  Let $\nu$ be a finite measure on $\mathbb R$ whose Laplace transform is
analytic in a neighborhood of zero. An anyon L\'evy white noise on $(\mathbb
R^d,dx)$ is a certain family of noncommuting operators
$\langle\omega,\varphi\rangle$ in the anyon Fock space over $L^2(\mathbb
R^d\times\mathbb R,dx\otimes\nu)$. Here $\varphi=\varphi(x)$ runs over a space
of test functions on $\mathbb R^d$, while $\omega=\omega(x)$ is interpreted as
an operator-valued distribution on $\mathbb R^d$. Let $L^2(\tau)$ be the
noncommutative $L^2$-space generated by the algebra of polynomials in variables
$\langle \omega,\varphi\rangle$, where $\tau$ is the vacuum expectation state.
We construct noncommutative orthogonal polynomials in $L^2(\tau)$ of the form
$\langle P_n(\omega),f^{(n)}\rangle$, where $f^{(n)}$ is a test function on
$(\mathbb R^d)^n$. Using these orthogonal polynomials, we derive a unitary
isomorphism $U$ between $L^2(\tau)$ and an extended anyon Fock space over
$L^2(\mathbb R^d,dx)$, denoted by $\mathbf F(L^2(\mathbb R^d,dx))$. The usual
anyon
  Fock space over $L^2(\mathbb R^d,dx)$, denoted by $\mathcal F(L^2(\mathbb
R^d,dx))$, is a subspace of $\mathbf F(L^2(\mathbb R^d,dx))$. Furthermore, we
have the equality $\mathbf F(L^2(\mathbb R^d,dx))=\mathcal F(L^2(\mathbb
R^d,dx))$ if and only if the measure $\nu$ is concentrated at one point, i.e.,
in the Gaussian/Poisson case. Using the unitary isomorphism $U$, we realize the
operators $\langle \omega,\varphi\rangle$ as a Jacobi (i.e., tridiagonal) field
in $\mathbf F(L^2(\mathbb R^d,dx))$. We derive a Meixner-type class of anyon
L\'evy white noise for which the respective Jacobi field in $\mathbf
F(L^2(\mathbb R^d,dx))$ has a relatively simple structure.
