Coatings for Laser Related Applications

Most of the modern ultrafast laser systems include dispersive mirrors and other special coatings used for accurate phase control required for efficient pulse compression.

Laser related coatings are multilayers providing specified group delay (GD) or/and group delay dispersion (GDD) as well as required spectral characteristic (for example, high reflectance). 

Specific features/requirements of these multilayers:

  • Wide spectral range;
  • Many (70-150) layers; 
  • Stability to variations of layer parameters;
  • Accurate deposition and monitoring.
DesCol ChirpedSchem

Design and production of these coatings require using effective numerical design algorithms and high precision deposition techniques.

OptiLayer provides all design tools for successful designing of complicated laser related coatings.

 refractive index layer coatings

OptiLayer calculates all derivatives analytically! OptiLayer is only one software that provides such opportunity.

Completely analytical approach + needle optimization technique allow to solve many challenging design problems in the field of laser related coatings.

Main types of laser related coatings are:

  • Dispersive mirrors (broadband dispersive mirrors, high-dispersive mirrors);
  • Chirped mirrors;
  • Pre-compensation mirrors;
  • Ultra-high reflection mirrors;
  • Positive dispersion mirrors;
  • XUV mirrors;
  • Output couplers;
  • Input couplers;
  • Third-order dispersion mirrors;
  • Beamsplitters;
  • Pulse compressor;
  • Special filters

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 \(-40-10(\omega-\omega_0)\;fs^2\)
one-octave dispersive mirror
 dispersive mirror "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.

dispersive optical coating

group delay dispersion


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)

 complementary pair

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

 Application of robust  algorithm to designing dispersive mirrors

OptiLayer allows taking into account requirement on stability of the design on errors in layer parameters. This requirement is very important for ultrafast coatings.

Example: Dispersive mirror that has to compensate GDD of -200 fs2 in the spectral range from 700 to 900 nm.

Substrate: B260 glass;

Layer Materials: Nb2O5 and SiO2.

All OptiLayer algorithms can work in the Robust mode. Absolute errors in layer thicknesses can be estimated at the \(\sigma=0.5\) nm level:

DesCol RobustSettings

Convenient design solution: 88 layers, total thickness 9273.5 nm. Excellent GDD spectral performance has been obtained:

group delay dispersion

Robust design solution: 66 layers, total thickness 9957.5 nm. Good GDD spectral performance has been achieved:

robust chirped mirror

Error analysis of the convenient design solution: level of absolute thickness errors of 0.5 nm was specified.

error analysis chirp mirror

Error analysis of the robust design solution at the same level of absolute thickness errors. It is obvious, that the design is more stable.

robust dispersive mirror

Learn more in our publications:

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