Symmetric Directional Coupler Research Articles

Nonlinear mode coupling in graphene-buried optical waveguides

The photothermal effect of graphene, which refers to the effect of converting light absorbed by graphene into heat, offers an effective physical mechanism for the realization of all-optical control devices. In this paper, we explore this physical mechanism for the study of nonlinear mode-coupling effects with three graphene-buried waveguide structures: a graphene-buried long-period waveguide grating, a symmetric directional coupler with graphene buried in two cores, and a symmetric directional coupler with graphene buried in one core. We establish physical models for these graphene-buried waveguide structures based on the coupled-mode theory and experimentally implement these structures with polymer waveguides. Our experimental results agree well with the theoretical analyses. The nonlinear mode-coupling effects generated in the graphene-buried waveguide structures show similar characteristics as those achieved with Kerr nonlinearity, but the input powers required in our experiments are much lower (only several tens of milliwatts), which can be delivered by common continuous-wave lasers. The graphene-buried waveguide platform makes feasible the generation of strong nonlinear mode-coupling effects at low powers and offers much flexibility for nonlinearity engineering, which can greatly facilitate the investigation of nonlinear mode-coupling effects in different waveguide structures for practical applications.

An Integrated Pump-Controlled Variable Coupler Fabricated by Ultrafast Laser Writing.

The design and fabrication of a integrated symmetric directional coupler dependent o the pumping power and operating at a 1534 nm wavelength is reported. The twin-core waveguide was inscribed into Er3+/Yb3+ co-doped phosphate glass by a femtosecond laser direct writing technique. By optical pumping, the coupling ratio can be modulated due to the changes induced in the refractive index of the material. The experimental results demonstrated that the coupling ratio can be tuned continuously from 100/0 to 50/50 by increasing the pump's power from 0 to 350 mW. The developed twin-core coupler has promising applications for on-chip all-optical signal processing and communication systems.

Graded-index core-based polarization beam splitters realized with symmetric polymer directional couplers

In this paper, we design and demonstrate polymer-based polarization beam splitters realized with parabolic graded-index (GI) directional couplers at 1550 nm. We design and investigate these beam splitters by using the beam propagation method (BPM) and the RSoft CAD BeamPROP solver is used for model design and characterization. We study the splitting ratio of 50:50 and 100:0 of these beam splitters for both transverse electric (TE) and transverse magnetic (TM) modes of the polarized light. In particular, the 50:50 beam splitters exhibit an output efficiency of 95% due to the absence of polarization. However, in the presence of the polarization effect, the polarization dependency is analyzed and manipulated successfully, and the output efficiency increases by approximately 98% at an incident angle of 31∘ due to the polarized launch field. Moreover, the 100:0 beam splitters act as the switching devices realized with parabolic GI polymer directional couplers. The insertion losses of the GI beam splitters are 0.162 dB and 0.186 dB, while the excess losses are 0.148 dB and 0.149 dB for TE and TM modes, respectively. Also, the polarization extinction ratio (PER) of the 100:0 beam splitters is >25 dB and >20 dB for TE and TM modes, respectively.

Fabrication-tolerant directional couplers on thin-film lithium niobate.

Directional couplers (DCs) are essential components in integrated photonics. A symmetric DC with a large fabrication tolerance on thin-film lithium niobate is demonstrated here. The principle is based on the beat length compensation of the opposite trend of width and gap fabrication errors in the DC. The tolerance is greater than ±100 nm for an optimized structure. The experimental results support the simulated ones. The principle can be applied to DC-based devices, such as 3-dB couplers and waveguide array couplers with a high yield.

Analysis of splitting ratio of a symmetric directional coupler fabricated with triangular-index fibers in nonlinear condition-a design perspective

We report here one of the significant performance parameters of a 2 × 2 symmetric directional coupler, the splitting ratio, in the nonlinear conditions considering the coupler fabricated with two similar mono-mode triangular index fibers. Different sets of physical aspects like V-number, core-radius of the fibers used, core-to-core distance of separation between the fibers in coupler structure, operating wavelength, index of refraction of the core have been considered for evaluating the splitting ratio at different lengths of fused fiber coupler. This analytical exercise is an effort for extending an indication to the optical device design engineers. This has been worked out involving the reliable mathematical instrument, the Chebyshev technique. The change of behavior of the splitting ratio in different linear and nonlinear conditions and with different physical parameters has been studied rigorously. Our theoretical analysis goes superbly with that derived using the complicated and lengthy finite element technique. This exercise needs modest computation. Hence, this report on splitting ratio analysis of 2 × 2 symmetric directional coupler composed of two mono-mode triangular- index fibers will prove its feasibility as a ready reference in the area of nonlinear photonic design engineering.

Dual-Mode 2 × 2 Thermo-Optic Switch Based on Polymer Waveguide Mach-Zehnder Interferometer

A dual-mode <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times 2$ </tex-math></inline-formula> thermo-optic switch based on Mach-Zehnder interferometer with symmetric directional couplers is proposed and experimentally demonstrated by utilizing polymer waveguides. The present switch consists of two <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times 2\,\,3$ </tex-math></inline-formula> -dB directional couplers, which are designed to be mode-insensitive by choosing the core separation and coupling length optimally. Meanwhile, a mode-insensitive phase shifter is employed to alter the phase of the two different modes simultaneously. With the switching power of ~9.0 mW, the measured extinction ratios for the E11 mode and E21 mode can reach to 17.5 dB and 16.4 dB, respectively, at 1550 nm, and the switching time is ~1.30 ms. The performance of the switch is also independent to the polarization state of light. Our proposed dual-mode switch with the advantages of low power-consumption can accommodate MDM system and would be applied in future large capacity communication systems.

Few-mode 3-dB power splitters based on polymer waveguide directional couplers

Two designs of few-mode 3-dB power splitter based on symmetric directional couplers are proposed and experimentally demonstrated by utilizing polymer waveguides. The present devices are designed to be mode-insensitive by choosing the coupling distance and coupling length optimally. The power splitting ratio for the dual-mode 3-dB power splitter which supports E11 and E21 modes are measured to be about 0.5:0.5 with the insertion losses of ∼ 5.1 dB and ∼ 5.5 dB, respectively, at the wavelength of 1550 nm. The power splitting ratio for the three-mode 3-dB power splitter which supports E11, E21 and E12 modes are also measured to be about 0.5:0.5 with the insertion losses of ∼ 6.1 dB, ∼6.4 dB and ∼ 6.7 dB at 1550 nm, respectively. Our presented few-mode 3-dB power splitters could be extended to support more modes and find important applications in mode (de)multiplexing systems.

A Symmetrical Broadband Tight-Coupled Directional Coupler With High Directivity Using Three-Folded-Coupled Lines

In this brief, a novel symmetrical broadband tight-coupled directional coupler with high directivity using three-folded-coupled lines is proposed and implemented. The directional coupler is consisted of two simple coupled lines and two three-folded-coupled (TFC) lines, which realizes advantages of broadband, tight coupling, and high directivity. The TFC line is simplified as two-level coupled lines. Electrical lengths of coupled lines and precise mathematical equations for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${S}$ </tex-math></inline-formula> -parameters of the proposed TFC-structure coupler are calculated based on the method of even- and odd-mode analysis. The gap between the simplified two-level coupled lines is also considered and discussed. For demonstrative purposes, a broadband coupler using TFC lines is designed and fabricated at about 2 GHz with a power-dividing coefficient of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k} = 0.6$ </tex-math></inline-formula> . The measured fractional bandwidth (FBW) of the proposed coupler is about 54.0% as the return loss <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(|S_{11}|)$ </tex-math></inline-formula> and the isolation <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(|S_{41}|)$ </tex-math></inline-formula> are both higher than 20 dB. The fabricated directional coupler also shows advantages of tight coupling (about 3 dB) and high directivity (the highest directivity is about 33.1 dB).

Silicon rib-loaded LiNbO3 waveguide polarization beam splitter based on bound state in the continuum design

Over the last years, LiNbO3 on insulator (LNOI) has emerged as one of the most important platforms for integrated photonic applications because of its large refractive index contrast, outstanding electro-optical and nonlinear optical properties. Rib-loaded waveguide technology is an efficient approach to avoid high surface and sidewall roughness and to relax the difficulty in construction of sub-wavelength structures with steep sidewalls in case of dry-etched LNOI on-chip nanowires. The main issue for the development of rib-loaded LNOI waveguides is the intrinsic TM loss which is caused by the mode conversion between different polarizations at rib boundaries. In this work we show that the intrinsic TM loss can be eliminated by precise control of the waveguide cross section, and a silicon rib-loaded LNOI polarization beam splitter (PBS) is proposed theoretically based on a symmetric directional coupler design. The PBS is designed with a compact size of 42-μm coupling length and relatively large bandwidth of ∼90 nm for extinction ratio above 15 dB. It is, to the best of our knowledge, the first PBS proposed on rib-loaded LNOI waveguide. We believe this work paves the way for exploration of functional integrated devices based on rib-loaded LNOI waveguides.

Compact silicon-based TE-pass polarizer using a symmetrical triple-guide directional coupler including SWG structures and hybrid plasmonic waveguides

A compact and broadband silicon-based transverse-electric (TE)-pass polarizer based on a symmetrical triple-guide directional coupler (TW-DC) is presented and analyzed in detail, assisted with subwavelength gratings (SWGs) and hybrid plasmonic waveguides (HPWs), where the SWGs are involved at the inner part of its central waveguide and two HPWs are introduced and symmetrically located at its outer sides. By carefully improving the structural parameters, only the injected TE mode can be supported by SWGs, and it passes through the device directly due to phase mismatching, while the input TM mode will be supported in the strip waveguides and coupled to the adjacent HPWs due to phase matching and gradually attenuated via the metals. As a result, a compact TE-pass polarizer is realized. Results show that the proposed polarizer has a total coupling length of 6 µm, with an extinction ratio (ER) of 31.2 dB, insertion loss (IL) of 0.1 dB, and reflection loss (RL) of − 26.2 d B at 1.55 µm, and its operation bandwidth can be up to 270 nm (from 1.43 to 1.7 µm) for E R &gt; --> 20 d B and I L &lt; 1 d B . In addition, fabrication tolerances to the key structural parameters and field evolution through the proposed device are given.

Dark soliton steering in PT-symmetric couplers with third-order and intermodal dispersions

We demonstrate steering dynamics of dark solitons in a parity–time ( P T )-symmetric nonlinear directional coupler (NLDC) in the presence of third-order dispersion (TOD) and intermodal dispersion (IMD). A complete switch with an excellent efficiency at a very low critical power, even lower compared to the bright soliton switching, has been observed. The numerical results show that both TOD and IMD have no effect on soliton steering in P T -symmetric couplers with coupling length π / 2 . But, as we increase the coupling length to 2 π , IMD shows marginal effects for dark soliton steering in P T -symmetric couplers, while TOD shows no impact. Additionally, we have also studied the phase-controlled switching in P T -symmetric couplers with two different coupling lengths and demonstrated its advantage over the power-controlled one.

Design of a compact polarization beam splitter for silicon-based cross-slot waveguides

In this paper, a compact polarization beam splitter (PBS) for cross-slot waveguides is numerically proposed and designed. The device is based on the mode-coupling theory with an asymmetric directional coupler (DC) system, in which the input quasi-TM mode is fully coupled into the cross port and the quasi-TE mode remains transmitting in the through port. With properly chosen structural parameters, a compact PBS with a length of 13.2 µm, including the coupling and S-bend sections, is realized. This is much shorter than PBSs using the symmetric DC system. The numerical results show that the optimized extinction ratios (ERs) are 25.5 and 23.6 dB for the quasi-TE and quasi-TM modes, respectively. Moreover, the ERs are higher than 15 dB for both polarizations over the wavelength range from 1.5 to 1.6 µm, indicating a broad operating bandwidth.

Polarization-independent symmetrical directional coupler utilizing orientation-engineered method on the x-cut lithium-niobate-on-insulator

Due to the strong birefringence, symmetrical directional couplers (DCs) are typically polarization-sensitive in the high index contrast platforms. In this letter, we demonstrate polarization-independent directional couplers utilizing orientation-engineered method on the x-cut lithium-niobate-on-insulator (LNOI) platform. We show that the polarization-dependent coupling of a DC can be greatly engineered by controlling the orientation of the waveguides in LNOI utilizing the anisotropic property of lithium niobate (LN) material. Based on the design method, a polarization-independent DC of the representative 3dB coupling ratio is realized using the ultra-sample symmetrical structure. The DC exhibits high performance in excess losses (EL < 0.1 dB) and polarization independent losses (PDL < 0.08 dB) over a 100-nm wavelength range.

Parity-Time Symmetry in Laterally Coupled Bragg Waveguides

We investigate theoretically, in the frame of Coupled-Mode Theory (CMT), a system made of two laterally coupled, perfectly phase-matched, index-coupled Bragg waveguides, the modal gain of the amplifying one compensating exactly the modal losses of the other. Reverting to the supermode eigenbasis of the underlying “naked” (non-periodic) Parity-Time Symmetric (PTS) directional coupler, we derive analytically the scattering parameters of the whole structure. We also consider a system made of two purely gain-coupled Bragg waveguides, either in phase or in anti-phase. In each case, we comment upon the gain requirement for achieving a laser oscillation.

A novel Si four-wavelength multiplexer for 100/400GbE using higher-order mode composed of (a)symmetric directional couplers and TE1-TM0 mode converter.

A novel Si four-wavelength multiplexer (MUX) for 100/400GbE composed of (a)symmetric directional couplers and a rib-waveguide TE1-TM0 mode converter is proposed and experimentally demonstrated. Two-lane signals are multiplexed as TE0 modes via symmetric directional coupler (DC) and other two-lane signals are multiplexed as TE1 modes via asymmetric directional couplers (ADCs). Finally, TE1 modes are converted to TM0 modes and the device acts as a 4-lane MUX. The proposed device is fabrication-tolerant due to the removal of the 1600-GHz filter used in conventional two-stage Mach-Zehnder MUXs, and the insertion loss is smaller than those of previously reported Si-based MUXs.

Polarization-insensitive mode-independent thermo-optic switch based on symmetric waveguide directional coupler.

We propose a thermo-optic switch based on a symmetric directional coupler formed with two parallel identical two-mode waveguides, where the two modes in one waveguide can be simultaneously switched to the corresponding modes in the other waveguide. We design and fabricate such a device with polymer materials. Our fabricated device has a total length of 22.5 mm and operates at a switching power of 128 mW. The extinction ratios measured across the C-band are higher than ∼18 dB and ∼13 dB for the fundamental mode and the higher-order mode, respectively. The switching time is ∼1 ms. The performance of the device is insensitive to the polarization state of light. Our proposed mode-independent switch could find applications in reconfigurable mode-division-multiplexing transmission systems.

Ultracompact silicon-based wavelength diplexer for 155/2 μm using subwavelength gratings

An ultracompact silicon-based wavelength diplexer assisted by subwavelength grating (SWG) couplers is proposed for wavelengths of 1.55 and 2 μm. The embedded SWGs with the narrowed strip wires enable significantly reduced beat lengths for both wavelengths. Additionally, the use of symmetric directional couplers results in tuning of the required structural dimensions for further enhancing the device performance. As a result, the present device has a total length of only ∼13.9 μm, showing a nearly 20-fold reduction compared with the previous counterpart, and provides a high contrast (C) of 27.5 (24.7) dB, a low insertion loss (IL) of 0.14 (0.80) dB, and a low reflection loss of −30.9(−27.6) dB for a wavelength of 1.55 (2.0) μm. Its bandwidth of C>15 dB and IL<1.2 dB exceeds 100 nm for both wavelengths. In addition, fabrication tolerances are analyzed, and the modal field evolution is presented.

Broadband Electro-Optical Crossbar Switches Using Low-Loss Ge2Sb2Se4Te1 Phase Change Material

This theoretical modeling and simulation paper presents designs and projected performance of non-volatile broadband on-chip 1 × 2 and 2 × 2 electro-optical switches operating in the telecommunication C -band and based on the silicon-on-insulator technological platform. These optical switches consist of an asymmetric two-waveguide directional coupler and a symmetric three-waveguide directional coupler, in which the optical phase change material Ge2Sb2Se4Te1 (GSST) is the top cladding layer for one of the silicon strip waveguides. Reversible crossbar switching is attained by the amorphous (Am) to crystalline (Cr) and Cr-to-Am phase transitions in the GSST induced by heating the GSST in contact with an indium tin oxide (ITO) microstrip through Joule heating. We examined device performance in terms of mid-band insertion loss (IL), crosstalk (CT), and 0.3-dB IL bandwidth (BW). The 2 × 2 results were IL = –0.018 dB, CT L c of 15.4 μm, and IL = 0.046 dB, CT L c of 17.4 μm. Simulations of the 1 × 2 devices at 16.7-μm L c revealed that IL = 0.083 dB and CT < 12.8 dB along with an expanded BW of 95 nm. Thermal simulations showed that a 5-V pulse train applied to 1019-cm−3 doped ITO would produce crystallization; however, the process of amorphization required a 24-V pulse of 2.9-μs duration to raise the GSST temperature above the melting temperature of 900 K.

The effect of relative phase on the stability of temporal dark soliton in $${{\mathcal {PT}}}$$ PT -symmetric nonlinear directional fiber coupler

In this paper, we numerically investigate the effect of relative phase on the stability of dark solitons in $${\mathcal {PT}}$$ -Symmetric nonlinear directional coupler (NLDC), by considering gain in the bar and loss in the cross in the range of $$\theta =0^\circ$$ to $$180^\circ$$ . The $${\mathcal {PT}}$$ -Symmetric perturbed eigenfunctions are used to study the soliton stability. The results of simulations are shown that in the first half region of the relative phase the soliton is unstable while in the second one, is stable. In the stable region gain and loss cancel each other and also the perturbed eigenfunctions have no effect on solitons while in the unstable region solitons are amplified in the bar and attenuated in the cross except for some small intervals which the roles are changed. The behavior of such perturbation can be interpreted as self all-optical phase soliton switching and optical logic gates.

All-optical logic gates based on XPM effect under the PAM-ASK modulation in a symmetric dual NLDC

We investigate the possibility of achieving all-optical logical gates based in a symmetric double non-linear directional coupler (NLDC) working with pulses of 2 ps coded for the pulse amplitude modulation-amplitude shift keying (PAM-ASK), in a digital keying. The effects of group velocity dispersion, nonlinear self phase modulation and cross phase modulation (XPM) are taken into account in a lossless theoretical setup scheme. We analyze the amplitude and shape of the output pulses as a function of the modulation factor \((|\varepsilon |)\) to show that an OR gate can be readily realizable. Further, we also implement an optical sign phase shift in one of the NLDC input channels after the PAM-ASK modulator. We identify parameter regions on which the logical operations NAND, OR and XOR can be performed with the respective re-configurable scheme set by PAM-ASK modulation technique under the XPM effect.