We show that the large nonlinear phase shifts obtained from phase-mismatched second harmonic generation can be used to implement all-optical switching devices such as a nonlinear Mach-Zehnder interferometer and a nonlinear directional coupler

Assanto, Gaetano

Sheik-Bahae, Mansoor

Stegeman, George

Stryland, Eric Van

English

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University of Central Florida (UCF): STARS (Showcase of Text, Archives, Research & Scholarship)

University of Central Florida STARS Faculty Bibliography 1990s Faculty Bibliography 1-1-1993 All-Optical Switching Devices Based On Large Nonlinear Phase-Shifts From 2Nd Harmonic-Generation Gaetano Assanto University of Central Florida George Stegeman University of Central Florida Mansoor Sheik-Bahae University of Central Florida Eric Van Stryland University of Central Florida Find similar works at: https://stars.library.ucf.edu/facultybib1990 University of Central Florida Libraries http://library.ucf.edu This Article is brought to you for free and open access by the Faculty Bibliography at STARS. It has been accepted for inclusion in Faculty Bibliography 1990s by an authorized administrator of STARS. For more information, please contact STARS@ucf.edu. Recommended Citation Assanto, Gaetano; Stegeman, George; Sheik-Bahae, Mansoor; and Stryland, Eric Van, "All-Optical Switching Devices Based On Large Nonlinear Phase-Shifts From 2Nd Harmonic-Generation" (1993). Faculty Bibliography 1990s. 634. https://stars.library.ucf.edu/facultybib1990/634 Appl. Phys. Lett. 62, 1323 (1993); https://doi.org/10.1063/1.109611 62, 1323© 1993 American Institute of Physics.All-optical switching devices based onlarge nonlinear phase shifts from secondharmonic generationCite as: Appl. Phys. Lett. 62, 1323 (1993); https://doi.org/10.1063/1.109611Submitted: 12 August 1992 . Accepted: 24 December 1992 . Published Online: 05 August 1998Gaetano Assanto, George Stegeman, Mansoor Sheik-Bahae, and Eric Van StrylandARTICLES YOU MAY BE INTERESTED INNonlinear coupling of waveguide modesApplied Physics Letters 50, 801 (1987); https://doi.org/10.1063/1.98049 Second-harmonic generation in single-mode integrated waveguides based on mode-shape modulationApplied Physics Letters 110, 111109 (2017); https://doi.org/10.1063/1.4978696First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying anexternal field for efficient blue second-harmonic generationApplied Physics Letters 62, 435 (1993); https://doi.org/10.1063/1.108925All-optical switching devices based on large nonlinear phase shifts from second harmonic generation Gaetano Assanto, George Stegeman, Mansoor Sheik-Bahae, and Eric Van Sttyland CREOL, University of’ Central Florida, Orlando, FL 32686 (Received 12 August 1992; accepted for publication 24 December 1992) We show that the large nonlinear phase shifts obtained from phase-mismatched second harmonic generation can be used to implement all-optical switching devices such as a nonlinear Mach-Zehnder interferometer and a nonlinear directional coupler. It has proven difficult to find materials with large enough nonlinearities (Q) combined with low enough losses (a) to make high throughput all-optical switching (AOS) devices responding on picosecond time scales.’ Well-understood devices such as nonlinear Mach-Zehnder interferometers (NMZI) and directional couplers (NLDC) have been implemented successfully only in glass fibers,?13 and in AlGaAs channel waveguides operated with photon energies below half their band gap.js5 Recently it has been shown that the nonlinear phase shift experienced by a beam at the fundamental frequency during almost phase-matched second harmonic generation can achieve multiple values of 7r/2 without absorptive losses.“8 The evolution of this phase (and amplitude) of the fundamen- tal with distance and power is quite different from that associated with an intensity-dependent refractive index nz, and it has been an open question whether this source of nonlinear phase shift can be used in AOS devices.’ In this letter we examine the response of two such devices using noncentrosymmetric media, a NMZI and a NLDC, and show that the special features associated with second order cascaded processes are indeed useful for geometries relying on nonlinear phase shifts. The basic configuration of a Mach-Zehnder interfer- ometer and a directional coupler are well known and are shown as insets of Figs. 2(a) and 3 (cj .I For the Mach- Zehnder, the incident beam is split into two, and both beams undergo independent phase shifts on propagation until they are recombined at the second stem to produce an output. The goal for an NMZI is to change the relative phase between the channels by changing input power. In order to ensure complete destructive interference at low powers (which requires a phase differences of QT), we also introduce a phase offset element into one arm. For the NLDC there are two separate inputs, and the guides are sufficiently close to permit energy exchange between the fundamental beams in the two channels due to spatial beam overlap. Normally, for half beat length, a signal input into one channel exits from the second channel. For AOS, the relative channel outputs are changed by increasing the input power. The starting point of the analysis is the usual coupled mode equations describing second harmonic generation in two lossless channels (for example, waveguides) which can be coupled (NLDC) or not (NMZI) by the spatial overlap of optical fields,lm5 We write d dznao(zj=-iK(-22W;~,~ja:(~je~~~‘, (1) &n,(z) = -iK( --w;2w,-~,)az,(z>a~(z) Xe- iA~=+zn,(zj, (2) (3) $b,(z) = --iK( --o;2w,--wjb~o(z)b;(z) xe- iAp’z+ilYa,(z). (4) We assume that an index or nonlinearity is spatially mod- ulated along the direction of propagation in order to achieve quasi-phase-matching and that the wave vector mismatches A/3= 2/c&n (20) -n (w )] &tK and A/I’-2kV,,[n(2wj --n(wj]h:R can be different for the two channels with 2~/K (2?r/K’) the appropriate period of the modulation. The complex field amplitudes ai,(z) (channel 1) and b,(z) (channel 2) are normalized so that Iaim I2 and lb,(z) I2 have the units of power. K =K( --2w;w,wj =K( --w;2w,--0) is an effective nonlinear coefficient far from any material resonances and accounts for the field transverse distributions. The subscript i indi- cates either the fundamental (i= 1) or second harmonic (i=2>. r quantifies the coupling between the waveguides due to field overlap of the fundamental beams. 1P2P4 Since the FIG. 1. Nonlinear phase (dashed line) and throughput (solid line) of the fundamental beam vs cw input power in a channel with KL= I and APL =O. 1, The phase is graphed in units of 7~. 1323 A&. Phys. Lett. 62 (12), 22 March 1993 @I 1993 American Institute of Physics 1323 1.0 1 I' : I I : : +U : : /- : : : : : y.,yy : $I 0 a : \. ‘L sk>. ---..____ Id, -T-15o 200 -530 Input power %I.4 .c! %.2 sii,,> \ ‘7 \ 6 ‘\ *> \ “T 2:. i >% \ (1.0 , --.y--- , 0 1 Time (cI.~.)~ 04 --.. 3 FIG. 2. Mach-Zehnder interferometer: (a) transmission vs input funda- mental powers for cw (dashed line) and pulsed (solid) inputs; in the pulsed case, the horizontal axis represents the peak power of the Gaussian pulses. A sketch of the NMZI is shown in the inset. (b) Time response for a single pulse with a peak power of 65 W. The device is characterized by the same parameters listed in Fig. 1, with phase mismatches of opposite signs in the two arms and a phase offset of r. harmonic fields are more tightly bound to the individual waveguides than the fundamental, we assume that the per- tinent lY(20) for the harmonic waves can be neglected. While the assumption is valid in most practical situations, the inclusion of a small r(2w) does not alter significantly our numerical results. For NMZI, l?=O because there is no power (energy) exchange between the two arms. A typical example of the fundamental’s nonlinear phase shift and power throughout in single channels is shown in Fig. 1. For small detuning APL, the novel feature is the plateau in the phase shift versus input intensity. Note that to obtain large phase shifts at the smallest powers possible, large modulation in the output fundamental has to be dealt with. On the other hand, for large detunings the fundamental power is almost a constant, although higher input powers are needed for substantial phase shifts.’ First we discuss the NMZI with opposite Afl in the two arms, i.e., AfiO’L= -AL. Therefore the net d@erential phase shift achievable within one plateau is 37-= [ +?r/2 - ( -r/2)], enough for switching the output of this device from off to on or vice versa. If a phase offset of r is intro- duced into one channel (for example electro-optically or via a difference in channel lengths) the net phase shift can be 0 when operating on the first plateau. The resulting cw response is shown in Fig. 2(a) (dashed line) and exhibits 1 .o 1 : z! . . *\ a, %\. c 7 a .L cn g 2 0.5 -cl 2 -4 [ A.. 0.0 iime (0.u.) FIG. 3. Nonlinear directional coupler: (a) cross (solid) and bar (dashed) fractional output vs cw input power; (b) same as in (a) for pulsed excitation. The horizontal axis represents peak power. (c) Tem- poral profile of the output pulse in bar (solid) and cross (dash) channels for an input peak value of 93 W. A schematic of the NLDC is shown in the inset. The half-beat-length NLDC is characterized by &=4 and APL=8 in both guides. strong modulation versus input power. Since most AOS systems operate with pulse inputs, this response is of most interest. For pulses Gaussian in time, the energy through- put is also plotted in Fig. 2(a) (solid line) vs peak power. For a peak power at the maximum of the cw fundamental throughput, the output signal vs time for a single Gaussian pulse is shown in Fig. 2 (b) . Note that complete switching is obtained at the peak of the pulse, as well as pulse nar- rowing. Essentially no pulse break-up is obtained for these operating parameters, in contrast to similar devices based on electronic n2 nonlinearities.’ Note that to avoid pulse break-up with a third-order process temporal solitons (re- alizable only in fibers) or square pulses (difficult to syn- thesize) have to be used.‘*” 1324 Appl. Phys. Lett., Vol. 62, No. 12, 22 March 1993 Assanto et al. 1324 Phase cjt SH seed ( eg) FIG. 4. NLDC with seeding signal at the second harmonic in the input channel. Fractional powers in the bar (solid) and cross (dashed) ports vs initial phase of the seed. Parameters are as listed in Fig. 3, input and seeding powers are 100 and 0.1 W, respectively. The cw response of a NLDC for the parameters listed in the caption is shown in Fig. 3(a). Note that the output from the cross state decreases to zero with increasing input power and the power reverts back to the bar [input) chan- nel. The oscillation in the fundamental power occurs due to exchange of power with the second harmonic. This os- cillation can be reduced, but not eliminated, by optimizing the parameters. The pulsed response as a function of peak power is shown in Fig. 3 (b) . The oscillations are damped out because of the averaging, however, there is still a strong modulation of the output pulses, as shown in Fig. 3 (c) for a single Gaussian temporal profile. Due to the coherent nature of the SHG process, the outcome of the interaction is sensitive to the amplitude and phase of any other signal input at w or 2~. Such sensitivity is enhanced at high powers due to the related bandwidth reduction of the SHG process. In a NLDC, for instance, a weak signal at 2w can be used to control its operation. In particular, the phase of a second harmonic seed (0.1% of the fundamental beam in our simulations) input through the same bar channel as the fundamental is able to switch the cw fractional bar output of the strong beam, as shown in Fig. 4. A seed at w into the cross channel can also act as a control signal. A study of these devices in the presence of a seeding signal for cw and pulsed excitations will be pre- sented elsewhere. In summary, second order processes, for example sec- ond harmonic generation, can be used to generate the large nonlinear phase shifts needed for AOS devices. In fact, we predict that switching without pulse break-up should be possible in a Mach-Zehnder interferometer. Switching is also predicted in nonlinear directional couplers with pulse modulation different from that obtained when employing a Kerr n2. Although this, approach to switching is limited to second order noncentrosymmetric media, a number of ap- propriate materials already exist in waveguide formats to make such devices possible with switching powers of tens of watts and sub-cm lengths.11-13 This research was supported by DARPA and AR0 (DAAL03-9 l-C-0042). ‘G. I. Stegeman and E. M. Wright, J. Opt. Quantum Electron. 22, 95 (1990); G. Assanto, in Guided Wave Nonlinear Optics, edited by B. Ostrowsky and R. Reinisch (Kluwer, Dordrecht, 1992), NATO AS1 Vol. 214, p. 257. ‘D. S. Gusovskii, E. M. Dianov, A. A. Maier, V. B. Neustruev, V. V. Osoko, A. M. Prokhorov, K. Yu. Sitarskii, and I. A. Shcherbakov, Sov. J. Quantum Electron. 17, 724 ( 1987); S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. W. Smith, Opt. Lett. 13, 904 ( 1988). ‘B. K. Nayar, N. Finlayson, N. J. Doran, S. T. Davey, D. L. Williams, and J. W. Arkwrigth, Opt. Lett. 16, 408 (1991). 4A. Villeneuve, C. C. Yang, P. J. Wigley, G. I. Stegeman, J. S. Aitcheson, and C. N. Ironside, Appl. Phys. Lett. 61, 147 (1992). ‘K. Al-hemyari,.J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, Electron. Lett. 28, 1091 (1992). “N. R. Belashenkov, S. V. Gagarskii, and M. V. Inochkin, Opt. Spec- trosc. 66, 1383 (1989). ‘R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, Opt. Lett. 17, 28 (1992). sG. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, and G. Assanto, Opt. Lett. 18, 13 (1993). ‘S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, Opt. Lett. 13, 672 (1988). lo A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, IEEE J. Quantum Electron. 25, 2648 (1989). “G L. J. A. Rikken C J. E. Seppen. A. H. J. VenHuizen, S. Nijhuisen, and E. G. J. Staring Philips J. Res. 46, 215 (1992). I2 J. D. Bierlein, Technical Digest of Compact Blue-Green Lasers, Digest Series Vol. 6, Opt. Sot. Am., p. 119 (1992). I3 K. Yamamoto, K. Mizuuchi, and T. 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All-Optical Switching Devices Based On Large Nonlinear Phase-Shifts From 2Nd Harmonic-Generation

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All-Optical Switching Devices Based On Large Nonlinear Phase-Shifts From 2Nd Harmonic-Generation

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