Starting designs for broadband chirped mirrors

The chirped mirror (CM) is one of the key elements in ultrafast optics. We investigate a problem of a CM designing. The series of starting designs for broadband CM are reported. The appropriate starting design can significantly simplify a problem of design searching, and improved a performance of...

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Datum:	2008
Hauptverfasser:	Pervak, V.Yu., Telyatnikov, V.O., Pervak, Yu.O.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2008
Schriftenreihe:	Semiconductor Physics Quantum Electronics & Optoelectronics
Online Zugang:	http://dspace.nbuv.gov.ua/handle/123456789/118860
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Zitieren:	Starting designs for broadband chirped mirrors / V.Yu. Pervak, V.O. Telyatnikov, Yu.O. Pervak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 2. — С. 154-158. — Бібліогр.: 17 назв. — англ.

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spelling	irk-123456789-1188602017-06-01T03:05:16Z Starting designs for broadband chirped mirrors Pervak, V.Yu. Telyatnikov, V.O. Pervak, Yu.O. The chirped mirror (CM) is one of the key elements in ultrafast optics. We investigate a problem of a CM designing. The series of starting designs for broadband CM are reported. The appropriate starting design can significantly simplify a problem of design searching, and improved a performance of a final solution. The acceptable performance of CM was achieved by optimization one of the proposed starting design. The achieved design has comparable performance in comparison with the best design which was realized up to now. 2008 Article Starting designs for broadband chirped mirrors / V.Yu. Pervak, V.O. Telyatnikov, Yu.O. Pervak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 2. — С. 154-158. — Бібліогр.: 17 назв. — англ. 1560-8034 PACS 42.79.Bh http://dspace.nbuv.gov.ua/handle/123456789/118860 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	The chirped mirror (CM) is one of the key elements in ultrafast optics. We investigate a problem of a CM designing. The series of starting designs for broadband CM are reported. The appropriate starting design can significantly simplify a problem of design searching, and improved a performance of a final solution. The acceptable performance of CM was achieved by optimization one of the proposed starting design. The achieved design has comparable performance in comparison with the best design which was realized up to now.
format	Article
author	Pervak, V.Yu. Telyatnikov, V.O. Pervak, Yu.O.
spellingShingle	Pervak, V.Yu. Telyatnikov, V.O. Pervak, Yu.O. Starting designs for broadband chirped mirrors Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet	Pervak, V.Yu. Telyatnikov, V.O. Pervak, Yu.O.
author_sort	Pervak, V.Yu.
title	Starting designs for broadband chirped mirrors
title_short	Starting designs for broadband chirped mirrors
title_full	Starting designs for broadband chirped mirrors
title_fullStr	Starting designs for broadband chirped mirrors
title_full_unstemmed	Starting designs for broadband chirped mirrors
title_sort	starting designs for broadband chirped mirrors
publisher	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate	2008
url	http://dspace.nbuv.gov.ua/handle/123456789/118860
citation_txt	Starting designs for broadband chirped mirrors / V.Yu. Pervak, V.O. Telyatnikov, Yu.O. Pervak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 2. — С. 154-158. — Бібліогр.: 17 назв. — англ.
series	Semiconductor Physics Quantum Electronics & Optoelectronics
work_keys_str_mv	AT pervakvyu startingdesignsforbroadbandchirpedmirrors AT telyatnikovvo startingdesignsforbroadbandchirpedmirrors AT pervakyuo startingdesignsforbroadbandchirpedmirrors
first_indexed	2025-07-08T14:47:43Z
last_indexed	2025-07-08T14:47:43Z
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fulltext	Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 154-158. © 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 154 PACS 42.79.Bh Starting designs for broadband chirped mirrors V.Yu. Pervak1, V.O. Telyatnikov2 and Yu.O. Pervak2* 1International Center “Institute of Applied Optics”, National Academy of Sciences of Ukraine 2Taras Shevchenko Kyiv National University, Radiophysics Department E-mail: yupervak@univ.kiev.ua Abstract. The chirped mirror (CM) is one of the key elements in ultrafast optics. We investigate a problem of a CM designing. The series of starting designs for broadband CM are reported. The appropriate starting design can significantly simplify a problem of design searching, and improved a performance of a final solution. The acceptable performance of CM was achieved by optimization one of the proposed starting design. The achieved design has comparable performance in comparison with the best design which was realized up to now. Keywords: ultrafast optics, chirped mirrors. Manuscript received 16.04.08; accepted for publication 15.05.08; published online 30.06.08. 1. Introduction In recent decades, femtosecond lasers were significantly developed [1-3]. One of the key elements in femtosecond laser systems is a chirped mirror (CM). One has to control both the reflectivity and group delay dispersion (GDD) (the second deviation of the phase in a frequency domain). Since invention of CM mirrors in 1994 [4], 14 years has already passed. In previous years, CM performance was considerably improved: the wavelength bandwidth – increased, the GDD comes closer to desired values [5-11]. As usually, in thin film optics, to solve such an inverse problem one employed mathematics optimization algorithms to find one of local minima, because analytical solution of this problem is impossible [12-16]. Unfortunately, the local minima are often insufficient solution. Most of modern optimization algorithms cannot jump from one local minimum to another. To overcome this problem, the starting design has to be changed and the optimization procedure has to be launched again. Due to complication of CM designing, the modern computer to optimize one of the starting designs needs from tens of minutes to several hours. Therefore, a proper starting design may save hours, and what is more important allows us to find a design, which has better performance. In this paper, being based on performances of symmetrical and classical multilayer structures, we demonstrate a way in which one can obtain an appropriate design. The different designs were considered. The most valuable of them are reported. One of the designs was optimized with a modern algorithm to demonstrate efficiency of our approach. 2. The calculation of spectral characteristics of multilayer structures In the case, when basic parameters of multilayer structure are known (q is the number of layers, rn - refractive index, rk – extinction, rd – thickness for each layer, and mk – substrate optical constants, 0n and 0k – optical constants of external media, 0θ – angle of incidence), we calculate the spectra of reflection, transmittance, phase changes both for reflection and transmission, and, respectively, the group delay, group delay dispersion can be calculated. Using the matrix method [17], we can write: The reflection is 0 0 0 0 ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ +η −η ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ +η −η = CB CB CB CBR , (1) the phase change is ( )[ ] ( )2 0 0Im tg CCBB BCCB −η −η =φ . (2) Where the characteristic matrix of the assembly is ( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ η⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ δδη ηδδ =⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ∏ = m q r rrr rrr i i C B 1 cossin sincos 1 , (3) the phase thickness of the layer r is λ θπ =δ rrr r dN cos2 , (4) Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 154-158. © 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 155 800 1000 1200 Wavelenght, nm 80 20 0 300 R, % 600 200 100 0 40 60 GD, fs 100 Fig. 1. Reflectivity and GD of multilayer structure S(0.5H0L00.5H0)15(0.5H1L10.5H1)15(0.5H2L20.5H2)15S0. 800 1000 1200 Wavelenght, nm 80 20 0 300 R, % 600 200 100 0 40 60 GD, fs 100 Fig. 1. Reflectivity and GD of multilayer structure S(0.5H0L00.5H0)15(0.5H1L10.5H1)15(0.5H2L20.5H2)15S0. the layer admittances are rrr N θχ=η cosvac for TE waves or rrr N θχ=η cosvac for TM waves, (5) mmm N θχ=η cosvac for TE waves or mmm N θχ=η cosvac for TM waves, (6) where λ is the wavelength, rrr iknN −= , =χ vac 2.6544·10–3 S – vacuum admittance, 0η and mη – external and substrate admittances, respectively. The values of rθ can be found from Snell’s law mmrr NNN θ=θ=θ sinsinsin 00 . (7) The group delay is λ φ ⋅ π λ = ω φ −= d d cd d GD 2 2 , (8) where φ is given in the equation (2), c = 3·108 m/s is the speed of light. The group delay dispersion is ( ) ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ λ φ λ+ λ φ λ⋅ π λ −= ω φ −= d d d d cd dGDD 2 2 2 2 2 2 2 2 2 (9) 3. The starting designs - results and discussions To investigate the influence of layer thickness changes in CM, it was chosen a starting multilayer structure (SMS) with the high reflection (as high as 99.7 %) within the wavelength range 600 to 1200 nm. This wavelength range is equivalent to one optical octave. The SMS consist of three multilayer mirrors based on symmetrical periods, and its structures looks as shown below: S(0.5H0L00.5H0)15(0.5H1L10.5H1)15(0.5H2L20.5H2)15S0 , (10) where S0 is the fused silica substrate (refractive index nS = 1.4656 at the wavelength λ0 = 1100 nm) and S is an external medium (air, n0 = 1.0); H0, H1, H2 and L0, L1, L2 – the niobium oxide layers (Nb2O5, nH = 2.2393 at the wavelength λ0 = 1100 nm) and the silica dioxide layers (SiO2, nL = 1.4656 at wavelength λ0 = 1100 nm), respectively. At simulation, the optical constants of magnetron sputtering thin films were used [5]. The optical thicknesses of layers are equal: .nm 275459091.059091.0 77273.077273.0 0HH HHHH 2222 11110000 =λ=== ==== LL LLLL dndn dndndndn (11) The reflectivity and GD of these structures are shown in Fig. 1. Three wavelength ranges with different GD characteristics versus the wavelength are crearly defined at 780 and 1000 nm. The sharp picks in GD were obtained at passing ranges at the edge of a high reflection ranges and strong ripples are observed in various wavelength ranges. These spectral ranges are superposed with high reflection bands of each single mirror; its structures are determined in the expression (10). The structure (10) has 91 layers, as selection of internal layers on the symmetrical periods is symbolical. How does thickness changes influence on the GD and is it possible to obtain a smooth-linear wavelength depen- dence of GD by monotonous? To answer, the reflectivity and GD characteristics for about 100 different structures were investigated. They consist of alternating of 91 Nb2O5 and SiO2 layers. We conclude that GD is strong oscillating function inside of high reflection bands, when optical thicknesses monotonous are increased or decreased. In case of mismatch of external media and the last layer, GD oscillations can be reduced. Shown in Fig. 2 are GD characteristics of the multilayer structure with linear changes of optical thicknesses. 600 800 1000 1200 0 100 200 600 800 1000 1200 99,90 99,95 100,00 600 800 1000 1200 0 100 200 5 6 R, % GD, fs wavelenght, nm GD, fs 1 2 3 4 Fig. 2. Reflectivity (1, 2) and GD (3-6) of 91-layer structures with alternating Nb2O5 and SiO2 layers (first and final layers are Nb2O5) on the fused silica substrate. Optical thicknesses are increased from 0.5λ0/4 to 1.15λ0/4, beginning from substrate (3, 4) and external media (5, 6). External media: air (3, 6), fused silica (4, 5). Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 154-158. © 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 156 R, % 99,5 0,50 1,00 nd, in unit λ0/4 0 20 40 Number of layer 99,0 600 800 1000 1200 0 600 800 1000 1200 50 100 A ve ra ge G D , f s Wavelength, nm R, % 99,5 0,50 1,00 nd, in unit λ0/4 0 20 40 Number of layer 99,0 600 800 1000 1200 0 600 800 1000 1200 40 100 A ve ra ge G D , f s Wavelength, nm 1 2 3 4 5 6 (a) (b) (c) (k) (e) (d) 1 3 4 5 6 2 1 2 3 4 5 6 1 2 34 5 6 1 2 5 6 1 5 6 Fig. 3. The optical thicknesses of layers (a, d), reflectivity (b, e) and GD (c, k) of 91-layer structures with alternating Nb2O5 and SiO2 layers. Curves 4 and 5 in Fig. 2 correspond to structures on the fused silica substrate with external media of fused silica. In this case, in the structure significant mismatch with external media is observed, in contrast to the case when external media is air (curves 3 and 6). It is known that oscillations can be reduced by utilizing the complementary pair approach [6]. The average group delay is important characteristic, namely, this characteristic determines the total GD of the complementary pair of CM. So, to choose optimal initial optimization approximation, the structure with a similar average GD are required. To create CM with a negative group delay dispersion (GDD), it is necessary for GD to behave linearly. In the most modern laser schemes, the negative GDD is used to compress ultrashort pulses. Simulation results of optical properties for some structures with different dependences of optical thicknesses versus the layer number are shown in Fig. 3. In the wavelength domain, the linear thickness change provides us nearly a linear average GD (see Fig. 3). When a thickness change is decreased with the number of layers (layer number are counted from media of incidence), then an average GD is increased. And vice versa. The structure, which has the GDD value closed to – 80 fs2, was chosen to be optimum. By uncomplicated homemade software the optimization procedure was performed. As target for optimization procedure, we used the reflectivity value as high as 100 % and the main value of GDD –80 fs2. CM with –80 fs2 GDD is often used in femtosecond laser systems to compensate the second order of dispersion. The designs before and after optimization are shown in Fig. 4. After the optimization procedure, GDD oscillations were significantly reduced. This design consists of 86 layers, what is less than respective starting design. This design has an optical Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 154-158. © 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 157 nd, in unit λ0/4 nd, in unit λ0/4 0 1,0 0 1,0 0 20 40 60 80 Layer number 0 20 40 60 80 Layer number 99,8 R, % 99,4 99,8 R, % (a) (b) 99,4 800 1000 1200 1400 800 1000 1200 1400 800 1000 1200 1400 Wavelenght, nm 0 100 200 GD, fs 0 -10000 10000 GDD, fs2 800 1000 1200 1400 800 1000 1200 1400 800 1000 1200 1400 Wavelenght, nm 0 100 200 GD, fs -200 100 GDD, fs2 -300 (c) (d) (e) (g) (k) (m) Fig. 4. Multilayer structures (a, e), reflectivity (b, g), GD (e, k) and GDD (d, m) of the starting design (a, b, c, d) and optimized one (e, g, k, m). Arrows show the average values of GD (c) and GDD (d, m). 600 800 1000 1200 1400 0 2000 4000 6000 8000 10000 12000 λ, nm d, n m 0,12 0,25 0,50 1,00 1,50 2,00 3,00 4,00 Fig. 5. Penetration of electric field through the multilayer structure of optimized CM. Parameters of CM are shown in Fig. 4. Light comes from the top of the figure. The electric field intensity is shown in the inset. d is the physical layer thickness, and λ is the wavelength. performance comparable with the design reported [5]. Shown in Fig. 5 is penetration of electric field through the multilayer structure of the optimized CM. Parameters of this CM are shown in Fig. 4. Fig. 5 shows how the chirped mirror operates. The electric field components at 1400 nm penetrate much deeper into the multilayer structure than the components at 700 nm. This means that the longwave components become delayed relatively to the shortwave ones. Fig. 5 gives an additional hint for optimizing the design: the longwave components must penetrate almost down to the first layer on the substrate. If this is not the case in the design, several layers must be removed. In the opposite case, viz. when longwave components penetrate through the entire multilayer structure including the substrate, several layers must be added. This only applies to mirrors with a negative dispersion. 4. Conclusion The proposed design can be successfully used as the starting one for CM manufacturing. Keep it in mind that Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 154-158. © 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 158 CM designing is challenging and important optical problem. Additionally, the designing procedure for one- octave CM (700-1400 nm) can take hours when using the modern computer equips Pentium 4 Xeon 3 GHz. Therefore, for standardization of the way for CM designing we proposed procedure and series of designs that can be utilized as the starting ones. At the same time, a proper starting design significantly accelerates designing the complicated CM and provides complicated solution even after minor-local optimization. References 1. F. Krausz, M.E. Fermann, Th. Brabec, P.F. Curley, M. Hofer, M.H. Ober, Ch. Spielmann, E. Wintner, A.J. Schmidt, Femtosecond solid-state lasers // IEEE J. Quantum Electron. 28, p. 2097-2122 (1992). 2. A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, Chirped-pulse oscil- lators: a route to high-power femtosecond pulses without external amplification // Opt. Lett. 29, p. 1366-1368 (2004). 3. A. Fernandez, A. Verhoef, V. Pervak, G. Lermann, F. Krausz, A. Apolonski, Generation of 60-nJ sub- 40-fs pulses at 70 MHz repetition rate from a Ti:sapphire chirped pulse-oscillator // Appl. Phys. B 87, p. 395-398 (2007). 4. R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, Chirped multilayer coatings for broadband dispersion control in femtosecond lasers // Opt. Lett. 19, p. 201–203 (1994). 5. V. Pervak, S. Naumov, G. Tempea, V. Yakovlev, F. Krausz, A. Apolonski, Synthesis and manufacturing the mirrors for ultrafast optics // Proc. SPIE 5963, p. 490-499 (2005). 6. V. Pervak, A.V. Tikhonravov, M.K. Trubetskov, S. Naumov, F. Krausz, A. Apolonski, 1.5-octave chirped mirror for pulse compression down to sub- 3 fs //Appl. Phys. B 87, p. 5-12 (2007). 7. G. Steinmeyer, G. Stibenz, Generation of sub-4-fs pulses via compression of a white-light continuum using only chirped mirrors // Appl. Phys. B 82, p. 175-181 (2006). 8. G. Steinmeyer, Femtosecond dispersion compen- sation with multiplayer coatings: toward the optical octave // Appl. Opt. 45, p. 1484-1490 (2006). 9. N. Matuschek, L. Gallmann, D.H. Sutter, G. Stein- meyer, U. Keller, Back-side-coated chirped mirrors with ultra-smooth broadband dispersion charac- teristics // Appl. Phys. B 71, p. 509-522 (2000). 10. F.X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H.A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, and T. Tschudi, Design and fabrication of double-chirped mirrors // Opt. Lett. 22, p. 831- 833 (1997). 11. G.F. Tempea, B. Považay, A. Assion, A. Isemann, W. Pervak, M. Kempe, A. Stingl, and W. Drexler, All-Chirped-Mirror Pulse Compressor for Nonlinear Microscopy, In: Biomedical Optics, Technical Digest (CD) (Optical Society of America, 2006), paper WF2. 12. N. Tikhonov, A.V. Tikhonravov, M.K. Trubetskov, Second order optimization methods in the synthesis of multilayer coatings // Comp. Meth. Math. Phys. 33, p. 1339-1352 (1993). 13. V. Tikhonravov, M.K. Trubetskov, G.W. DeBell, Application of the needle optimization technique to the design of optical coatings // Appl. Opt. 35, p. 5493-5508 (1996). 14. V. Tikhonravov, M.K. Trubetskov, T.V. Amot- chkina, M.A. Kokarev, Key role of the coating total optical thickness in solving design problems // Proc. SPIE 5250, p. 312-321 (2004). 15. V. Pervak, F. Krausz and A. Apolonski, Dispersion control over the UV-VIS-NIR spectral range with HfO2/SiO2 chirped dielectric multilayers // Opt. Lett. 32, p. 1183-1185 (2007). 16. V. Pervak, A.V. Tikhonravov, M.K. Trubetskov, J. Pistner, F. Krausz, A. Apolonski, Band filter: 2- material technology versus rugate // Appl. Opt. 46, p. 1190-1193 (2007). 17. A. MacLeod, Optical Coatings from Design Through Manufacture. Thin Film Center Inc., 1999-2007.

Starting designs for broadband chirped mirrors

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