### One-octave Dispersive Mirror

 Spectral range: 550-1100 nm (one octave); Substrate: Suprasil; Layer Materials: SiO2, Nb2O5 described by Cauchy formula; Incidence Angle 70, P-polarization; Target Reflectance 100%; Target GDD $$-40-10(\omega-\omega_0)\;fs^2$$ "Classical approach" (Gradual evolution with combination of thin Layer Removal) leads to oscillations in GDD. It is mathematically proved that oscillations of GDD are inevitable. It means that it is required to find a way to suppress them or to reduce their effect on the output pulse characteristics.  OptiLayer provides various tricks/design tools to solve this problem. Approach 1: Phase optimization with floating constants: Any given dependence $$GDD(\omega)$$ can be integrated twice and converted to phase target: $\varphi(\omega)=\int\limits_{\omega_0}^\omega\int\limits_{\omega_0}^{\omega_1}GDD(\omega_2)d\omega_2+C_1\omega+C_2$ $$C_1$$ and $$C_2$$ – arbitrary constants. Merit function now depends on these constants: $MF=F(d_1,...,d_m; C_1, C_2)$ For any set of thicknesses $$\{d_1,...,d_m\}$$ constants can be excluded from the merit function analytically, because $$F$$ is quadratic function with respect to $$C_1$$ and $$C_2$$: $\frac{\partial F}{\partial C_1}=0, \;\;\frac{\partial F}{\partial C_2}=0$ Resulting merit function is optimized with needle optimization technique. This approach can be applied to coatings of all types. Learn more... Result: 69-layer one-octave dispersive mirror. Approach 2: Complimentary pairs For dispersive mirror pair reflectance and GDD can be defined as: $R_p=\sqrt{R_1\cdot R_2}; \;\; GDD_p=\frac{GDD_1+GDD_2}{2}$ It is possible to achieve suppression of GDD oscillations if GDDs for each mirror are almost in anti-phase; Production is extremely challenging since it is necessary to deposit precisely matching pair with extremely high accuracy; Special procedures for reducing sensitivity of the designs to the production errors, i.e., in order to find more robust design; It is possible to achieve pulse compression in the range up to 1.5 octave (400nm – 1200nm) Result: A pair of 72-layer and 70-layer dispersive mirrors (complimentary pair). Green and blue curves represent GDD of two diespersive mirrors and black curve shows resulting GDD

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