(a)) is at right angle to each other.

Figure 3 (
b) shows the observed error signal as a function of the round-trip phase shift δ.As can be seen in Fig.3(b), this signal is consistent

Fig. 3 .
Fig. 3. (a) Observation of the intracavity power, measured with a PD through one of the cavity mirror (Black) while scanning the cavity length by the piezo-controlled mirror (Red).(b) Experimentally observed error signal for R 1 = 0.95 as a function of the round-trip phase shift δ.The lock-points (zero-crossing point) are denoted by crosses (a) θ = 45° and Fig. 4(b) θ = −45° with respect to the horizontal plane with a HWP before the cavity (Pos.A in Fig. 1(a)).The transmitted light from one of the cavity mirrors (Pos.B in Fig. 1(a)), is polarized almost horizontally [Fig.4(a)] and vertically [Fig.4(b)] direction at right angles to the horizontal plane, and the polarization is linearly polarized.
(a).The cavity locking stability can be further improved by suppressing the mechanical vibration and air turbulence in the laboratory environment.Also shown in Fig. 5(b) are the M 2 measurement and the spatial profile of the enhanced beam, recorded at Pos. B in Fig. 1(a).Using a scanning beam profiler and a focusing lens (f = 200

Fig. 5 .
Fig. 5. (a) Locking stability of the enhancement cavity recorded over a period of 30 min., which is 0.8% standard deviation.(b) M 2 measurement and spatial profile of the enhanced beam (inset).