Compiler construction in java

OK i know this:

The compiler was originally written in C with bits of C++ and I assume that it still is (why do you think the compiler is written in Java as well?). javac.exe is just the C/C++ code that is the compiler.
As a side point you could write the compiler in java, but you're right, you have to avoid the chicken and egg problem.

Immersing students in Java and the Java Virtual Machine (JVM), Introduction to Compiler Construction in a Java World enables a deep understanding of the Java programming language and its implementation.
The text focuses on design, organization, and testing, helping students learn good software engineering skills and become better programmers.

The compiler javac.exe is a .exe file.
What exactly is this .exe file.
Isn't the java compiler written in java, then how come there is .exe file which executes it.
If the compiler code is written is java, then how come compiler code is executed at the compilation stage, since its the job of the jvm to execute java code.