I believe simplesamlphp is meant for native php, and there's no direct documentation for laravel integration. What you can do is to find laravel compatible saml authentication library.

I think you can use this library if you want your laravel app to act as the IDP.

https://github.com/codegreencreative/laravel-samlidp

If you want your laravel app to act as the SP, then this library should work.

https://github.com/24Slides/laravel-saml2

I personally have used laravel-saml2 for microsoft Azure AD integration, and it works well, but I haven't tried the laravel-samlidp yet.

Regards,