--- title: Static Phase Reconfiguration url: https://www.emergentmind.com/topics/static-phase-reconfiguration type: topic --- # Static Phase Reconfiguration Static phase reconfiguration denotes a class of techniques in which a phase-related state is set by non-volatile material switching, a precomputed schedule, a one-time planning decision, or a slow or quasi-static hardware update, rather than by dense continuous tuning. In the cited literature, the phrase spans several technically distinct objects: optical phase profiles in phase-change metasurfaces, synchronized communication phases in optical reconfigurable networks, voltage phasors and user-to-phase assignments in distribution systems, and output-wire assignments or topology modes in reconfigurable converters [1604.01330][2605.26930][1804.02080][2507.05910][2402.03978]. The unifying feature is that the phase-related configuration is deliberately chosen to persist over a useful interval, so that switching overhead, control complexity, or static power consumption is reduced. ## 1. Scope and terminology A recurring source of ambiguity is that the word “phase” does not denote the same object across the literature. In metasurfaces it usually denotes the optical phase imparted by a unit cell or pixel; in optical reconfigurable networks it denotes synchronized communication phases in a collective schedule; in distribution engineering it can denote either the voltage phasor angle or the discrete connection of single-phase users to phases \(1,2,3\); and in reconfigurable converters it appears through phase-to-wire assignments or three-phase topology changes [1604.01330][2605.26930][1804.02080][1710.10242]. | Domain | Meaning of “phase” | Reconfigured quantity | |---|---|---| | Metasurfaces and intelligent surfaces | Optical phase or phase-shift profile | Material state, geometry, or slide-position-dependent composite phase map | | Optical reconfigurable networks | Synchronized communication phases | Sparse reusable topology states and reconfiguration schedule | | Distribution systems | Voltage phasor or feeder phase connection | DER dispatch across switches or user phase assignment | | Power converters | Phase-to-wire or topology association | Switch networks and selector matrices | “Static” is likewise domain-dependent. In GST and Sb\(_2\)S\(_3\) devices, the written state is non-volatile and remains stable until another optical, thermal, or electrical stimulus is applied [1604.01330][2412.16856]. In low-voltage distribution networks, static phase reconfiguration is explicitly a multi-period planning exercise in which selected consumers are manually re-phased during routine maintenance [2507.05910]. In movable intelligent surfaces, the phase shifts themselves are static, while reconfiguration is achieved by mechanical sliding of a secondary metasurface layer [2511.17058]. In reconfigurable converters for unbalanced systems, the reconfiguration stage is updated on a slow “static” timescale and is not part of the high-frequency modulation loop [2402.03978]. ## 2. Non-volatile optical phase control in phase-change metasurfaces In the all-dielectric GST metasurface of Karvounis et al., the reconfigurable element is a \(300\) nm-thick film of Ge\(_2\)Sb\(_2\)Te\(_5\) patterned into a one-dimensional subwavelength grating with period \(P\) in the range \(750\)–\(950\) nm, slot width \(s\approx130\) nm, nanowire width \(d=P-s\), and height \(h=300\) nm. Under normal incidence with TE polarization, these gratings support high-\(Q\) (\(>20\)) Mie-type resonances in reflection and transmission. The optical response is written through the complex coefficients \[ r(\omega)=|r(\omega)|e^{i\phi(\omega)}, \qquad t(\omega)=|t(\omega)|e^{i\psi(\omega)}, \] with a rapid phase variation of order \(\pi\) across resonance. Switching GST from the amorphous to the crystalline state shifts the resonance frequency by \(\Delta\omega \approx \omega_0\cdot(\Delta n/n)\), approximately \(10\%\) in practice, producing \[ \Delta\phi(\omega)=\phi_c(\omega)-\phi_a(\omega). \] Rigorous-coupled wave analysis or finite-element simulation yields \(\Delta\phi(\lambda)\) that peaks near the original resonance; in practice, \(\Delta\phi\) can approach \(\pi\) over a \(\sim50\) nm bandwidth in reflection, with similar behavior in transmission [1604.01330]. The switching mechanism is laser-induced and non-volatile. The amorphous\(\to\)crystalline transition uses a \(532\) nm CW laser with spot diameter \(\approx5\ \mu\)m and intensity \(\approx3\) mW/\(\mu\)m\(^2\), holding GST between \(T_g\approx110\,^\circ\)C and \(T_m\approx630\,^\circ\)C for \(\sim\mu\)s until crystallization nucleates. Once set, each phase is stable at room temperature, yielding reflection contrast up to \(5{:}1\) (\(7\) dB) and transmission contrast up to \(1{:}3\) (\(-5\) dB). Static phase patterns can be created either by geometric tuning, for example varying \(P\), \(s\), or the resonator diameter, or by phase-state multiplexing that locally toggles GST between amorphous and crystalline states. In reflection the imposed phase is \[ \phi(P,\mathrm{state};\lambda)=\arg[r(P,\mathrm{state};\lambda)]. \] The reported phase-modulation depth is \(\Delta\phi\approx\pi\) per resonance shift of \(\sim150\) nm, while full \(2\pi\) coverage is described as achievable by cascading multiple resonances or by combining geometry and state switching [1604.01330]. A related but electrically addressed implementation is the hybrid plasmonic–phase-change architecture of Abdollahramezani et al. Each pixel is a one-dimensional Au/GST/SiO\(_2\)/Au stack with period \(p=550\) nm, Au nanoribbon width \(w=340\) nm, thickness \(t=30\) nm, GST stripe height \(h=180\) nm, and a \(100\) nm Au back-reflector. GST forms the dielectric gap under each Au ribbon, and its phase is switched by Joule heating. A short, high-amplitude voltage pulse of approximately \(150\) ns melts GST above \(630\,^\circ\)C and rapid quenching re-amorphizes it, whereas a longer, lower-amplitude pulse of approximately \(1\ \mu\)s heats GST above its glass-transition/crystallization temperature of approximately \(160\,^\circ\)C to nucleate and grow the crystalline phase. Thermal isolation by SiO\(_2\) ensures neighboring pixels remain below \(160\,^\circ\)C, enabling individual pixel addressing [1809.08907]. The phase modulation is governed by interference between a nearly constant non-resonant metallic reflection and a resonant Lorentzian term, \[ r_{\mathrm{tot}}(m)=r_{\mathrm{non-res}}e^{i\theta_{\mathrm{non-res}}}+r_{\mathrm{res}}(m)e^{i\theta_{\mathrm{res}}(m)}, \] with \(r_{\mathrm{non-res}}\simeq -1\) and \(\theta_{\mathrm{non-res}}\simeq \pi\). The GST crystallinity fraction \(L_c\in[0,1]\) is described by a Lorentz–Lorenz effective-medium model, \[ \frac{\epsilon_{\mathrm{eff}}(m)-1}{\epsilon_{\mathrm{eff}}(m)+2} = L_c\frac{\epsilon_c-1}{\epsilon_c+2} + (1-L_c)\frac{\epsilon_a-1}{\epsilon_a+2}. \] At \(\lambda=1550\) nm, full-wave FEM/FIT simulations yield a reflected-phase sweep of nearly \(315^\circ\), from \(+208^\circ\) to \(-107^\circ\), with reflection amplitude above approximately \(15\%\) throughout. Eleven discrete states, \(L_c=0,10\%,20\%,\ldots,100\%\), were simulated, with approximately \(30^\circ\) phase increment per step. The device supports a \(\simeq200\) nm bandwidth, approximately \(1.5\)–\(1.7\ \mu\)m, over which the phase can be reliably mapped to \(L_c\), enabling focusing, beam steering, holography, amplitude modulation, and polarization conversion [1809.08907]. A common misconception is that static optical phase reconfiguration is equivalent to a fixed-function device. These studies show the opposite: the written state is static only between updates, while the overall platform remains rewritable and non-volatile [1604.01330][1809.08907]. ## 3. Static phase shifts with mechanical or material-state reconfigurability The movable intelligent surface framework extends static phase design by separating phase synthesis from reconfiguration actuation. The proposed MIS consists of two transmissive metasurfaces separated by a small air gap \(g\ll\lambda\): a fixed primary layer MS1 with \(M=M_r\times M_c\) elements and static phase shifts \(\phi=[e^{j\phi_1},\ldots,e^{j\phi_M}]^T\), and a smaller secondary layer MS2 with \(N=N_r\times N_c\) elements and static phase shifts \(\theta=[e^{j\theta_1},\ldots,e^{j\theta_N}]^T\), which slides discretely over MS1 along rows and columns. The number of slide positions is \(U=U_r\times U_c\), where \(U_r=M_r-N_r+1\) and \(U_c=M_c-N_c+1\). At slide position \(u\), the equivalent phase-shift vector is \[ \bar{\theta}_u=S_u\theta+e_u\in\mathbb{C}^M, \] where \(S_u\in\{0,1\}^{M\times N}\) is a binary selection matrix and \(e_u\in\{0,1\}^M\) is a padding vector. Defining \(v_u=\bar{\theta}_u\odot\phi\), the received signal at user \(k\) is \[ y_k=(v_u)^H\operatorname{diag}(h_k^H)\,G\,w_{k,u}\,s_k+n_k. \] The design problem jointly optimizes the static phase shifts and the slide-position selection, interpreted as beam-pattern scheduling [2511.17058]. Two optimization classes are reported. For max–min rate, a penalty-assisted BCD-SCA method relaxes the binary scheduling variables, adds a penalty \(-\rho\sum_{k,u}(\xi_{k,u}-\xi_{k,u}^2)\), and alternates over \(\xi\), \(\phi\), and \(\theta\). For sum rate, a Riemannian conjugate-gradient method operates on a product manifold formed by the complex-circle manifolds of \(\phi\) and \(\theta\) and the probability-simplex manifold of the scheduling matrix \(X=[\xi_{k,u}]\). Simulation results report that even a \(1\times1\) MS2 increases min-rate by approximately \(10\)–\(15\) bit/Hz over a static RIS, larger MS2 sizes such as \(4\times4\) add up to \(20\)–\(25\) bit/Hz, and element-wise MS2 mobility recovers approximately \(60\%\) of the gap between block-MIS and a fully dynamic RIS. At \(P=34\) dBm, the reported sum rates are approximately \(180\) bit/Hz for block-MIS, \(300\) bit/Hz for dynamic RIS, and approximately \(240\) bit/Hz for element-wise MIS. Reconfiguration is quasi-static, with switching latency on the order of seconds or minutes and control overhead of only \(\log_2U\) bits per re-pointing [2511.17058]. Phase-change metasurfaces for reconfigurable image processing provide a different static mechanism. In the Sb\(_2\)S\(_3\)-based device of Liu et al., each nanobrick with height \(h\approx100\) nm, radius \(r\approx160\) nm, and lattice constant \(a\approx500\) nm supports magnetic-dipole and electric-dipole Mie resonances in the visible, observed at \(\lambda\approx652\) nm and \(\lambda\approx689\) nm, respectively. In the amorphous state, \(n_a(\lambda)\approx2.4\)–\(2.8\) and \(k_a(\lambda)\approx0\), yielding high-\(Q\), narrow Mie resonances and a transmission profile suitable for edge detection; in the crystalline state, \(n_c(\lambda)\approx3.2\)–\(3.4\) and \(k_c(\lambda)\approx0.15\), which blueshifts and broadens the resonances, lowers the \(Q\)-factor, and produces nearly angle-independent transmission. The target transfer functions are \[ T_a(k_x,k_y)\approx-\alpha(k_x^2+k_y^2), \qquad T_c(k_x,k_y)\approx\beta. \] Near resonance and for small absorption, the angular dependence satisfies \[ T(\theta)\propto (k_\parallel/k_0)^2=\sin^2\theta, \] and the simulated transmission at \(\lambda=652\) nm and \(689\) nm was fitted to \(|t|_{\mathrm{fit}}(\theta)=A\sin^2\theta\), with \(A\sim0.87\) at \(\theta=10^\circ\). The reported modulation depth is \(>10\times\), the high-\(k\) transmission is \(\sim87\%\) at \(\theta\approx10^\circ\) versus near \(0\%\) at \(\theta=0\), the numerical aperture is approximately \(0.17\), and the spatial resolution is approximately \(2.4\ \mu\)m at \(\lambda\approx650\) nm [2412.16856]. These works show two distinct meanings of static phase reconfiguration in wave-control systems. In MIS, the phase values are static but the geometry changes; in Sb\(_2\)S\(_3\) and GST metasurfaces, the geometry is fixed but the material state changes [2511.17058][2412.16856]. ## 4. Phase-matched topology states in optical reconfigurable networks In optical reconfigurable networks, static phase reconfiguration concerns collective communication phases rather than electromagnetic phase delay. ReTri is designed for a minimal two-transceiver-per-node ORN, equivalently a ring-degree-two topology with \(2n\) OCS ports. Assuming \(n=3^s\), each source block \(B[r\to d]\) is assigned a signed offset \[ \Delta_{(r,d)}=\mathrm{ucr}_n((d-r)\bmod n)\in\{-(n-1)/2,\ldots,0,\ldots,(n-1)/2\}, \] which admits a unique balanced-ternary expansion \[ \Delta_{(r,d)}=\sum_{k=0}^{s-1}\tau_k(r,d)\cdot 3^k, \qquad \tau_k(r,d)\in\{-1,0,+1\}. \] In phase \(k\), blocks with \(\tau_k=+1\) are sent right, blocks with \(\tau_k=-1\) are sent left, and blocks with \(\tau_k=0\) stay. This completes All-to-All in \[ T=\lceil \log_3 n\rceil \] synchronized phases, each served by a sparse reusable subring [2605.26930]. The topology states are induced by residue classes \[ S_i^k=\{u\in[0,n-1]\mid u\equiv i \pmod{3^k}\}, \] with bidirectional links \(u\leftrightarrow (u\pm 3^k\bmod n)\) inside each \(S_i^k\). Each \(S_i^k\) is a simple ring of size \(n/3^k\). The paper states that no smaller subgraph can both connect the sender/receiver pairs for phase \(k\) and keep all future peers reachable. Reconfiguration is controlled by a binary schedule \(x=(x_0,\ldots,x_{s-1})\), where \(x_k=1\) means the OCS is reconfigured to the subrings \(S_i^k\) before phase \(k\), and \(x_k=0\) means the previous topology is reused. If the last reconfiguration occurred at phase \(j