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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 5 — Mar. 5, 2007
  • pp: 2019–2032
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Delay interferometric single-shot measurement of a petawatt-class laser longitudinal chromatism corrector

C. Rouyer, N. Blanchot, J. Neauport, and C. Sauteret  »View Author Affiliations


Optics Express, Vol. 15, Issue 5, pp. 2019-2032 (2007)
http://dx.doi.org/10.1364/OE.15.002019


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Abstract

In this paper we present a self-referenced interferometric single-shot measurement technique that we use to evaluate the longitudinal chromatism compensation made by a diffractive lens corrector. A diffractive lens with a delay of 1 ps is qualified for a 60 mm beam aperture. This corrector was implemented on the Alisé Nd:glass power chain. We qualify the corrector and the Alisé power chain chromatism, demonstrating the potential of this measuring principle as well as the interest of diffractive lenses to correct longitudinal chromatism of petawatt-class lasers.

© 2007 Optical Society of America

1. Introduction

Ignition scale facilities now under construction, the LMJ [1

1. C. Cavailler, N. Fleurot, T. Lonjaret, and J. M. Di-Nicola, “Prospects and progress at LIL and Megajoule,” Plasma Phys. Controlled Fusion 46, B135–B141 (2004). [CrossRef]

] (Laser MégaJoule, in France) and the NIF [2

2. B. M. Van Wonterghem, S. C. Burkhart, C. A. Haynam, K. R. Manes, C. D. Marshall, J. E. Murray, M. L. Spaeth, D. R. Speck, S. B. Sutton, and P. J. Wegner, “National Ignition Facility commissioning and performance,” Proc. SPIE 5341, 55–65 (2004). [CrossRef]

] (National Ignition Facility, in the USA), constitute a remarkable opportunity in science and for inertial confinement fusion applications. The LIL, the LMJ laser prototype consists of an elementary unit of the LMJ, equipped with eight beams. Each beam is able to deliver a nanosecond pulse of 18 kJ at the fundamental wavelength of 1.053 μm and 7 kJ on target at 351 nm. The LIL facility will be split into eight independent beams to obtain a symmetrical irradiation on target. Moreover, an additional laser line, called PETAL (PETawatt Aquitaine Laser), offering multi-petawatt, high energy capabilities is currently being constructed [3

3. N. Blanchot, E. Bignon, H. Coïc, A. Cotel, E. Couturier, G. Deschaseaux, N. Forget, E. Freysz, E. Hugonnot, C. LeBlanc, N. Loustalet, J. Luce, G. Marre, A. Migus, S. Montant, S. Mousset, S. Noailles, J. Néauport, C. Rouyer, C. Rulliére, C. Sauteret, L. Videau, and P. Vivini, “Multi - Petawatt High Energy Laser Project on the LIL Facility in Aquitaine,” Proc. SPIE 5975, 30 (2005).

].

The PETAL facility is designed to deliver an energy of 3.6 kJ in 500 fs at the wavelength of 1.053 μm. It is based on the Chirped Pulse Amplification (CPA) technique [4

4. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985). [CrossRef]

] and uses a synthetic aperture compression scheme detailed previously [5

5. N. Blanchot, G. Marre, J. Neauport, E. Sibe, C. Rouyer, S. Montant, A. Cotel, C. Le Blanc, and C. Sauteret, “Synthetic aperture compression scheme for multi-Petawatt high energy laser,” Appl. Opt. 45, 1–8 (2006). [CrossRef]

]. PETAL, such as any other high energy Petawatt project (Omega-EP [6

6. L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy Petawatt capability for the Omega laser,” Opt. Photon. News 16, 30 (2005). [CrossRef]

], NIF-ARC [7

7. C. P. J. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Dawson, A. C. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones II, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Ngyuen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short-pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44, S266–S275 (2004). [CrossRef]

], PICO2000 [8

8. C. Le Blanc, C. Felix, J. C. Lagron, N. Forget, Ph. Hollander, A. M. Sautivet, C. Sauteret, F. Amiranoff, and A. Migus, “The petawatt laser glass chain at LULI: from the diode-pumped front end to the new generation of compact compressors,” in Proceedings of Third International Conference on Inertial Fusion Sciences and Applications, B. A. Hammel, D. D. Meyerhofer, J. Meyer ter Vehn, and H. Azechi, eds., (American Nuclear Soc. Inc, La Grange Park, IL, USA, 2004), pp. 608–611.

], VULCAN [9

9. C. N. Danson, P. A. Brummitt, R. J. Clarke, J. L. Collier, B. Fell, A. J. Frackiewicz, S. Hancock, S. Hawkes, C. Hernandez-Gomez, P. Holligan, M. H. R. Hutchinson, A. Kidd, W. J. Lester, I. O. Musgrave, D. Neely, D. R. Neville, P. A. Norreys, D. A. Pepler, C. J. Reason, W. Shaikh, T. B. Winstone, R. W. W. Wyatt, and B. E. Wyborn, “Vulcan Petawatt-an ultra-high-intensity interaction facility,” Nucl. Fusion 44, S239–S246 (2004). [CrossRef]

], FIREX [10

10. K. Mima, H. Azechi, Y. Johzaki, Y. Kitagawa, R. Kodama, Y. Kozaki, N. Miyanaga, K. Nagai, H. Nagatomo, M. Nakai, H. Nishimura, T. Norimatsu, H. Shiraga, K. Tanaka, Y. Izawa, Y. Nakao, and H. Sakagami, “Present status of fast ignition research and prospects of FIREX project,” Fusion Sci. Technol. 47, 662 (2005).

] or the Texas Petawatt Laser [11

11. M. Martinez, E. Gaul, T. Ditmire, S. Douglas, D. Gorski, W. Henderson, J. Blakeney, D. Hammond, M. Gerity, J. Caird, A. Erlandson, I. Iovanovic, C. Ebbers, and B. Molander, “The Texas Petawatt Laser,” Proc. SPIE 5991 (Feb. 7, 2006).

], uses a series of spatial filters in its amplifier section to extend, image-relay and clean the laser beam of unwanted spatial frequency modulations. These spatial filters, formed with a pair of lenses, introduce longitudinal chromatism and thus temporal delay. If this effect can be neglected for nanosecond regime lasers, it becomes a crucial issue for short pulses [12

12. J. D. Zuegel, S. Borneis, C. Barty, B. Le Garrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Le Blanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” Special Issue on Fast Ignition, Fus. Sci. Technol. 49, 453 (2006).

] and has consequently to be corrected. Many solutions, from classical achromats to diffractive optics [11–13

11. M. Martinez, E. Gaul, T. Ditmire, S. Douglas, D. Gorski, W. Henderson, J. Blakeney, D. Hammond, M. Gerity, J. Caird, A. Erlandson, I. Iovanovic, C. Ebbers, and B. Molander, “The Texas Petawatt Laser,” Proc. SPIE 5991 (Feb. 7, 2006).

], exist to compensate this longitudinal chromatism. The PETAL corrector, called CROCO (ChROmatism COrrector), takes benefit of the inverse chromatism of a diffractive optic with respect to a transparent material [14

14. J. Néauport, N. Blanchot, C. Rouyer, and C. Sauteret, “Chromatism compensation of the PETAL multi-petawatt high energy laser,” Appl. Opt. (to be published). [PubMed]

].

In order to validate the chromatic correction, we need an accurate measurement of the spatial dependence of the pulse delay induced by the longitudinal chromatic aberrations in the power chain as well as the one induced by the corrector component. Several methods have been proposed using a reference pulse [15

15. R. Netz, T. Feuer, R. Wolleschensky, and R. Sauerbrey, “Measurement of the pulse-front distortion in high-numerical-aperture optics,” Appl. Phys. B 70, 833–837 (2000). [CrossRef]

]. These methods are based on spatial interferometry, spectral interferometry or autocorrelation processes. “Inverted field autocorrelation” [16

16. G. Petzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1–9 (2000). [CrossRef]

] is a measurement without a reference pulse. Its extension, “shifted field autocorrelation” [17

17. H.-M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in Petawatt class laser,” Appl. Phys B 84, 421–428 (2006). [CrossRef]

], with a spatial shift in one interferometer arm limits the interference pattern in the overlapping region of the two pulses. However, all these methods require multiple shots to estimate the delay inside the beam. We herein present an extension of the spectral interferometry technique using the principle of the shifted arm to realize a 2D-spectral interferometry allowing the measurement of the pulse delay with a single shot. Moreover, this technique does not require an unaberrated mutually coherent simultaneous reference beam to interfere with the test beam.

We therefore propose to experimentally measure the delay compensation introduced by the CROCO using a single shot technique. The experimental setup consists of an interferometer coupled with a spectrometer to give access to the CROCO’s induced delay. The second section of this paper recalls the total delay introduced by the amplifier section of the PETAL facility and details the CROCO system. Section 3 is devoted to experimental measurements. After a description of the corrector manufacturing and the optical characterisation, we detail the experimental setup and the physical principles of the delay measurement. We then conclude by the obtained experimental delay to show that it is in good agreement with the CROCO specifications.

2. Evaluation and correction of the longitudinal chromatism for the PETAL facility

Let’s consider a single lens presenting some chromatism, its focal length variation with the wavelength can be expressed as, at the first order:

f(λ)=f0+f˙(λλ0)
(1)

Where f0 is the focal length at central wavelength λ0 and f is the derivative of the function f with respect to the wavelength λ.

We can then define a value ΔZ which is characteristic of the amount of chromatism obtained for a spectral bandwidth of Δλ:

ΔZ=f˙Δλ
(2)

This chromatism can be also expressed as the phase difference Δϕ of the wavefront, on the edges of the pupil and of the spectrum. This phase shift characteristizes a defocusing of the beam:

Δϕ=2πλ0h2f02ΔZ2
(3)

Let’s define ZR, the Rayleigh length [18

18. H. Kogelnik and T. Li, “Laser beams and Resonators,” Appl. Opt. 5, 1550–1567 (1966). [CrossRef] [PubMed]

]:

ZR=A∙f02λ0h2
(4)

Where A is a form factor close to unity and h is the radius of the pupil.

From Eqs. (3) and (4) we obtain the expression of the phase difference induced by the chromatism for a spectral bandwidth Δλ:

Δϕ=π∙A∙ΔZZR
(5)

The chromatic aberration can also be described, for the central wavelength λ0, by the optical path length difference and defined by Δϕ=2π∙Δλ0::

Δλ0=Δϕ2π=A2ΔZZR
(6)

Note that here the chromatism is proportional to the spectral bandwidth. From a temporal point of view, the chromatism can be seen as the time delay Td between the rays propagating through respectively the edges and the center of the pupil. Hence, Z. Bor [19

19. Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119- (1989). [CrossRef] [PubMed]

] and H. M. Heuck [17

17. H.-M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in Petawatt class laser,” Appl. Phys B 84, 421–428 (2006). [CrossRef]

] demonstrated that:

Td=λ02c·h2f02f˙
(7)

From Eqs. (2

2. B. M. Van Wonterghem, S. C. Burkhart, C. A. Haynam, K. R. Manes, C. D. Marshall, J. E. Murray, M. L. Spaeth, D. R. Speck, S. B. Sutton, and P. J. Wegner, “National Ignition Facility commissioning and performance,” Proc. SPIE 5341, 55–65 (2004). [CrossRef]

) and (4

4. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985). [CrossRef]

), we deduce that:

Td=λ02ΔλA2cΔZZR
(8)

If we now introduce the Fourier limited pulse length associated with the spectral width Δv:

τΔv=B
(9)

where B is a form factor close to unity and τ is the pulse duration. Hence, the delay Td characteristizing the chromatism can be written as:

Tdτ=A2BΔZZR
(10)

In consequence, we conclude that both temporal and spectral descriptions lead to an expression of the chromatism with the same adimensioned ratio. This ratio is algebraic and is cumulative at the traversing of a succession of lenses.

Δλ0=Δϕ2π=A2ΔZZR=BTdτ
(11)

These two temporal and spectral descriptions of the chromatism are depicted on Fig. 1.

Fig. 1. Description of various characteristic quantities of the chromatism brought by a lens. Δ is the optical path length difference and ΔΦ is the phase difference on the border of the pupil h and for a spectral bandwidth Δλ=λ+-λ-. ΔZ is the defocusing for the same spectral bandwidth and Td the time delay between centre and border of the pupil. Both approaches depict the same chromatism phenomenon.

To measure the chromatism, we thus need an experimental setup enabling us to estimate this ratio. As described in section 3, the temporal approach is used for our measurements. As explained above, the same work can be made in the spectral domain leading to the same conclusion. For the PETAL facility, the four pass amplifier section uses 6 lenses of various foci and radii so that the total induced delay is equal to 1520 fs i.e. about 3 times the PETAL expected pulse duration. The effect of a 2 ps additional delay on the focal spot on target for a flat top square beam can be numerically predicted and is illustrated in Fig. 2 [3

3. N. Blanchot, E. Bignon, H. Coïc, A. Cotel, E. Couturier, G. Deschaseaux, N. Forget, E. Freysz, E. Hugonnot, C. LeBlanc, N. Loustalet, J. Luce, G. Marre, A. Migus, S. Montant, S. Mousset, S. Noailles, J. Néauport, C. Rouyer, C. Rulliére, C. Sauteret, L. Videau, and P. Vivini, “Multi - Petawatt High Energy Laser Project on the LIL Facility in Aquitaine,” Proc. SPIE 5975, 30 (2005).

]. We can see that the peak intensity is divided by 8 in absence of chromatism correction.

Fig. 2. Effect of longitudinal chromatism on peak intensity on target for the PETAL facility. Left: with longitudinal chromatism, Right: without longitudinal chromatism, Top: focal spot radius evolution versus time. Bottom: central focal spot intensity versus time.

Several methods can be proposed to compensate the longitudinal chromatism [11

11. M. Martinez, E. Gaul, T. Ditmire, S. Douglas, D. Gorski, W. Henderson, J. Blakeney, D. Hammond, M. Gerity, J. Caird, A. Erlandson, I. Iovanovic, C. Ebbers, and B. Molander, “The Texas Petawatt Laser,” Proc. SPIE 5991 (Feb. 7, 2006).

, 13

13. Z. Bor, “Distortions of femtosecond laser pulses in lens systems,” J. of Modern Opt. 35, 1907–1918 (1988). [CrossRef]

, 14

14. J. Néauport, N. Blanchot, C. Rouyer, and C. Sauteret, “Chromatism compensation of the PETAL multi-petawatt high energy laser,” Appl. Opt. (to be published). [PubMed]

, 17

17. H.-M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in Petawatt class laser,” Appl. Phys B 84, 421–428 (2006). [CrossRef]

]. Due to the significant amount of pulse delay to be corrected and the laser line architecture, a diffractive based solution has been retained for the PETAL facility [14

14. J. Néauport, N. Blanchot, C. Rouyer, and C. Sauteret, “Chromatism compensation of the PETAL multi-petawatt high energy laser,” Appl. Opt. (to be published). [PubMed]

]. We have demonstrated that a focusing grating with an edge line density of N = 12.767 l/mm is adequate to compensate the 1520 fs delay, this corresponds to a 2.523 m diffractive lens. Such a low line density focusing grating would exhibit very low diffraction efficiency. Therefore, a diffractive Fresnel lens was preferred. It consists of a Fresnel lens with a binarized one wave deep profile. Using a four-mask manufacturing process, the 16 level diffractive Fresnel lenses can exhibit a theoretical diffraction efficiency of 98.5% [20]. Implementation of a CROCO in the L-turn of the PETAL amplifier section is done by placing a null power optical system constituted of the diffractive corrector and of a diverging lens in front of the L-turn mirror (M2) as illustrated in Fig. 3.

Fig. 3. The CROCO system in front of the M2 (L-turn) mirror. Ldiff is the diffractive lens, Ldiv is the diverging lens. The (Ldiff-Ldiv) ensemble has a null power.

It can be noticed that if this null power corrector is placed in a diverging or converging beam, a simple translation of the CROCO modifies the number of grooves on the diffractive lens overlapped by the beam and therefore the degree of correction of the system. A patent is currently pending on this tunable chromatism corrector.

Based on an early design, the work detailed in this paper is done with a 1.5 m diffractive lens, instead of the 2.523 m lens specified for PETAL. It has no impact on the announced conclusion.

3. Experimental demonstration

3.1 Experimental set-up: interferometric single shot chromatism measurement

Fig. 4. Spectral interferences observed on the spectrograph. Left: regular fringes in the case of constant delay between the two replicas. Right: variation of the fringes frequency in the case of chromatic beam.

The electric fields of two replicas delayed by T = 2 Δt are, in the spectral domain:

E1(ω)=A(ω)exp(iωΔt)
(12)

and

E2(ω)=A(ω)exp(iωΔt)
(13)

At the output of the spectrograph, the total electric field is given by:

E(ω)=E1(ω)+E2(ω)=2A(ω)cos(ωΔt)
(14)

and its intensity is:

I(ω)=E(ω)E*(ω)=2A(ω)A*(ω)[cos(2ωΔt)+1]
(15)

The period p of the cosine has the following property:

p=πΔt=2πT
(16)

The relation between the temporal width τo and the spectral bandwidth Δω is given by τoΔω) = 2π∙B. The number of visible fringes N in the spectrum Δω is N=Δω/p and is defined by:

N=B∙Tτ0
(17)

Let us consider a longitudinal chromatic beam such as depicted in Fig. 5, its energy front is curved and its temporal delay depends on the spatial coordinate Y:

τ(y)=Tr(ya)2,, where a is the radius of the beam and Tr the delay between the centre and the edge of the beam.

Fig. 5. Spatial shift dy in the case of a chromatic beam having a temporal delay T between the two replicas. Tr is the chromatic temporal delay.

For a spatial shift dy, the delay between two replicas is:

Δτ=τ(y)+Tτ(ydy)=Tr2ydya2+TTrdy2a2
(18)

The maximum delay variation, giving the maximum variation of the number of fringes, is obtained for a spatial shift equal to the beam radius: dy = a. Under this condition, the delay is:

Δτ=T+Tr2yaTr
(19)

The maximum delay is obtained for y = a given Δτ(y = a) = T + Tr, and the minimum delay for y = 0 given Δτ(y = 0) = T - Tr.

So, the number of fringes defined in Eq. (17) increases linearly because of the shift:

Nmin=B∙TTrτ0;Nmax=B∙T+Trτ0;ΔN=NmaxNmin=B∙2Trτ0
(20)

Fig. 6. Experimental set-up used on the Alisé facility to realize a single shot measurement of the chromatism induced by a diffractive lens.

3.1. Diffractive Fresnel lens specifications and optical performances

A 1.5 m diffractive lens was manufactured by the SILIOS Company [23] using a multi-mask dry etching process with the following specifications. This lens induces a 1 ps delay. A photo of the manufactured component is given in Fig. 7:

Substrate material: Corning 7980 fused silica

Full size: 100 mm -0.1/-0.4 mm

Clear aperture: 60x60 mm2

Thickness: 8 mm +/-0.1 mm

Parallelism: <1″

Substrate form: plane-plane

Transmitted wavefront quality before Fresnel lens engraving: <λ/10 @ 1.053μm

Side A and B planarity before Fresnel lens engraving: <λ/5 @ 1.053μm

Fresnel lens etched on side A, focal length of 1.5 m

Fresnel lens maximal depth: λ/(n-1) @ 1.053μm where n is the index of fused silica

at this wavelength

Fresnel lens profile binarized on 16 levels

No antireflection coating on sides A and B

Fig. 7. Picture of the diffractive lens (SILIOS Company) used in these experiments.

The diffraction efficiency of this lens was measured on a specific photometer. This device was previously described [24

24. J. Neauport, E. Journot, G. Gaborit, and P. Bouchut, “Design, optical characterization and operation of large transmission gratings for the laser integration line and laser megajoule facilities,” Appl. Opt. 44, 3143–3152, (2005). [CrossRef] [PubMed]

]. It consists of a single point scanning system with a 5 mm diameter beam of that can operate at 351 nm, 523 nm or 1053 nm at variable incidence angles. The estimated absolute accuracy of the apparatus is ± 0.0015. The first transmitted order diffraction efficiency was measured at normal incidence on the clear aperture with a sampling step of 4.3 mm × 4.3 mm. The obtained result is given in Fig. 8.

Fig. 8. Diffraction efficiency of the 1.5 m Fresnel lens at 1053 nm, normal incidence.

If we take into account the 4% losses of the uncoated side, a mean diffraction efficiency of 0.897 is obtained. A maximal value of 0.9672 is measured at the centre of the part, which is close to the theoretical maximal value for a 16 level part of 0.985. Fall off of the diffraction efficiency in the corner is due to the reduction of the size of the Fresnel lens pattern. The theoretical pattern in the corner is probably not respected by the manufacturing process.

3.2. Experimental results

As explained in section 3.1., the experiment consists of two series of measurements to observe variations of the interference pattern. The analyses of these measurements with a Fourier transformation technique are detailed after.

A first measure is made with a refractive lens instead of the diffractive lens. This is a kind of a reference for the qualification of the diffractive lens. Indeed, in this case, the accumulated chromatism is the sum of both the Alisé power chain chromatism and the diagnostic chromatism i.e. the refractive lens, the second lens of the telescope and the imagery telescope (see Fig. 6). As shown in Fig. 9, the period of the obtained interference pattern is quasi-constant on the full image. The global distortion of the fringes is due to wavefront aberrations of the input beam. In a future paper, we will demonstrate how an adequate use of this specific pattern can also give access to spectrally resolved wavefront aberrations in the manner of a large bandwidth shearing interferometer.

Fig. 9. Experimental interference pattern with the classical refractive lens. The interference period seems to be quasi-constant on the whole image. The horizontal axis is the wavelength axis in CCD pixel numbers. The vertical axis is the transverse coordinate axis along the spectrograph slit in CCD pixel numbers.

In the second series of measurements, the refractive lens is replaced by the diffractive lens described in section 3.2. Due to the variation of the delay between the top and the bottom of the overlapping zone, we observe in Fig. 10 a variation of the period of the interference pattern. The cut-off in the spatial profile comes from the limited size of the diffractive lens with a 60 mm aperture.

Fig. 10. Experimental interference pattern with the diffractive lens. A variation of the interference period is clearly observable between the top and the bottom of the image. The horizontal axis is the wavelength axis in CCD pixel numbers. The vertical axis is the transverse coordinate axis along the spectrograph slit in CCD pixel numbers.

Finally, the delay created by the diffractive lens is obtained by comparing these two series of data and by taking into account the theoretical chromatism estimated for the refractive lens.

The complete analysis of the interference pattern is made using a 1D-Fourier transform along the wavelength axis. Taking the expression of the fringes, the Fourier transform in the wavelength direction gives:

I˜(t,y)=FT[2A(ω)∙A*(ω)[1+cos(ω∙Δτ(y))]]
(21)

where Δτ is the delay given by Eq. (20).

I˜(t,y)=2∙A˜(t)A˜*(t)[δ(t)+δ(tΔτ(y))2+δ(t+Δτ(y))2]
(22)

The Fourier transform of the signal for each Y coordinate presents a central peak and two satellites. The central peak contains information on the spectral shape of the pulses. The satellites contain information on the modulations of the spectrum. For our diagnostic, the satellite positions give information on the delay Δτ between the two replicas for each Y coordinate in the overlapping zone. Figure 11 shows the differences of the Fourier signals for a perfect and and for a chromatic beam. The satellite positions are not constant for a chromatic beam because of the variation of the delay along the Y coordinate.

Fig. 11. Differences of the Fourier signals in the case of a perfect (top) and of a chromatic (bottom) beam. Due to the variation of the delay along the Y axis in the case of a chromatic beam, the satellite positions are not constant.

In Figs. 12 and 13 we plot the Fourier transform of the interference patterns of the two series of experiments shown in Figs. 9 and 10 respectively. The inversion of the tilt of the satellite locations induced by the diffractive Fresnel lens is visible.

Fig. 12. Fourier transform of the interference pattern in the case of the refractive lens. A small variation of the satellite positions appears due to the chromatism accumulated in the Alisé chain, the refractive lens and in the diagnostic lenses. The horizontal axis is the delay axis in CCD pixel numbers. The vertical axis is the transverse coordinate axis along the spectrograph slit in CCD pixel numbers.
Fig. 13. Fourier transform of the interference pattern in the case of the diffractive lens. A strong variation of the satellite positions appears due to the chromatic aberrations of the diffractive lens. The horizontal axis is the delay axis in CCD pixel numbers. The vertical axis is the transverse coordinate axis along the spectrograph slit in CCD pixel numbers.

To extract the delay from these signals, three different calibrations are required. First, we need to calibrate the spectral response of the spectrometer. This is done using two lasers with different wavelengths: 1047 nm and 1053 nm. This calibration suppresses the Tr delay error that might come from a lack of parallelism between the spectrograph grating axis and the CCD X axis. Then, in order to estimate the spatial characteristics, the beam size (a) and the spatial shift (dy) in the interferometer must be measured. For these two points, a calibrated etalon aperture is inserted in the input pupil of the system near the lens aperture which is imaged with the spectrograph slit. In a first calibration measurement, an opaque mask is also inserted in one of the two interferometer arms. We calibrate this way the Y axis on the CCD. In a second calibration measurement, the opaque mask is removed and two separated images are recorded on the spectrograph CCD without overlapping, which allows us to calibrate the spatial shift: dy. These two spatial calibrations cancel the systematic error induced by a lack of parallelism between the slit direction, the shearing direction and the Y direction of the CCD.

Using these calibrations the slope of the satellite position variation, and, finally Eq. (19), the total delay measured is Tr1 = 109 fs in the first experiment with the refractive lens and Tr2 = -903 fs with the diffractive lens. The unique contribution of the diffractive lens Tdiff is the difference between the two measurements (Tr2 - Tr1) to which is added the estimated delay of the refractive lens Tref. Tref is calculated using Eq. (7) for a silica substrate and is equal to Tref = 34 fs.

Finally, the diffractive lens introduces a delay Tdiff = -978 fs for the 60 mm aperture, in good agreement with the specifications (1 ps). Moreover, with this interferometric single-shot diagnostic, we have measured the Alisé longitudinal chromatism to be 75 fs for a 60 mm aperture corresponding to 150 fs for the operating full beam aperture (85 mm). Again, this value for the Alisé chain is in good agreement with the calculation giving 183 fs.

4. Conclusion

We developed a self-referenced interferometric single-shot longitudinal chromatism diagnostic and used it to characterize a diffractive lens able to correct chromatism on Petawatt class lasers. Our measurements demonstrate that our diffractive lens delay is in good agreement with what we specified: a measured delay of 978 fs for a 1 ps delay specified. Being single shot, this measuring principle is well suited for high energy power chains like the PETAL facility. The potential of this diagnostic to realize spectrally resolved 1D-shearing interferometry has been pointed out and shall be detailed in a future work.

Acknowledgments

This work is supported by the Conseil Régional d’Aquitaine and is performed under the auspices of the Institut Lasers et Plasmas. We thank the Alisé facility for access and modular capabilities and the Alisé team, particularly C. Lepage, O. Bonville and E. Mazataud for their help in setting up the experiments, S. Montant from the CELIA laboratory for analyses of the experimental results, the LMO team (Optical Metrology Laboratory at CEA-CESTA) for the optical measurements on the 1.5 m Fresnel lens and H. Ward for the redaction.

References and links

1.

C. Cavailler, N. Fleurot, T. Lonjaret, and J. M. Di-Nicola, “Prospects and progress at LIL and Megajoule,” Plasma Phys. Controlled Fusion 46, B135–B141 (2004). [CrossRef]

2.

B. M. Van Wonterghem, S. C. Burkhart, C. A. Haynam, K. R. Manes, C. D. Marshall, J. E. Murray, M. L. Spaeth, D. R. Speck, S. B. Sutton, and P. J. Wegner, “National Ignition Facility commissioning and performance,” Proc. SPIE 5341, 55–65 (2004). [CrossRef]

3.

N. Blanchot, E. Bignon, H. Coïc, A. Cotel, E. Couturier, G. Deschaseaux, N. Forget, E. Freysz, E. Hugonnot, C. LeBlanc, N. Loustalet, J. Luce, G. Marre, A. Migus, S. Montant, S. Mousset, S. Noailles, J. Néauport, C. Rouyer, C. Rulliére, C. Sauteret, L. Videau, and P. Vivini, “Multi - Petawatt High Energy Laser Project on the LIL Facility in Aquitaine,” Proc. SPIE 5975, 30 (2005).

4.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985). [CrossRef]

5.

N. Blanchot, G. Marre, J. Neauport, E. Sibe, C. Rouyer, S. Montant, A. Cotel, C. Le Blanc, and C. Sauteret, “Synthetic aperture compression scheme for multi-Petawatt high energy laser,” Appl. Opt. 45, 1–8 (2006). [CrossRef]

6.

L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy Petawatt capability for the Omega laser,” Opt. Photon. News 16, 30 (2005). [CrossRef]

7.

C. P. J. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Dawson, A. C. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones II, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Ngyuen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short-pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44, S266–S275 (2004). [CrossRef]

8.

C. Le Blanc, C. Felix, J. C. Lagron, N. Forget, Ph. Hollander, A. M. Sautivet, C. Sauteret, F. Amiranoff, and A. Migus, “The petawatt laser glass chain at LULI: from the diode-pumped front end to the new generation of compact compressors,” in Proceedings of Third International Conference on Inertial Fusion Sciences and Applications, B. A. Hammel, D. D. Meyerhofer, J. Meyer ter Vehn, and H. Azechi, eds., (American Nuclear Soc. Inc, La Grange Park, IL, USA, 2004), pp. 608–611.

9.

C. N. Danson, P. A. Brummitt, R. J. Clarke, J. L. Collier, B. Fell, A. J. Frackiewicz, S. Hancock, S. Hawkes, C. Hernandez-Gomez, P. Holligan, M. H. R. Hutchinson, A. Kidd, W. J. Lester, I. O. Musgrave, D. Neely, D. R. Neville, P. A. Norreys, D. A. Pepler, C. J. Reason, W. Shaikh, T. B. Winstone, R. W. W. Wyatt, and B. E. Wyborn, “Vulcan Petawatt-an ultra-high-intensity interaction facility,” Nucl. Fusion 44, S239–S246 (2004). [CrossRef]

10.

K. Mima, H. Azechi, Y. Johzaki, Y. Kitagawa, R. Kodama, Y. Kozaki, N. Miyanaga, K. Nagai, H. Nagatomo, M. Nakai, H. Nishimura, T. Norimatsu, H. Shiraga, K. Tanaka, Y. Izawa, Y. Nakao, and H. Sakagami, “Present status of fast ignition research and prospects of FIREX project,” Fusion Sci. Technol. 47, 662 (2005).

11.

M. Martinez, E. Gaul, T. Ditmire, S. Douglas, D. Gorski, W. Henderson, J. Blakeney, D. Hammond, M. Gerity, J. Caird, A. Erlandson, I. Iovanovic, C. Ebbers, and B. Molander, “The Texas Petawatt Laser,” Proc. SPIE 5991 (Feb. 7, 2006).

12.

J. D. Zuegel, S. Borneis, C. Barty, B. Le Garrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Le Blanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser Challenges for Fast Ignition,” Special Issue on Fast Ignition, Fus. Sci. Technol. 49, 453 (2006).

13.

Z. Bor, “Distortions of femtosecond laser pulses in lens systems,” J. of Modern Opt. 35, 1907–1918 (1988). [CrossRef]

14.

J. Néauport, N. Blanchot, C. Rouyer, and C. Sauteret, “Chromatism compensation of the PETAL multi-petawatt high energy laser,” Appl. Opt. (to be published). [PubMed]

15.

R. Netz, T. Feuer, R. Wolleschensky, and R. Sauerbrey, “Measurement of the pulse-front distortion in high-numerical-aperture optics,” Appl. Phys. B 70, 833–837 (2000). [CrossRef]

16.

G. Petzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1–9 (2000). [CrossRef]

17.

H.-M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in Petawatt class laser,” Appl. Phys B 84, 421–428 (2006). [CrossRef]

18.

H. Kogelnik and T. Li, “Laser beams and Resonators,” Appl. Opt. 5, 1550–1567 (1966). [CrossRef] [PubMed]

19.

Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119- (1989). [CrossRef] [PubMed]

20.

http://www.llnl.gov/nif/psa/diffractive-optics/fresnel.html.

21.

N. Blanchot, J. Néauport, C. Rouyer, and C. Sauteret, “Chromatism compensation of the PETAL multi-petawatt high energy laser,” in proc. of International Conference on Ultrahigh Intensity Laser (ICUIL), p211, Cassis, 24–29 September 2006.

22.

N. Blanchot, D. Le Goff, I. Le Goff, P. Manac’h, E. Mazataud, M. Nicolaizeau, M. Padois, L. Videau, D. Villate, and L. Voisin, “A new versatile Nd:glass 200 J facility: ALISE; or from monochromatic and smoothed nanosecond pulses towards the ultra-intense femtosecond regime,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, Technical Digest (Optical Society of America, 2002), paper CWB4, 364–365.

23.

http://www.silios.com.

24.

J. Neauport, E. Journot, G. Gaborit, and P. Bouchut, “Design, optical characterization and operation of large transmission gratings for the laser integration line and laser megajoule facilities,” Appl. Opt. 44, 3143–3152, (2005). [CrossRef] [PubMed]

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(140.7090) Lasers and laser optics : Ultrafast lasers
(220.1000) Optical design and fabrication : Aberration compensation

ToC Category:
Diffraction and Gratings

History
Original Manuscript: December 12, 2006
Revised Manuscript: January 17, 2007
Manuscript Accepted: January 17, 2007
Published: March 5, 2007

Citation
C. Rouyer, N. Blanchot, J. Neauport, and C. Sauteret, "Delay interferometric single shot measurement of a petawatt-class laser longitudinal chromatism corrector," Opt. Express 15, 2019-2032 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-2019


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References

  1. C. Cavailler, N. Fleurot, T. Lonjaret, and J. M. Di-Nicola, "Prospects and progress at LIL and Megajoule," Plasma Phys. Controlled Fusion 46, B135-B141 (2004). [CrossRef]
  2. B. M. Van Wonterghem, S. C. Burkhart, C. A. Haynam, K. R. Manes, C. D. Marshall, J. E. Murray, M. L. Spaeth, D. R. Speck, S. B. Sutton, and P. J. Wegner, "National Ignition Facility commissioning and performance," Proc. SPIE 5341, 55-65 (2004). [CrossRef]
  3. N. Blanchot, E. Bignon, H. Coïc, A. Cotel, E. Couturier, G. Deschaseaux, N. Forget, E. Freysz, E. Hugonnot, C. LeBlanc, N. Loustalet, J. Luce, G. Marre, A. Migus, S. Montant, S. Mousset, S. Noailles, J. Néauport, C. Rouyer, C. Rullière, C. Sauteret, L. Videau, and P. Vivini, "Multi - Petawatt High Energy Laser Project on the LIL Facility in Aquitaine," Proc. SPIE 5975, 30 (2005).
  4. D. Strickland and G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56, 219-221 (1985). [CrossRef]
  5. N. Blanchot, G. Marre, J. Neauport, E. Sibe, C. Rouyer, S. Montant, A. Cotel, C. Le Blanc, and C. Sauteret, "Synthetic aperture compression scheme for multi-Petawatt high energy laser," Appl. Opt. 45, 1-8 (2006). [CrossRef]
  6. L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, "High-energy Petawatt capability for the Omega laser," Opt. Photon. News 16, 30 (2005). [CrossRef]
  7. C. P. J. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Dawson, A. C. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. JonesII, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Ngyuen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, "An overview of LLNL high-energy short-pulse technology for advanced radiography of laser fusion experiments," Nucl. Fusion 44, S266-S275 (2004). [CrossRef]
  8. C. Le Blanc, C. Felix, J. C. Lagron, N. Forget, Ph. Hollander, A. M. Sautivet, C. Sauteret, F. Amiranoff, and A. Migus, "The petawatt laser glass chain at LULI: from the diode-pumped front end to the new generation of compact compressors," in Proceedings of Third International Conference on Inertial Fusion Sciences and Applications, B. A. Hammel, D. D. Meyerhofer, J. Meyer ter Vehn, and H. Azechi, eds., (American Nuclear Soc. Inc, La Grange Park, IL, USA, 2004), pp. 608-611.
  9. C. N. Danson, P. A. Brummitt, R. J. Clarke, J. L. Collier, B. Fell, A. J. Frackiewicz, S. Hancock, S. Hawkes, C. Hernandez-Gomez, P. Holligan, M. H. R. Hutchinson, A. Kidd, W. J. Lester, I. O. Musgrave, D. Neely, D. R. Neville, P. A. Norreys, D. A. Pepler, C. J. Reason, W. Shaikh, T. B. Winstone, R. W. W. Wyatt, and B. E. Wyborn, "Vulcan Petawatt-an ultra-high-intensity interaction facility," Nucl. Fusion 44, S239-S246 (2004). [CrossRef]
  10. K. Mima, H. Azechi, Y. Johzaki, Y. Kitagawa, R. Kodama, Y. Kozaki, N. Miyanaga, K. Nagai, H. Nagatomo, M. Nakai, H. Nishimura, T. Norimatsu, H. Shiraga, K. Tanaka, Y. Izawa, Y. Nakao, H. Sakagami, "Present status of fast ignition research and prospects of FIREX project," Fusion Sci. Technol. 47, 662 (2005).
  11. M. Martinez, E. Gaul, T. Ditmire, S. Douglas, D. Gorski, W. Henderson, J. Blakeney, D. Hammond, M. Gerity, J. Caird, A. Erlandson, I. Iovanovic, C. Ebbers, B. Molander, "The Texas Petawatt Laser," Proc. SPIE 5991 (Feb. 7, 2006).
  12. J. D. Zuegel, S. Borneis, C. Barty, B. Le Garrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Le Blanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, "Laser Challenges for Fast Ignition," Special Issue on Fast Ignition, Fus. Sci. Technol. 49, 453 (2006).
  13. Z. Bor, "Distortions of femtosecond laser pulses in lens systems," J. of Modern Opt. 35, 1907-1918 (1988). [CrossRef]
  14. J. Néauport, N. Blanchot, C. Rouyer and C. Sauteret, "Chromatism compensation of the PETAL multi-petawatt high energy laser," Appl. Opt. (to be published). [PubMed]
  15. R. Netz, T. Feuer, R. Wolleschensky, R. Sauerbrey, "Measurement of the pulse-front distortion in high-numerical-aperture optics," Appl. Phys. B 70, 833-837 (2000). [CrossRef]
  16. G. Petzler, A. Kasper, K. J. Witte, "Angular chirp and tilted light pulses in CPA lasers," Appl. Phys. B 70, 1-9 (2000). [CrossRef]
  17. H.-M. Heuck, P. Neumayer, T. Kühl, U. Wittrock, "Chromatic aberration in Petawatt class laser," Appl. Phys B 84, 421-428 (2006). [CrossRef]
  18. H. Kogelnik and T. Li, "Laser beams and Resonators," Appl. Opt. 5, 1550-1567 (1966). [CrossRef] [PubMed]
  19. Z. Bor, "Distortion of femtosecond laser pulses in lenses," Opt. Lett. 14, 119- (1989). [CrossRef] [PubMed]
  20. http://www.llnl.gov/nif/psa/diffractive-optics/fresnel.html.
  21. N. Blanchot, J. Néauport, C. Rouyer and C. Sauteret, "Chromatism compensation of the PETAL multi-petawatt high energy laser," in Proc. of International Conference on Ultrahigh Intensity Laser (ICUIL), p211, Cassis, 24-29 September 2006.
  22. N. Blanchot, D. Le Goff, I. Le Goff, P. Manac'h, E. Mazataud, M. Nicolaizeau, M. Padois, L. Videau, D. Villate, L. Voisin, "A new versatile Nd:glass 200 J facility: ALISE; or from monochromatic and smoothed nanosecond pulses towards the ultra-intense femtosecond regime," in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, Technical Digest (Optical Society of America, 2002), paper CWB4, 364-365.
  23. http://www.silios.com.
  24. J. Neauport, E. Journot, G. Gaborit and P. Bouchut, "Design, optical characterization and operation of large transmission gratings for the laser integration line and laser megajoule facilities," Appl. Opt. 44, 3143-3152, (2005). [CrossRef] [PubMed]

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